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Adaptively Constrained Stochastic Model Predictive Control for Closed-Loop Constraint Satisfaction


F. Oldewurtel, D. Sturzenegger, P. Mohajerin Esfahani, G. Andersson, M. Morari, J. Lygeros

American Control Conference, Washington, DC, USA

Stochastic Model Predictive Control (SMPC) for discrete-time linear systems subject to additive disturbances with chance constraints on the states and hard constraints on the inputs is considered. Current chance constrained MPC methodsóbased on analytic reformulations or on sampling approachesótend to be conservative partly because they fail to exploit the predefined violation level in closed-loop. For many practical applications, this conservatism can lead to a loss in performance. We propose an adaptive SMPC scheme that starts with a standard conservative chance constrained formulation and then on-line adapts the formulation of constraints based on the experienced violation frequency. Using martingale theory we establish guarantees of convergence to the desired level of constraint violation in closed-loop for a special class of linear systems. Comments are given on how to extend this to a broader class of (non-)linear systems. The developed methodology is demonstrated with an illustrative example.


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J. Lygeros

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% Autogenerated BibTeX entry
@InProceedings { OldEtal:2013:IFA_4483,
    author={F. Oldewurtel and D. Sturzenegger and P. Mohajerin Esfahani and G.
	  Andersson and M. Morari and J. Lygeros},
    title={{Adaptively Constrained Stochastic Model Predictive Control
	  for Closed-Loop Constraint Satisfaction}},
    booktitle={American Control Conference},
    address={Washington, DC, USA},
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