Constraint-Tightening and Stability in Stochastic Model Predictive Control

Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference between existence of a solution and feasibility of a suitable,...

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Veröffentlicht in:IEEE transactions on automatic control Jg. 62; H. 7; S. 3165 - 3177
Hauptverfasser: Lorenzen, Matthias, Dabbene, Fabrizio, Tempo, Roberto, Allgower, Frank
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IEEE 01.07.2017
Schlagworte:
Asymptotic stability
Chance constraints
constrained control
discrete-time stochastic systems
Numerical stability
Optimization
Predictive control
randomized algorithms
receding horizon control
Robustness
stochastic model predictive control
Stochastic processes
Uncertainty
ISSN:0018-9286, 1558-2523
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Zusammenfassung:Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference between existence of a solution and feasibility of a suitable, a priori known candidate solution. Subsequently, a Stochastic Model Predictive Control algorithm which unifies previous results is derived, leaving the designer the option to balance an increased feasible region against guaranteed bounds on the asymptotic average performance and convergence time. Besides typical performance bounds, under mild assumptions, we prove asymptotic stability in probability of the minimal robust positively invariant set obtained by the unconstrained LQ-optimal controller. A numerical example, demonstrating the efficacy of the proposed approach in comparison with classical, recursively feasible Stochastic MPC and Robust MPC, is provided.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2016.2625048