Jump to Content
Your Recent History
View CartTop 20 Most Read Articles
April 2012
The 20 articles with the most full-text downloads during the month, in descending order.
 |
SIAM J. Control Optim. 50, pp. 601-628 (28 pages) Online Publication Date: March 06, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
In this paper, we study the optimal time for a time optimal control problem $(\mathcal{P})$, where the state system is an internally controlled heat equation. By projecting the original problem via the finite element method, we obtain another time optimal control problem $(\mathcal{P}_{hl})$ governed by a linear system of ordinary differential equations. Here, $h$ and $l$ are the mesh sizes of the finite element spaces of the state space and the control space, respectively. The purpose of this study is to approach the optimal time for the problem $(\mathcal{P})$ through the optimal time for the problem $(\mathcal{P}_{hl})$. We prove that the optimal time for the problem $(\mathcal{P}_{hl})$ converges to the optimal time for the problem $(\mathcal{P})$ when $h$ and $l$ are approaching zero. More significantly, we obtain error estimates between the optimal times in terms of $h$ and $l$ for certain cases. |
|||
|
|
Adaptive Sampling for Linear State Estimation SIAM J. Control Optim. 50, pp. 672-702 (31 pages) Online Publication Date: March 13, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
When a sensor has continuous measurements but sends occasional messages over a data network to a supervisor which estimates the state, the available packet rate fixes the achievable quality of state estimation. When such rate limits turn stringent, the sensor's messaging policy should be designed anew. What are good causal messaging policies? What should message packets contain? What is the lowest possible distortion in a causal estimate at the supervisor? Is Delta sampling better than periodic sampling? We answer these questions for a Markov state process under an idealized model of the network and the assumption of perfect state measurements at the sensor. If the state is a scalar, or a vector of low dimension, then we can ignore sample quantization. If in addition we can ignore jitter in the transmission delays over the network, then our search for efficient messaging policies simplifies. First, each message packet should contain the value of the state at that time. Thus a bound on the number of data packets becomes a bound on the number of state samples. Second, the remaining choice in messaging is entirely about the times when samples are taken. For a scalar, linear diffusion process, we study the problem of choosing the causal sampling times that will give the lowest aggregate squared error distortion. We stick to finite horizons and impose a hard upper bound $N$ on the number of allowed samples. We cast the design as a problem of choosing an optimal sequence of stopping times. We reduce this to a nested sequence of problems, each asking for a single optimal stopping time. Under an unproven but natural assumption about the least-square estimate at the supervisor, each of these single stopping problems are of standard form. The optimal stopping times are random times when the estimation error exceeds designed envelopes. For the case where the state is a Brownian motion, we give analytically: the shape of the optimal sampling envelopes, the shape of the envelopes under optimal Delta sampling, and their performances. Surprisingly, we find that Delta sampling performs badly. Hence, when the rate constraint is a hard limit on the number of samples over a finite horizon, we should not use Delta sampling. |
|||
|
|
Quantum Measurement-Based Feedback Control: A Nonsmooth Time Delay Control Approach SIAM J. Control Optim. 50, pp. 845-863 (19 pages) Online Publication Date: April 04, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
This paper addresses the problem of measurement-based feedback control for quantum systems, in which the time to compute the filter-based control input is taken into account by considering the input delay. It starts with a new Lyapunov–LaSalle-like theorem for delay-dependent stochastic stability of a class of time delay stochastic nonlinear systems. Nonsmooth time delay control is then constructed to compensate for the control-computation time, which is known but arbitrarily long, while globally stabilizing the quantum filters almost surely. The nonsmooth property enables the control to deal with the symmetric topology of filter state space. The effectiveness of the proposed control is illustrated through the global stabilization of the spin-$1/2$ systems. Simulation results are presented and discussed to show the effectiveness of the proposed control. |
|||
|
|
Approximations of Equilibrium Problems SIAM J. Control Optim. 50, pp. 1038-1070 (33 pages) Online Publication Date: April 26, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
In this paper we study the scalar equilibrium problem (EP). We employ variational convergences of bifunctions (lopsided convergence in the maxinf framework, hypo-convergence, and continuous convergence) to study this problem by means of an approximation method. This method allows us to obtain not only existence but also stability results. We introduce a new notion of approximate solution of EPs and study its properties. Then, by coupling this notion of approximate solution and the above-mentioned variational convergences, we introduce new notions of well-posedness for EPs and characterize them. We identify various classes of problems that are well-posed. Finally, by employing the obtained results we prove convergence results of two numerical methods for pseudomonotone bifunctions. |
|||
|
|
Optimal Switching with Constraints and Utility Maximization of an Indivisible Market SIAM J. Control Optim. 50, pp. 629-651 (23 pages) Online Publication Date: March 08, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
This work focuses on optimal switching with constraints. Our motivation stems from utility maximization of an indivisible market. The dynamic programming approach is used; the value function is characterized as the unique viscosity solution of a quasi-variational inequality. The unbounded domain introduces new challenges. By studying the sample paths of the diffusion at the boundary, a sufficient condition for the continuity of the value function is provided, yielding the desired characterization. Not only are the results of this work applicable to the utility maximization problem, but also they can be used for general optimal switching problems with finite regimes. |
|||
|
|
Boundary Controllability and Observability of a Viscoelastic String SIAM J. Control Optim. 50, pp. 820-844 (25 pages) Online Publication Date: March 27, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
In this paper we consider an integrodifferential system, which governs the vibration of a viscoelastic one-dimensional object. We assume that we can act on the system at the boundary and we prove that it is possible to control both the position and the velocity at every point of the body and at a certain time $T$, large enough. We shall prove this result using moment theory and we shall prove that the solution of this problem leads to identification of a Riesz sequence which solves controllability and observability. The results presented here are constructive and can lead to simple numerical algorithms. |
|||
|
|
SIAM J. Control Optim. 50, pp. 652-671 (20 pages) Online Publication Date: March 08, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
Feedback gain and feedforward input of conventional linear quadratic (LQ) hard terminal controllers tend to infinity at terminal time, so that the conventional controllers have to go open-loop for a short interval before the final time. This short interval is called blind time. To avoid the terminal infinite feedback control gain and feedforward input, new optimal control laws are proposed for hard terminal control of linear time-varying systems. Furthermore, a structure-preserving numerical method is also presented to evaluate the time-varying optimal feedback and feedforward control gains and corresponding optimal trajectory. The analytical and numerical methods being developed here are based on the application of symplectic (canonical) transformation and generating functions of Hamiltonian systems. Different from the existing generating function method for optimal control, the first type of generating function plays a key role in solving the associated Hamiltonian two-point boundary-value problem (TPBVP), while the second generating function is employed to recover the first type. This note uses the second and third types of generating functions to find novel optimal control laws by solving the Hamiltonian TPBVP, which eliminates the infinite control gains of conventional optimal control laws near terminal time. Since the optimal trajectory of the closed-loop system is a solution of the Hamiltonian TPBVP, by using symplecticity of the solution operator of the linear Hamiltonian system, this paper also derives a structure-preserving matrix recursive algorithm for the computation of time-varying optimal control gains and the systems optimal trajectories. Numerical simulations show that this structure-preserving algorithm gives accurate results for relative large discrete steps and keeps geometric properties of the solutions. |
|||
|
|
Backstepping Control in Vector Form for Stochastic Hamiltonian Systems SIAM J. Control Optim. 50, pp. 925-942 (18 pages) Online Publication Date: April 17, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
In this paper, the problem of adaptive tracking for a class of stochastic Hamiltonian control systems with unknown drift and diffusion functions is considered. Some difficulties come forth—the integral chain consists of vectors, and control and tracking errors are in different channels—which are rarely considered in the existing references about stochastic nonlinear controls. To resolve these problems, an adaptive backstepping controller in vector form is designed such that the closed-loop system has a unique solution that is globally bounded in probability and the fourth moment of the tracking error converges to an arbitrarily small neighborhood of zero. As an application, the modeling and the control for spring pendulum in stochastic surroundings are researched. |
|||
|
|
Optimal Regulation of Nonlinear Dynamical Systems SIAM J. Control 7, pp. 75-100 (26 pages) Online Publication Date: July 18, 2006
Full Text:
|
Download PDF
|
||
|
Abstract Unavailable
|
|||
|
|
Directional Sparsity in Optimal Control of Partial Differential Equations SIAM J. Control Optim. 50, pp. 943-963 (21 pages) Online Publication Date: April 19, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
We study optimal control problems in which controls with certain sparsity patterns are preferred. For time-dependent problems the approach can be used to find locations for control devices that allow controlling the system in an optimal way over the entire time interval. The approach uses a nondifferentiable cost functional to implement the sparsity requirements; additionally, bound constraints for the optimal controls can be included. We study the resulting problem in appropriate function spaces and present two solution methods of Newton type, based on different formulations of the optimality system. Using elliptic and parabolic test problems we research the sparsity properties of the optimal controls and analyze the behavior of the proposed solution algorithms. |
|||
|
|
Optimal Control for Stochastic Volterra Equations with Completely Monotone Kernels SIAM J. Control Optim. 50, pp. 748-789 (42 pages) Online Publication Date: March 22, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
In this paper, we study a class of optimal control problems for stochastic Volterra equations in infinite dimensions. We are concerned with a class of stochastic Volterra integro-differential problem with completely monotone kernels, where we assume that the noise enters the system when we introduce a control. We provide a semigroup setting for the problem, by the state space setting; the applications to optimal control provide other interesting results and require a precise description of the properties of the generated semigroup. In our stochastic optimal control problems, the drift term of the equation has a linear growth in the control variable, the cost functional has a quadratic growth, and the control process belongs to the class of square integrable, adapted processes with no bound assumed on it. Our main results are the existence for the optimal feedback control, the identification of the optimal cost with the value $Y_0$ of the maximal solution $(Y,Z)$ of the backward stochastic differential equation, the existence of a weak solution to the so-called closed loop equation and, finally, the construction of an optimal feedback in terms of the process $Z$. |
|||
|
|
SIAM J. Control Optim. 50, pp. 888-899 (12 pages) Online Publication Date: April 17, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
We prove higher integrability properties of solutions to the problem of minimizing $\int_{\Omega}L(x,u(x),\nabla u(x))\rm{ d}x,$ where $\xi\mapsto L(x,u,\xi)$ is a convex function satisfying some additional conditions. As an application, we prove the validity of the Euler–Lagrange equation for a class of functionals with growth faster than exponential. |
|||
|
|
Backward Stochastic Differential Equation Driven by Fractional Brownian Motion SIAM J. Control Optim. 48, pp. 1675-1700 (26 pages) Online Publication Date: May 07, 2009
Full Text:
|
Download PDF
|
||
|
Show Abstract
We study general linear and nonlinear backward stochastic differential equations driven by fractional Brownian motions. The existence and uniqueness of the solutions are obtained under some mild assumptions. In the nonlinear case we obtain an inequality of the type similar to in the classical backward stochastic differential equations. This leads to a fixed point principle. An important tool is the quasi-conditional expectation introduced in [Y. Hu and B. Øksendal, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6 (2003), pp. 1–32]. We also give a detailed study on this new “expectation.” |
|||
|
|
Optimal Investment with High-watermark Performance Fee SIAM J. Control Optim. 50, pp. 790-819 (30 pages) Online Publication Date: March 27, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
We consider the problem of optimal investment and consumption when the investment opportunity is represented by a hedge fund charging proportional fees on profit. The value of the fund evolves as a geometric Brownian motion and the performance of the investment and consumption strategy is measured using discounted power utility from consumption on infinite horizon. The resulting stochastic control problem is solved using dynamic programming arguments. We show by analytical methods that the associated Hamilton–Jacobi–Bellman equation has a smooth solution and then obtain the existence and representation of the optimal control in feedback form using verification arguments. |
|||
|
|
SIAM J. Control Optim. 50, pp. 964-990 (27 pages) Online Publication Date: April 19, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
This paper develops a sufficient stochastic maximum principle for a stochastic optimal control problem, where the state process is governed by a continuous-time Markov regime-switching jump-diffusion model. We also establish the relationship between the stochastic maximum principle and the dynamic programming principle in a Markovian case. Applications of the stochastic maximum principle to the mean-variance portfolio selection problem are discussed. |
|||
|
|
Optimal Control Models of Goal-oriented Human Locomotion SIAM J. Control Optim. 50, pp. 147-170 (24 pages) Online Publication Date: January 17, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
In recent papers it has been suggested that human locomotion may be modeled as an inverse optimal control problem. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem that has to be determined. We discuss the modeling of both the dynamical system and the cost to be minimized, and we analyze the corresponding optimal synthesis. The main results describe the asymptotic behavior of the optimal trajectories as the target point goes to infinity. |
|||
|
|
A General Stochastic Maximum Principle for Optimal Control Problems SIAM J. Control Optim. 28, pp. 966-979 (14 pages) Online Publication Date: August 01, 2006
Full Text:
|
Download PDF
|
||
|
Show Abstract
The maximum principle for nonlinear stochastic optimal control problems in the general case is proved. The control domain need not be convex, and the diffusion coefficient can contain a control variable. |
|||
|
|
SIAM J. Control Optim. 50, pp. 507-531 (25 pages) Online Publication Date: February 28, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
A linear-quadratic control problem with a finite time horizon for some infinite-dimensional controlled stochastic differential equations driven by a fractional Gaussian noise is formulated and solved. The feedback form of the optimal control and the optimal cost are given explicitly. The optimal control is the sum of the well-known linear feedback control for the associated deterministic linear-quadratic control problem and a suitable prediction of the adjoint optimal system response to the future noise. The covariance of the noise as well as the control operator in the system equation can in general be unbounded, so the results can also be applied where the noise or the control are on the boundary of the domain or at discrete points in the domain. Some examples of controlled stochastic partial differential equations are given. |
|||
|
|
Martingale and Duality Methods for Utility Maximization in an Incomplete Market SIAM J. Control Optim. 29, pp. 702-730 (29 pages) Online Publication Date: July 14, 2006
Full Text:
|
Download PDF
|
||
|
Show Abstract
The problem of maximizing the expected utility from terminal wealth is well understood in the context of a complete financial market. This paper studies the same problem in an incomplete market containing a bond and a finite number of stocks whose prices are driven by a multidimensional Brownian motion process $W$. The coefficients of the bond and stock processes are adapted to the filtration (history)of $W$, and incompleteness arises when the number of stocks is strictly smaller than the dimension of $W$. It is shown that there is a way to complete the market by introducing additional “fictitious” stocks so that the optimal portfolio for the thus completed market coincides with the optimal portfolio for the original incomplete market. The notion of a “least favorable” completion is introduced and is shown to be closely related to the existence question for an optimal portfolio in the incomplete market. This notion is expounded upon using martingale techniques; several equivalent characterizations are provided for it, examples are studied in detail, and a fairly general existence result for an optimal portfolio is established based on convex duality theory. |
|||
|
|
Some Controllability Results for Linear Viscoelastic Fluids SIAM J. Control Optim. 50, pp. 900-924 (25 pages) Online Publication Date: April 17, 2012
Full Text:
|
Download PDF
|
||
|
Show Abstract
We analyze the controllability properties of systems which provide a description, at first approximation, of a kind of viscoelastic fluid. We consider linear Maxwell fluids. First, we establish the large time approximate-finite dimensional controllability of the system, with distributed or boundary controls supported by arbitrary small sets. Then, we prove the large time exact controllability of fluids of the same kind with controls supported by suitable large sets. The proofs of these results rely on classical arguments. In particular, the approximate controllability result is implied by appropriate unique continuation properties, while exact controllability is a consequence of observability (inverse) inequalities. We also discuss questions concerning the controllability of viscoelastic fluids and some related open problems. |
|||
ALL SIAM Content
Scitation
Google Scholar