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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| Vydáno v: | IEEE transactions on automatic control Ročník 62; číslo 7; s. 3165 - 3177 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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01.07.2017
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| 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. |
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| 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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