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The Linear Quadratic Regulator with Chance Constraints


G. Schildbach, P.J. Goulart, M. Morari

European Control Conference (ECC), Zurich, Switzerland, pp. 2746-2751

This paper is concerned with the design of linear state feedback control for linear systems with additive stochastic disturbances. The objective is to find the feedback gain that minimizes a quadratic cost function in closed-loop operation, while observing chance constraints on the input and/or the state (i.e. a `Linear Quadratic Regulator with Chance Constraints'). It is shown that this problem can be cast as a semi-definite program (SDP), in which the chance constraints appear as linear matrix inequalities (LMIs). Both individual chance constraints (ICCs) and joint chance constraints (JCCs) can be considered. In the case of ICCs only, the resulting SDP is linear and can be solved efficiently as a convex optimization program. In the presence of JCCs the SDP becomes bilinear, however it can still be solved efficiently by an iterative algorithm described in the paper, at least to a local optimum. The application of the method is demonstrated for several numerical examples, underscoring its flexibility and ease of implementation.


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% Autogenerated BibTeX entry
@InProceedings { SchGou:2013:IFA_4339,
    author={G. Schildbach and P.J. Goulart and M. Morari},
    title={{The Linear Quadratic Regulator with Chance Constraints}},
    booktitle={European Control Conference (ECC)},
    address={Zurich, Switzerland},
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