Convexity and convex approximations of discrete-time stochastic control problems with constraints

Eugenio Cinquemani 1, * Mayank Agarwal 2 Debasish Chatterjee 3 John Lygeros 3
* Corresponding author
1 IBIS - Modeling, simulation, measurement, and control of bacterial regulatory networks
LAPM - Laboratoire Adaptation et pathogénie des micro-organismes [Grenoble], Inria Grenoble - Rhône-Alpes, Institut Jean Roget
Abstract : We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost subject to probabilistic constraints. We study the convexity of a finite-horizon optimization problem in the case where the control policies are affine functions of the disturbance input. We propose an expectation-based method for the convex approximation of probabilistic constraints with polytopic constraint function, and a Linear Matrix Inequality (LMI) method for the convex approximation of probabilistic constraints with ellipsoidal constraint function. Finally, we introduce a class of convex expectation-type constraints that provide tractable approximations of the so-called integrated chance constraints. Performance of these methods and of existing convex approximation methods for probabilistic constraints is compared on a numerical example.
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Submitted on : Thursday, February 21, 2013 - 2:33:37 PM
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Eugenio Cinquemani, Mayank Agarwal, Debasish Chatterjee, John Lygeros. Convexity and convex approximations of discrete-time stochastic control problems with constraints. Automatica, Elsevier, 2011, 47, pp.2082-2087. 〈10.1016/j.automatica.2011.01.023〉. 〈hal-00793041〉

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