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Zbl 1227.93130
Wang, Yang; Boyd, Stephen
Performance bounds and suboptimal policies for linear stochastic control via LMIs. (English)
[J] Int. J. Robust Nonlinear Control 21, No. 14, 1710-1728 (2011). ISSN 1049-8923

Summary: In a recent paper, the authors showed how to compute performance bounds for infinite-horizon stochastic control problems with linear system dynamics and arbitrary constraints, objective, and noise distribution. In this paper, we extend these results to the finite-horizon case, with asymmetric costs and constraint sets. In addition, we derive our bounds using a new method, where we relax the Bellman equation to an inequality. The method is based on bounding the objective with a general quadratic function, and using Linear Matrix Inequalities (LMIs) and SemiDefinite Programming (SDP) to optimize the bound. The resulting LMIs are more complicated than in the previous paper (which only used quadratic forms) but this extension allows us to obtain good bounds for problems with substantial asymmetry, such as supply chain problems. The method also yields very good suboptimal control policies, using control-Lyapunov methods.

MSC 2000:: *93E20 Optimal stochastic control (systems)
49L20 Dynamic programming method (infinite-dimensional problems)
90C25 Convex programming

Keywords: dynamic programming; stochastic control; convex optimization

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