A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization

A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization

By
Dan A. Iancu, Dimitris Bertsimas, Pablo Parrilo
IEEE Transactions on Automatic Control. December
2011, Vol. 56, Issue 12, Pages 2809-2824

In this paper, we propose a new tractable framework for dealing with linear dynamical systems affected by uncertainty, applicable to multistage robust optimization and stochastic programming. We introduce a hierarchy of near-optimal polynomial disturbance-feedback control policies, and show how these can be computed by solving a single semidefinite programming problem. The approach yields a hierarchy parameterized by a single variable (the degree of the polynomial policies), which controls the trade-off between the optimality gap and the computational requirements. We evaluate our framework in the context of three classical appli- cations—two in inventory management, and one in robust regulation of an active suspension system—in which very strong numerical performance is exhibited, at relatively modest computational expense.