Model Predictive Control, Cost Controllability, and Homogeneity
Abstract
We are concerned with the design of Model Predictive Control (MPC) schemes such that asymptotic stability of the resulting closed loop is guaranteed---even if the linearization at the desired set point fails to be stabilizable. Therefore, we propose constructing the stage cost based on the homogeneous approximation and rigorously show that applying MPC yields an asymptotically stable closed-loop behavior if the homogeneous approximation is asymptotically null controllable. To this end, we verify cost controllability---a condition relating the current state, the stage cost, and the growth of the value function with respect to time---for this class of systems in order to provide stability and performance guarantees for the proposed MPC scheme without stabilizing terminal costs or constraints.
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Information & Authors
Information
Published In
SIAM Journal on Control and Optimization
Pages: 2979 - 2996
DOI: 10.1137/19M1265995
ISSN (online): 1095-7138
Copyright
© 2020, Society for Industrial and Applied Mathematics.
History
Submitted: 4 June 2019
Accepted: 8 July 2020
Published online: 13 October 2020
Keywords
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Authors
Funding Information
Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley https://doi.org/10.13039/100007247
Funding Information
Agence Nationale de la Recherche https://doi.org/10.13039/501100001665 : ANR Finite4SoS
Funding Information
Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : WO 2056/6-1
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