Society for Industrial and Applied Mathematics: SIAM Journal on Control and Optimization: Table of Contents

Controllability Analysis of a Class of Differential-Variational Inequalities with Nonlocal Conditions

Shengda Zeng — 2026-05-07T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 985-1010, June 2026.
Abstract. This paper is devoted to the controllability analysis of a class of differential variational inequalities subject to nonlocal initial conditions in Hilbert spaces. Our main contributions are twofold, addressing both exact and approximate controllability. First, we establish sufficient conditions for exact controllability by leveraging a fixed-point principle for multivalued condensing mappings, combined with the theory of measures of noncompactness. Second, recognizing the practical limitations of exact controllability for many infinite-dimensional systems, we develop two distinct theorems for approximate controllability. These results are derived from different methodologies: one employs a fixed-point argument based on the resolvent operator technique, while the other utilizes a perturbation approach. Finally, the applicability of our abstract framework is demonstrated by analyzing the approximate controllability of a coupled elliptic-parabolic partial differential system with mixed boundary conditions. This example illustrates the effectiveness of our results, particularly for systems where exact controllability is known to fail.

Event-Based Adaptive Distributed Observer with a Positive Minimum Inter-Event Time

Haoxuan Zhu — 2026-05-07T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1011-1039, June 2026.
Abstract. Reducing communication resource consumption and enhancing autonomy are critical challenges in advancing the engineering application of distributed state estimation, while the event-based communication and fully distributed design are potential solutions to realize these goals. This paper tackles a class of event-based fully distributed state estimation problems with positive minimum inter-event time (MIET) and provides a framework of node-based adaptive distributed event-triggered strategy for the networked system to cooperatively estimate the target system state. First, by introducing robust adaptive laws and corresponding event-triggered mechanisms (ETMs), an event-based robust adaptive distributed observer is designed, which allows each agent to effectively reconstruct the target system state using partial measurement output information and event-based interaction information in the presence of measurement disturbances, without relying on any global information. Second, in order to accurately estimate the target system state in the absence of measurement disturbances, an event-based adaptive distributed observer is proposed, ensuring that the estimation error could asymptotically converge to zero. Moreover, each ETM proposed in these two event-based distributed observers guarantees a strictly positive MIET separately, effectively excluding Zeno behavior in direct proofs. Finally, the effectiveness of the proposed observers is illustrated through several simulation examples.

Recovering Nesterov Accelerated Dynamics from Heavy Ball Dynamics via Time Rescaling

Hedy Attouch — 2026-05-07T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1040-1067, June 2026.
Abstract. In a real Hilbert space, we consider two classical problems: the global minimization of a smooth and convex function [math] (i.e., a convex optimization problem) and finding the zeros of a monotone and continuous operator [math] (i.e., a monotone equation). Attached to the optimization problem, first we study the asymptotic properties of a generalization of Polyak’s heavy ball dynamics introduced in 1964; namely, we consider a positive function [math] multiplying [math]. We show small [math] convergence rates of the function values dependent on [math] and weak convergence of trajectories toward minimizers of [math]. In 2015 [J. Mach. Learn. Res., 17 (2016), pp. 1–43], Su, Boyd, and Candès introduced a second-order system which could be seen as the continuous-time counterpart of Nesterov’s accelerated gradient. As the first key point of this paper, we show that for a special choice for [math], these two seemingly unrelated dynamical systems are connected: namely, they are time reparametrizations of each other. Every statement regarding the continuous-time accelerated gradient system can be recovered from its heavy ball counterpart. As the second key point of this paper, we observe that this connection extends beyond the optimization setting. Attached to the monotone equation involving the operator [math], we again consider a heavy ball-like system suited for the monotone operator setting. We derive small [math] rates for the norm of the operator along the trajectories, and show the weak convergence of the trajectories toward zeros of [math]. For a particular case of this system, we establish a time reparametrization equivalence with the Fast Optimistic Gradient Descent Ascent (Fast OGDA) dynamics introduced by Boţ, Csetnek, and Nguyen in 2022 [Found. Comput. Math., 25 (2025), pp. 162–222], which can be seen as an analog of the continuous accelerated gradient dynamics, but for monotone operators. Every statement regarding the Fast OGDA system can be recovered from a heavy ball-like system.

Optimal Control of Treatment in a Free Boundary Problem Modeling Multilayered Tumor Growth

Xinyue Evelyn Zhao — 2026-05-07T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1068-1098, June 2026.
Abstract. We study the optimal control problem of a free boundary PDE model describing the growth of a multilayered tumor tissue in vitro. We seek the optimal amount of tumor growth inhibitor that simultaneously minimizes the thickness of the tumor tissue and mitigates side effects. The existence of an optimal control is established, and the uniqueness and characterization of the optimal control are investigated. Numerical simulations are presented for some scenarios, including the steady-state and parabolic cases.

Separable Approximations of Optimal Value Functions and Their Representation by Neural Networks

Mario Sperl — 2026-05-07T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1099-1126, June 2026.
Abstract. The use of separable approximations is proposed to mitigate the curse of dimensionality related to the approximation of high-dimensional value functions in optimal control. The separable approximation exploits intrinsic decaying sensitivity properties of the system, where the influence of a state variable on another diminishes as their spatial, temporal, or graph-based distance grows. This property allows the efficient representation of global functions as a sum of localized contributions. A theoretical framework for constructing separable approximations in the context of optimal control is proposed by leveraging decaying sensitivity in both discrete and continuous time. Results extend prior work on decay properties of solutions to Lyapunov and Riccati equations, offering new insights into polynomial and exponential decay regimes. Connections to neural networks are explored, demonstrating how separable structures enable scalable representations of high-dimensional value functions while preserving computational efficiency.

Quadratic Convergence of an SQP Method for Some Optimization Problems with Applications to Control Theory

Eduardo Casas — 2026-05-07T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1127-1149, June 2026.
Abstract. We analyze a sequential quadratic programming (SQP) algorithm for solving a class of abstract optimization problems. Assuming that the initial point is in an [math] neighborhood of a local solution that satisfies no-gap second-order sufficient optimality conditions and a strict complementarity condition, we obtain stability and quadratic convergence in [math] for all [math] where [math] depends on the problem. Many of the usual optimal control problems of partial differential equations fit into this abstract formulation. Some examples are given in the paper. Finally, a computational comparison with other versions of the SQP method is presented.

Minimal Time Control for the Heat Equation with Multiple Impulses

Ya Xin — 2026-05-11T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1150-1171, June 2026.
Abstract. This paper investigates a minimal time control problem for the heat equation with multiple impulse controls. We first establish the maximum principles for this problem and then prove the equivalence between the minimal time impulse control problem and its corresponding minimal norm impulse control problem. Extending our analysis to the minimal time function itself, we examine its analytical properties (particularly continuity and monotonicity) with respect to the control constraint. This leads to a notable discovery: despite being continuous and generally monotonic, the function may fail to be strictly decreasing.

A Risk-Sensitive Ergodic Singular Stochastic Control Problem

Justin Gwee — 2026-05-11T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1172-1187, June 2026.
Abstract. We consider a two-sided singular stochastic control problem with a risk-sensitive ergodic criterion. In particular, we consider a stochastic system whose uncontrolled dynamics are modeled by a linear diffusion. The control that can be applied to the system is modeled by an additive finite variation process. The objective of the control problem is to minimize a risk-sensitive long-term average criterion that penalizes deviations of the controlled process from a given interval, as well as the expenditure of control effort. The stochastic control problem has been partly motivated by the problem faced by a central bank that wishes to control the exchange rate between its domestic currency and a foreign currency so that this fluctuates within a suitable target zone. We derive the complete solution to the problem under general assumptions by deriving a [math] solution to its HJB equation. To this end, we use the solutions to a suitable family of Sturm–Liouville eigenvalue problems.

Relationship between Controllability of the Semilinear Parabolic Equation and That of Its Linear Version

Xu Liu — 2026-05-11T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1188-1209, June 2026.
Abstract. According to the derivation of thermal diffusion models, a controlled semilinear parabolic equation can be formally replaced by its linear version, when their initial data and control actions are sufficiently small. In this paper, we shall prove this fact and also establish a relationship on the null controllability of these equations. More precisely, we shall prove that both equations are not only null controllable, but the errors between their associated solutions are also a high-order infinitesimal with respect to small initial values. This indicates that, in some sense, the study on null controllability of the semilinear parabolic equation with small initial data can be indeed replaced by that of the linear problem.

De Finetti’s Problem with Fixed Transaction Costs and Regime Switching

Wenyuan Wang — 2026-05-11T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1210-1234, June 2026.
Abstract. This paper examines a modified version of de Finetti’s optimal dividend problem, incorporating fixed transaction costs and altering the surplus process by introducing two-valued drift and two-valued volatility coefficients. This modification aims to capture the transitions or adjustments in the company’s financial status. We identify the optimal dividend strategy, which maximizes the expected total net dividend payments (after accounting for transaction costs) until ruin, as a two-barrier impulsive dividend strategy. Notably, the optimal strategy can be explicitly determined for almost all scenarios involving different drifts and volatility coefficients. Our primary focus is on exploring how changes in drift and volatility coefficients influence the optimal dividend strategy.

Duality-Based Algorithm and Numerical Analysis for Optimal Insulation Problems on Nonsmooth Domains

Harbir Antil — 2026-05-12T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1235-1268, June 2026.
Abstract. This article develops a numerical approximation of a convex nonlocal and nonsmooth minimization problem. The physical problem involves determining the optimal distribution, given by [math], of a given amount [math] of insulating material attached to a boundary part [math] of a thermally conducting body [math], [math], subject to conductive heat transfer. To tackle the nonlocal and nonsmooth character of the problem, the article introduces a (Fenchel) duality framework: (a) At the continuous level, using (Fenchel) duality relations, we derive an a posteriori error identity that can handle arbitrary admissible approximations of the primal and dual formulations of the convex nonlocal and nonsmooth minimization problem. (b) At the discrete level, using discrete (Fenchel) duality relations, we derive an a priori error identity that applies to a Crouzeix–Raviart discretization of the primal formulation and a Raviart–Thomas discretization of the dual formulation. The proposed framework leads to error decay rates that are optimal with respect to the specific regularity of a minimizer. In addition, we prove convergence of the numerical approximation under minimal regularity assumptions. Since the discrete dual formulation can be written as a quadratic program, it is solved using a primal-dual active set strategy interpreted as the semismooth Newton method. A solution of the discrete primal formulation is reconstructed from the solution of the discrete dual formulation by means of an inverse generalized Marini formula. This is the first such formula for this class of convex nonlocal and nonsmooth minimization problems.

Analysis of the SQP Method for Hyperbolic PDE-Constrained Optimization in Acoustic Full Waveform Inversion

Luis Ammann — 2026-05-12T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1269-1296, June 2026.
Abstract. In this paper, the SQP method applied to a hyperbolic PDE-constrained optimization problem is considered. The model arises from the acoustic full waveform inversion in the time domain. The analysis is mainly challenging due to the involved hyperbolicity and second-order bilinear structure. This notorious character leads to an undesired effect of loss of regularity in the SQP method, calling for a substantial extension of developed parabolic techniques. We propose and analyze a novel strategy for the well-posedness and convergence analysis based on the use of a smooth-in-time initial condition, a tailored self-mapping operator, and a two-step estimation process along with Stampacchia’s method for second-order wave equations. Our final theoretical result is the R-superlinear convergence of the SQP method.

New Global Carleman Estimates and Null Controllability for Forward/Backward Semilinear Parabolic SPDEs

Lei Zhang — 2026-05-11T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1297-1326, June 2026.
Abstract. In this paper, we study the null controllability for parabolic SPDEs involving both the state and the gradient of the state. To start with, an improved global Carleman estimate for linear forward (resp. backward) parabolic SPDEs with general random coefficients and square-integrable source terms is derived. Based on this, we further develop a new global Carleman estimate for linear forward (resp. backward) parabolic SPDEs with source terms in the Sobolev space of negative order, which enables us to deal with the null controllability for linear backward (resp. forward) parabolic SPDEs with gradient terms. As a byproduct, a special weighted energy-type estimate for the controlled system that explicitly depends on the parameters [math] and weighted function [math] is obtained, which makes it possible to extend the previous null controllability to semilinear backward (resp. forward) parabolic SPDEs by applying the fixed-point argument in appropriate Banach space.

Markov Perfect Equilibria in Discrete Finite-Player and Mean-Field Games

Felix Höfer — 2026-05-12T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1327-1356, June 2026.
Abstract. We study dynamic finite-player and mean-field stochastic games within the framework of Markov perfect equilibria (MPE). Our focus is on discrete time and space structures without monotonicity. Unlike their continuous-time analogues, discrete-time finite-player games generally do not admit unique MPE. However, we show that uniqueness is remarkably recovered when the time steps are sufficiently small, and we provide examples demonstrating the necessity of this assumption. This result, established without relying on any monotonicity conditions, underscores the importance of inertia in dynamic games. In both the finite-player and mean-field settings, we show that MPE correspond to solutions of the Nash–Lasry–Lions equation, which is known as the master equation in the mean-field case. We exploit this connection to establish the convergence of discrete-time finite-player games to their mean-field counterpart in short time. Finally, we prove the convergence of discrete-time finite-player games to their continuous-time version on every time horizon.

Optimal Control of Quantum Systems in Fermion Fields: The Pontryagin-Type Maximum Principle (I)

Penghui Wang — 2026-05-14T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1357-1382, June 2026.
Abstract. In this paper, we derive a Pontryagin-type maximum principle for optimal control of quantum systems in fermion fields. These systems have gained significant prominence in numerous quantum applications ranging from physical chemistry to multidimensional nuclear magnetic resonance experiments. Furthermore, we establish the existence and uniqueness of solutions to backward quantum stochastic differential equations driven by fermion Brownian motion. The application of noncommutative martingale inequalities and the martingale representation theorem enables this achievement.

Equilibrium Strategies for Singular Dividend Control Problems under the Mean-Variance Criterion

Jingyi Cao — 2026-05-14T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1383-1405, June 2026.
Abstract. We revisit the optimal dividend problem of de Finetti by adding a variance term to the usual criterion of maximizing the expected discounted dividends paid until ruin, in a singular control framework. Investors do not like variability in their dividend distribution, and the mean-variance (MV) criterion balances the desire for large expected dividend payments with small variability in those payments. The resulting MV singular dividend control problem is time-inconsistent, and we follow a game-theoretic approach to find a time-consistent equilibrium strategy. Our main contribution is a new verification theorem for the novel dividend problem, in which the MV criterion is applied to an integral of the control until ruin, a random time that is endogenous to the problem. We demonstrate the use of the verification theorem in two cases for which we obtain the equilibrium dividend strategy (semi)explicitly, and we provide a numerical example to illustrate our results.

On the Navier–Stokes Equations and the Hamilton–Jacobi–Bellman Equation on the Group of Volume Preserving Diffeomorphisms

Xiang-Dong Li — 2026-05-20T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1406-1432, June 2026.
Abstract. In this paper, we give a new characterization of the incompressible Navier–Stokes equations on a compact Riemannian manifold [math] via the Bellman dynamic programming principle on [math], the group of volume preserving diffeomorphisms on [math]. The main result of this paper indicates the interesting relationships among the incompressible Navier–Stokes equations on [math], the Hamilton–Jacobi–Bellman equation, and the viscous Burgers equation on [math]. In particular, we derive the incompressible Navier–Stokes equations and the revised incompressible Navier–Stokes equations on the two-dimensional torus. This extends Arnold’s famous theorem on the geometric interpretation of the incompressible Euler equation to the incompressible Navier–Stokes equations on compact Riemannian manifolds.

Data Scheduling and State Estimation for Large-Scale Event-Based Sensor Arrays

Xinhui Liu — 2026-05-20T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1433-1455, June 2026.
Abstract. In this paper, we study the problem of sensor scheduling and state estimator design for large-scale array-based event sensors, where each sensor incorporates an inherent event-based output transmission mechanism. To effectively extract the information from sensor arrays, an online sensor scheduling strategy based on similarity of measurement data is introduced. The observability of systems equipped with dynamic spatial-temporal data selection mechanisms (consisting of event-based and sensor scheduling protocols) is analyzed, where a criterion for [math]-observability is derived. Furthermore, an event-based state estimator aimed at obtaining ellipsoidal regions containing system states is designed. The convergence property of the proposed state estimation algorithm is proved through analyzing the asymptotic boundness of sizes of the estimated state ellipsoids. A comparative analysis of estimation performances with and without sensor scheduling is conducted. The computational complexity of the designed state estimation algorithm is also discussed. Finally, the effectiveness of the proposed event-based estimator is demonstrated by numerical simulations.

Asynchronous Stochastic Approximation with Applications to Average-Reward Reinforcement Learning

Huizhen Yu — 2026-05-20T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1456-1481, June 2026.
Abstract. This paper investigates the stability and convergence properties of asynchronous stochastic approximation (SA) algorithms, with a focus on extensions relevant to average-reward reinforcement learning. We first extend a stability proof method of Borkar and Meyn to accommodate more general noise conditions than previously considered, thereby yielding broader convergence guarantees for asynchronous SA. To sharpen the convergence analysis, we further examine the shadowing properties of asynchronous SA, building on a dynamical systems approach of Hirsch and Benaïm. These results provide a theoretical foundation for a class of relative value iteration-based reinforcement learning algorithms—developed and analyzed in a companion paper—for solving average-reward Markov and semi-Markov decision processes.

Online Feedback Optimization and Singular Perturbation via Contraction Theory

Liliaokeawawa Cothren — 2026-05-22T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1482-1506, June 2026.
Abstract. In this paper, we provide a novel contraction-theoretic approach to analyze two-time scale systems, including those commonly encountered in online feedback optimization (OFO). Our framework endows these systems with several robustness properties, enabling a more comprehensive characterization of their behaviors. The primary assumptions are the contractivity of the fast subsystem and the reduced model, along with an explicit upper bound on the time-scale parameter. For two-time scale systems subject to disturbances, we show that the distance between solutions of the nominal system and solutions of its reduced model is uniformly upper bounded by a function of contraction rates, Lipschitz constants, the time-scale parameter, and the variability of the disturbances over time. Applying these general results to the OFO context, we establish new individual tracking error bounds, showing that solutions converge to their time-varying optimizer, provided the plant and steady-state feedback controller exhibit contractivity and the controller gain is suitably bounded. Finally, we explore two special cases: for autonomous nonlinear systems, we derive sharper bounds than those in the general results, and for linear time-invariant systems, we present novel bounds based on induced matrix norms and induced matrix log norms.

Dynkin Ghost Games with Asymmetry and Consolation

Erik Ekström — 2026-05-27T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1507-1521, June 2026.
Abstract. We study a stopping game of preemption type between two players who both act under uncertain competition. In this framework we introduce, and study the effect of, (i) asymmetry of payoffs, allowing, e.g., for different investment costs, and (ii) consolation, i.e., partial compensation to the forestalled stopper. In general, this setting does not offer an explicit equilibrium. Instead, we provide a general verification theorem, which we then use to explore various situations in which a solution can be constructed so that an equilibrium is obtained.

Consensus of Multiagent Systems under Communication Failure

Mohamed Bentaibi — 2026-05-27T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1522-1544, June 2026.
Abstract. We consider multiagent systems with cooperative interactions and study the convergence to consensus in the case of time-dependent connections, with possible communication failure. We prove a new condition ensuring consensus: we define a graph in which directed arrows correspond to connection functions that converge (in the weak sense) to some function with a positive integral on all intervals of the form [math]. If the graph has a node reachable from all other indices, i.e., “globally reachable”, then the system converges to consensus. We show that this requirement generalizes some known sufficient conditions for convergence, such as Moreau’s or the Persistent Excitation one. We also give a second new condition, transversal to the known ones: total connectedness of the undirected graph formed by the nonvanishing of limiting functions.

A Class of Differential Evolution Inclusions: From Process Controllability to Latter-Phase Controllability

Shengda Zeng — 2026-05-27T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1545-1572, June 2026.
Abstract. In this paper, we introduce and consider a large class of differential evolution inclusions with a control in infinite-dimensional Hilbert spaces. First, we apply the theory of measure of noncompactness, the fixed point theory of multivalued condensing operators, as well as the argument of multivalued analysis, for examining the solvability of the differential evolution inclusion (DEI) under consideration. Then a time discrete technique and the approximating approaches are applied to study the process exact controllability and process approximate controllability of the DEI, when the Gramian of the DEI is coercive. These results extend and improve the ones established in [Y. Liang, Z. Fan, and G. Li, SIAM J. Control Optim., 61 (2023), pp. 3664–3694]. Let [math] and [math] be the terminal of time interval. Furthermore, the new concepts of [math]-latter-phase exact controllability and [math]-latter-phase approximate controllability of the DEI are introduced which inherit both the essential characteristic of process controllability and final state controllability. We develop a unified analysis framework for determining the [math]-latter-phase controllability of the DEI. Finally, in order to illustrate the applicability of the theoretical results established in this paper, a nonsmooth circuit problem and a transport equation with multivalued source are studied, and the numerical experiments are carried out for demonstrating the coincidence with the theoretical results.

A Particle Consensus Approach to Solving Nonconvex-Nonconcave Min-Max Problems

Giacomo Borghi — 2026-05-27T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1573-1601, June 2026.
Abstract. We propose a zero-order optimization method for sequential min-max problems that employs two populations of interacting particles. The systems are coupled so that one population aims to solve the inner maximization problem, while the other aims to solve the outer minimization problem. The dynamics are characterized by a consensus-type interaction with additional stochasticity to promote exploration of the landscape of the objective function. Without relying on convexity or concavity assumptions, we establish theoretical convergence guarantees of the algorithm via a suitable mean-field approximation of the particle systems. Numerical experiments illustrate the validity of the proposed approach. In particular, the algorithm is able to identify a global min-max solution, in contrast to gradient-based methods, which typically converge to possibly suboptimal stationary points.

Mean Field Social Optimization: Feedback Person-by-Person Optimality and the Dynamic Programming Equation

Minyi Huang — 2026-05-28T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1602-1630, June 2026.
Abstract. We consider mean field social optimization in nonlinear diffusion models. By dynamic programming with a representative agent employing cooperative optimizer selection, we derive a new Hamilton–Jacobi–Bellman (HJB) equation to be called the master equation of the value function. Under some regularity conditions, we establish [math]-person-by-person optimality of the master equation–based control laws, which may be viewed as a necessary condition for nearly attaining the social optimum. A major challenge in the analysis is to obtain tight estimates, within an error of [math], of the social cost having order [math]. This will be accomplished by multiscale analysis via constructing two auxiliary master equations. We illustrate explicit solutions of the master equations for the linear-quadratic (LQ) case and give an application to systemic risk.

Convergence Rates for Ensemble-Based Solutions to Optimal Control of Uncertain Dynamical Systems

Olena Melnikov — 2026-06-01T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1631-1650, June 2026.
Abstract. We consider risk-neutral optimal control problems governed by nonlinear ordinary differential equations with uncertain inputs. Using sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems. Leveraging techniques for metric entropy bounds, we derive nonasymptotic Monte Carlo–type convergence rates for the ensemble-based optimal values and critical points. Our theoretical framework is validated through numerical simulations on a harmonic oscillator problem and a vaccination scheduling problem for epidemic control under model parameter uncertainty.

Stochastic Maximum Principle for Weighted Mean-Field System with Jumps

Yanyan Tang — 2026-06-02T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 3, Page 1651-1671, June 2026.
Abstract. In this article, we consider a weighted mean-field control problem with jump-diffusion as its state process. The main difficulty is from the non-Lipschitz property of the coefficients. We overcome this difficulty by an [math]-estimate of the solution processes with a suitably chosen [math] and [math]. A convex perturbation method combined with the aforementioned [math]-estimation method is utilized to derive the stochastic maximum principle for this control problem. A sufficient condition for the optimality is also given. Two motivating examples and one solvable example are also presented.

A Relaxed Control Problem with [math] Cost and Jump Dynamics Motivated by Cyber Risks Insurance

Dan Goreac — 2026-03-02T08:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 523-553, April 2026.
Abstract. This paper has a double aim. On the one hand, we introduce a uninodal network model for cyber risks with firewalled edges and SIR intraedge spreading. In connection to this, we formulate an insurance problem in which one seeks the running maximal reputation index against all control strategies of the companies represented by edges. On the other hand, we seek to characterize the value function with [math] cost through linear programming techniques and more standard Hamilton–Jacobi integro-differential inequalities.

Stabilizability of Nash Equilibrium for Game-Based Control Systems

Renren Zhang — 2026-03-03T08:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 554-579, April 2026.
Abstract. We investigate the stabilizability of Nash equilibrium for a general class of the nonlinear game-based control system (GBCS), which was initially introduced to model the control systems with strategic behavior, such as social, economic, and “intelligent” systems. The GBCS exhibits a hierarchical structure comprising a higher-level regulator and multiple lower-level rational agents. The regulator functions as the global controller and makes decisions first, after which the agents attempt to optimize their respective objective functions. For a given control of the regulator, the lower-level agents engage in a noncooperative game. The stabilizability problem addresses whether the regulator can stabilize the system by regulating the Nash equilibrium established by the agents at the lower level. In this paper, we will first formulate the stabilizability problem of the general nonlinear GBCS. Some explicit necessary and/or sufficient algebraic conditions on the stabilizability of Nash equilibrium are given by investigating the solvability relationship between the associated Hamilton–Jacobi–Isaacs equations and the algebraic Riccati equations related to an approximated linear-quadratic GBCS.

Strictly Abnormal Geodesics with a Degeneracy Point in the Interior of Their Domain

Nicola Paddeu — 2026-03-06T08:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 580-592, April 2026.
Abstract. In this article, we study abnormal curves in a family of sub-Riemannian manifolds of rank 2. We focus on abnormal curves whose lifts to the cotangent bundle annihilate, at an interior point of the domain, all Lie brackets of length up to three of vector fields tangent to the distribution. We present a method to prove that such curves are length-minimizing. Finally, we prove that strictly abnormal geodesics may cease to be locally length-minimizing after a change of the metric.

Uniform-in-Time Convergence Rates to a Nonlinear Markov Chain for Mean-Field Interacting Jump Processes

Asaf Cohen — 2026-03-10T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 593-623, April 2026.
Abstract. We consider a system of [math] particles interacting through their empirical distribution on a finite state space in continuous time. In the formal limit as [math], the system takes the form of a nonlinear (McKean–Vlasov) Markov chain. This paper rigorously establishes this limit. Specifically, under the assumption that the mean field system has a unique, exponentially stable stationary distribution, we show that the weak error between the empirical measures of the [math]-particle system and the law of the mean field system is of order [math] uniformly in time. Our analysis makes use of a master equation for test functions evaluated along the measure flow of the mean field system, and we demonstrate that the solutions of this master equation are sufficiently regular. We then show that exponential stability of the mean field system is implied by exponential stability for solutions of the linearized Kolmogorov equation with a source term. Finally, we show that our results can be applied to the study of mean field games and give a new condition for the existence of a unique stationary distribution for a nonlinear Markov chain.

Tangent Semigroup and Controllability of Control System

Victor Ayala — 2026-03-11T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 624-644, April 2026.
Abstract. A nonlinear control system on a manifold [math] is locally controllable at a point [math] if an open set [math] contains [math] such that its system semigroup is transitive on [math]. In this paper, we derived the local controllability property of a control system from the global controllability of its induced system on the tangent bundle [math]. We consider the following context to achieve this: Let [math] be a connected Lie group acting on a differentiable manifold [math] and its induced lifting Lie group [math] acting on [math]. Similarly, we lift a semigroup [math] to the tangent semigroup [math]. We show that the controllability of [math] on a fiber of [math] implies local controllability at its base point in [math]. The reciprocal is true under some hypotheses. We then applied these results to some classes of nonlinear control systems, treating the system’s dynamics as those of its semigroup; for instance, we obtained a global controllability property for a bilinear control systems class on the real projective space [math].

Stability Criteria for Rough Systems

Luu Hoang Duc — 2026-03-12T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 645-672, April 2026.
Abstract. We propose a quantitative direct method to prove the local stability of a stationary solution for a rough differential equation and its regular discretization scheme. Using the Doss–Sussmann technique and stopping time analysis, we provide stability criteria for a stationary solution of the continuous system to be exponentially stable, provided the diffusion term is bounded and its derivatives exhibit small growth. The same conclusions hold for the regular discretization scheme with a sufficiently small step size, but one needs to apply the sewing lemma and stopping times for the discrete time set. Our stability criteria are based on the linearization of the drift and require only information about the bound and growth rates of the diffusion, making them data-driven criteria.

Partially Observable Multiagent Reinforcement Learning with Information Sharing

Xiangyu Liu — 2026-03-13T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 673-697, April 2026.
Abstract. We study provable multiagent reinforcement learning (RL) in the general framework of partially observable stochastic games (POSGs). To circumvent the known hardness results and the use of computationally intractable oracles, we advocate leveraging the potential information sharing among agents, a common practice in empirical multiagent RL, and a standard model for multiagent control systems with communication. We first establish several computational complexity results to justify the necessity of information sharing, as well as the observability assumption that has enabled quasi-polynomial time and sample single-agent RL with partial observations, for tractably solving POSGs. Inspired by the inefficiency of planning in the ground-truth model, we then propose to further approximate the shared common information to construct an approximate model of the POSG, in which an approximate equilibrium (of the original POSG) can be found in quasi-polynomial-time, under the aforementioned assumptions. Furthermore, we develop a partially observable multiagent RL algorithm whose time and sample complexities are both quasi-polynomial. Finally, beyond equilibrium learning, we extend our algorithmic framework to finding the team-optimal solution in cooperative POSGs, i.e., decentralized partially observable Markov decision processes, a more challenging goal. We establish concrete computational and sample complexities under several structural assumptions of the model. We hope our study could open up the possibilities of leveraging and even designing different information structures, a well-studied notion in control theory, for developing both sample- and computation-efficient partially observable multiagent RL.

Minimal Time Nonlinear Control via Semi-infinite Programming

Antoine Oustry — 2026-03-20T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 698-726, April 2026.
Abstract. We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values of which converge to the value of the control problem. These semi-infinite programs are increasing restrictions of the dual of the nonlinear control problem, which is a maximization problem over the subsolutions of the Hamilton–Jacobi–Bellman (HJB) equation. Our approach is compatible with Lipschitz dynamical systems and state constraints. Specifically, we use an oracle that, for a given differentiable function, returns a point at which the function violates the HJB inequality. We solve the semi-infinite programs using a classical convex optimization algorithm with a convergence rate of [math], where [math] is the number of calls to the oracle. This algorithm yields subsolutions of the HJB equation that approximate the value function and provide a lower bound on the optimal time. We study the closed-loop control built on the obtained approximate value functions, and we give theoretical guarantees on its performance depending on the approximation error for the value function. We show promising numerical results for three nonpolynomial systems with up to 6 state variables and 5 control variables.

Observability Inequalities for the Backward Stochastic Evolution Equations and Their Applications

Yuanhang Liu — 2026-04-03T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 727-747, April 2026.
Abstract. The present article delves into the investigation of observability inequalities pertaining to backward stochastic evolution equations. This abstract framework not only reproduces existing results for the stochastic heat equation but is also applicable to two other types of equations: a stochastic degenerate equation and a stochastic fourth-order parabolic equation. Furthermore, we employ a combination of spectral inequalities, interpolation inequalities, and the telegraph series method as our primary tools to directly establish observability inequalities, and thus we succeed to obtain both null and approximate controllability with only one control in the drift term of these equations.

Scaling Limits for Exponential Hedging in the Brownian Framework

Yan Dolinsky — 2026-04-03T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 748-762, April 2026.
Abstract. In this paper, we consider scaling limits of exponential utility indifference prices for European contingent claims in the Bachelier model. We show that the scaling limit can be represented in terms of the specific relative entropy, and, in addition, we construct asymptotically optimal hedging strategies. To prove the upper bound for the limit, we formulate the dual problem as a stochastic control and show there exists a classical solution to its Hamilton–Jacobi–Bellman (HJB) equation. The proof for the lower bound relies on the duality result for exponential hedging in discrete time.

Consensus Behavior in the Anticipated Vlasov Equation with Attractive Potentials

Bohui Yu — 2026-04-03T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 763-788, April 2026.
Abstract. The capacity for anticipation is a fundamental characteristic observed frequently in self-propelled agents. In this paper, a Vlasov equation with pairwise attractive potentials is considered, and the influence of anticipation on its emergent behavior is investigated quantitatively. Based on the anticipated structure, it is crucial to construct a thoroughgoing anticipated energy and several new Lyapunov functionals. Then by refined estimations of the anticipated space diameter, the solution is shown to achieve weak consensus exponentially for general attractive potentials. More importantly, when the potentials are convex, the strong consensus and the precise convergence rate are established. Meanwhile, similar results also hold for the discrete and hydrodynamic models.

Reciprocity of Linear Time-Varying Systems

Yu Kawano — 2026-04-07T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 789-815, April 2026.
Abstract. In this paper, we investigate reciprocal linear time-varying (LTV) systems. Originally, reciprocity has been defined for linear time-invariant (LTI) systems, which becomes a symmetry property when the external signature matrix is identity. The notion of symmetry has been extended to LTV systems by utilizing the time-reverse representations of the Hilbert adjoint systems. Building on this idea with slight modifications, we start this paper by defining reciprocity for LTV systems and show that a reciprocal LTV system admits a normal form at least locally. Furthermore, by combining reciprocity with passivity, we demonstrate that a normal form has a more special structure. Finally, we focus on the lossless case, i.e., a special passive case and establish the equivalence between the combination of losslessness and reciprocity, and reversibility. These obtained results can be viewed as natural extensions of those in the LTI case.

Convergence Analysis for Entropy-Regularized Control Problems: A Probabilistic Approach

Jin Ma — 2026-04-09T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 816-842, April 2026.
Abstract. In this paper we investigate the convergence of the policy iteration algorithm (PIA) for a class of general continuous-time entropy-regularized stochastic control problems. In particular, instead of employing sophisticated PDE estimates for the iterative PDEs involved in the algorithm (see, e.g., Huang, Wang, and Zhou [SIAM J. Control Optim., 63 (2025), pp. 752–777]), we shall provide a simple proof from scratch for the convergence of the PIA. Our approach builds on probabilistic representation formulae for solutions of PDEs and their derivatives. Moreover, in the finite horizon model and in the infinite horizon model with large discount factor, similar arguments lead to a superexponential rate of convergence without tear. Finally, with some extra effort we show that our approach can be extended to the diffusion control case in the one-dimensional setting, also with a superexponential rate of convergence.

The Finite-Horizon Reversible Investment Problem with the Constant Elasticity of Variance Model

Junkee Jeon — 2026-04-09T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 843-868, April 2026.
Abstract. In this paper, we explore a two-dimensional parabolic Hamilton–Jacobi–Bellman (HJB) equation, constrained by two gradients, that arises from a firm’s finite-horizon reversible investment problem under economic uncertainty dynamics following the constant elasticity of variance (CEV) model or a similar diffusion model. The nature of the CEV model causes the differential operator of this HJB equation to exhibit degeneracy and singularity at zero. To tackle these challenges, we integrate a theory of the double obstacle problem with nonstandard arguments, examining the analytical properties of the HJB equation. Additionally, we show the smoothness of the two free boundaries associated with the HJB equation. Finally, we construct the solution to the original HJB equation, which corresponds to the solution of the firm’s problem, by utilizing the relationship between singular control and a family of switching control developed by [], derived from the solution of a double obstacle problem.

Rough Stochastic Pontryagin Maximum Principle and an Indirect Shooting Method

Thomas Lew — 2026-04-10T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 869-905, April 2026.
Abstract. We derive first-order Pontryagin optimality conditions for stochastic optimal control with deterministic control inputs for systems modeled by rough differential equations (RDE) driven by Gaussian rough paths. This Pontryagin maximum principle (PMP) applies to systems following stochastic differential equations (SDE) driven by Brownian motion, yet it does not rely on forward-backward SDEs and involves the same Hamiltonian as the deterministic PMP. The proof consists of first deriving various integrable error bounds for solutions to nonlinear and linear RDEs by leveraging recent results on Gaussian rough paths. The PMP then follows using standard techniques based on needle-like variations. As an application, we propose the first indirect shooting method for nonlinear stochastic optimal control. Numerical experiments on a stabilization problem show that it converges [math] faster than a direct method.

Optimal Withdrawals in a Diffusion Model with State-Dependent Control Rates

Hélène Guérin — 2026-04-20T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 906-930, April 2026.
Abstract. We consider a classical stochastic control problem in which a diffusion process is controlled by a withdrawal process up to a termination time. The objective is to maximize the expected discounted value of the withdrawals until the first-passage time below level zero. In this work, we are considering absolutely continuous control strategies in a general diffusion model. Our main contribution is a solution to the control problem under study, which is achieved by using a probabilistic guess-and-verify approach. We prove that the optimal strategy belongs to the family of bang-bang strategies, i.e., strategies in which, above an optimal barrier level, we withdraw at the highest-allowed rate, while no withdrawals are made below this barrier. Some nontrivial examples are studied numerically.

Exact Controllability for a Refined Stochastic Hyperbolic Equation with Internal Controls

Zengyu Li — 2026-04-24T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 931-958, April 2026.
Abstract. The stochastic hyperbolic equation models vibrations of strings and membranes under random perturbations, with broad applications in applied science. However, the exact controllability generally fails for classical stochastic hyperbolic equations due to the lack of regularity and the influence of noise. In this paper, we study the internal exact controllability of a refined version of the stochastic hyperbolic equation, introduced by Lü and Zhang [Exact Controllability for a Refined Stochastic Wave Equation, arXiv:1901.06074, 2019]. Our main contributions are threefold: (1) we establish the first result on internal exact controllability for this class of stochastic hyperbolic systems; (2) we derive improved waiting time conditions that match those of the corresponding deterministic systems and are significantly shorter than previously known bounds; (3) we relax the regularity requirements for the control inputs. The key technical tool is a new [math]-Carleman estimate for backward stochastic hyperbolic equations, established through the analysis of a specifically constructed auxiliary optimal control problem.

Systems of Singularly Perturbed Forward-Backward Stochastic Differential Equations and Control Problems

Yihao Sheng — 2026-04-30T07:00:00Z

SIAM Journal on Control and Optimization, Volume 64, Issue 2, Page 959-984, April 2026.
Abstract. This paper focuses on systems of singularly perturbed forward-backward stochastic differential equations (FBSDEs) and control problems. Assuming Lipschitz continuity on the coefficients and allowing degeneracy in the diffusion terms, the solution of a two-time-scale FBSDE is shown to converge to the solution of an averaged FBSDE as a small parameter [math] tending to zero. Moreover, it is shown that the value function of the singularly perturbed systems converges to the solution of a nonlinear partial differential equation (PDE). Furthermore, under additional conditions, it is demonstrated that the solution of the limit PDE is in fact the limit value function. These results provide insights into the convergence rate and extend existing results on the averaging principles for such stochastic control problems.