Stability and feasibility of state constrained MPC without stabilizing terminal constraints

In this paper we investigate stability and recursive feasibility of a nonlinear receding horizon control scheme without terminal constraints and costs but imposing state and control constraints. Under a local controllability assumption we show that every level set of the infinite horizon optimal val...

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Bibliographic Details
Published inSystems & control letters Vol. 72; pp. 14 - 21
Main Authors Boccia, Andrea, Grüne, Lars, Worthmann, Karl
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2014
Elsevier
Subjects
Feasibility
Linear systems
Mathematics
Nonlinear control
Optimal control
Optimal value functions
Optimization and Control
Predictive control
Stability
State constraints
Linear systems
Stability
Optimal control
State constraints
Feasibility
Optimal value functions
Nonlinear control
Predictive control
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ISSN0167-6911
1872-7956
DOI10.1016/j.sysconle.2014.08.002

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Summary:In this paper we investigate stability and recursive feasibility of a nonlinear receding horizon control scheme without terminal constraints and costs but imposing state and control constraints. Under a local controllability assumption we show that every level set of the infinite horizon optimal value function is contained in the basin of attraction of the asymptotically stable equilibrium for sufficiently large optimization horizon N. For stabilizable linear systems we show the same for any compact subset of the interior of the viability kernel. Moreover, estimates for the necessary horizon length N are given via an analysis of the optimal value function at the boundary of the viability kernel.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2014.08.002