A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization

• Published in: IEEE transactions on automatic control Vol. 56; no. 12; pp. 2809 - 2824
• Main Authors: Bertsimas, Dimitris, Iancu, Dan Andrei, Parrilo, Pablo A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptative systems; Adaptive control; Applied sciences; Approximation methods; Computation; Computer science; control theory; systems; Constrained control; Control; Control theory. Systems; Exact sciences and technology; Hierarchies; Inventory management; Machine components; Mechanical engineering. Machine design; Multistage; Optimal control; Optimization; Policies; Polynomials; Programming; robust adaptive control; Robustness; semidefinite programming; Springs and dampers; sums-of-squares; Uncertain systems; Multistage; uncertain systems; Optimal policy; Polynomial control; Feedback regulation; Semi definite programming; Dynamical system; Adaptive control; sums-of-squares; Hierarchized structure; Constrained optimization; Stochastic programming; Closed feedback; Robust control; semidefinite programming; Control constraint; Uncertain system; Vehicle suspension; robust adaptive control; Active system; optimization; Optimal control; Constrained control; Inventory control
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2011.2162878

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 applications-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.