Recursive Feasibility of Stochastic Model Predictive Control with Mission-Wide Probabilistic Constraints

This paper is concerned with solving chanceconstrained finite-horizon optimal control problems, with a particular focus on the recursive feasibility issue of stochastic model predictive control (SMPC) in terms of mission-wide probability of safety (MWPS). MWPS assesses the probability that the entire state trajectory lies within the constraint set, and the objective of the SMPC controller is to ensure that it is no less than a threshold value. This differs from classic SMPC where the probability that the state lies in the constraint set is enforced independently at each time instant. Unlike robust MPC, where strict recursive feasibility is satisfied by assuming that the uncertainty is supported by a compact set, the proposed concept of recursive feasibility for MWPS is based on the notion of remaining MWPSs, which is conserved in the expected value sense. We demonstrate the idea of mission-wide SMPC in the linear SMPC case by deploying a scenario-based algorithm.

[1]  Masahiro Ono.  Closed-loop chance-constrained MPC with probabilistic resolvability , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[2]  Masahiro Ono.  Joint chance-constrained model predictive control with probabilistic resolvability , 2012, 2012 American Control Conference (ACC).

[3]  Marco C. Campi,et al.  A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality , 2011, J. Optim. Theory Appl..

[4]  John Lygeros,et al.  Invariance in Stochastic Dynamical Control Systems , 2006 .

[5]  Giuseppe Carlo Calafiore,et al.  The scenario approach to robust control design , 2006, IEEE Transactions on Automatic Control.

[6]  Masahiro Ono,et al.  Iterative Risk Allocation: A new approach to robust Model Predictive Control with a joint chance constraint , 2008, 2008 47th IEEE Conference on Decision and Control.

[7]  Masahiro Ono,et al.  An Efficient Motion Planning Algorithm for Stochastic Dynamic Systems with Constraints on Probability of Failure , 2008, AAAI.

[8]  Richard D. Braatz,et al.  Stochastic model predictive control with joint chance constraints , 2015, Int. J. Control.

[9]  Marcello Farina,et al.  An approach to output-feedback MPC of stochastic linear discrete-time systems , 2015, Autom..

[10]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[11]  Marcello Farina,et al.  Stochastic linear Model Predictive Control with chance constraints – A review , 2016 .

[12]  Mark Cannon,et al.  Stochastic Model Predictive Control with Discounted Probabilistic Constraints , 2018, 2018 European Control Conference (ECC).

[13]  Giuseppe Carlo Calafiore.  A note on the expected probability of constraint violation in sampled convex programs , 2009, 2009 IEEE Control Applications, (CCA) & Intelligent Control, (ISIC).

[14]  Marco Pavone,et al.  Chance-constrained dynamic programming with application to risk-aware robotic space exploration , 2015, Autonomous Robots.