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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Abstract	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.
AbstractList	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.
Author	Lorenzen, Matthias Tempo, Roberto Allgower, Frank Dabbene, Fabrizio
Author_xml	– sequence: 1 givenname: Matthias surname: Lorenzen fullname: Lorenzen, Matthias email: matthias.lorenzen@ist.uni-stuttgart.de organization: Inst. for Syst. Theor. & Autom. Control, Univ. of Stuttgart, Stuttgart, Germany – sequence: 2 givenname: Fabrizio surname: Dabbene fullname: Dabbene, Fabrizio email: fabrizio.dabbene@polito.it organization: IEIIT, Politec. di Torino, Turin, Italy – sequence: 3 givenname: Roberto surname: Tempo fullname: Tempo, Roberto organization: IEIIT, Politec. di Torino, Turin, Italy – sequence: 4 givenname: Frank surname: Allgower fullname: Allgower, Frank email: frank.allgower@ist.uni-stuttgart.de organization: Inst. for Syst. Theor. & Autom. Control, Univ. of Stuttgart, Stuttgart, Germany
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SubjectTerms	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
Title	Constraint-Tightening and Stability in Stochastic Model Predictive Control
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