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

Author(s):

E. Cinquemani, M. Agarwal, D. Chatterjee, J. Lygeros
Conference/Journal:

Automatica, vol. 47, no. 9, pp. 2082 - 2087
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.

Year:

2011
Type of Publication:

(01)Article
Supervisor:



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% Autogenerated BibTeX entry
@Article { CinEtal:2011:IFA_3955,
    author={E. Cinquemani and M. Agarwal and D. Chatterjee and J. Lygeros},
    title={{Convexity and convex approximations of discrete-time
	  stochastic control problems with constraints}},
    journal={Automatica},
    year={2011},
    volume={47},
    number={9},
    pages={2082 -- 2087},
    month=jun,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=3955}
}
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