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A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization

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3 Author(s)
Bertsimas, D. ; Sloan Sch. of Manage. & the Oper. Res. Center, Massachusetts Inst. of Technol., Cambridge, MA, USA ; Iancu, D.A. ; Parrilo, P.A.

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.

Published in:

Automatic Control, IEEE Transactions on  (Volume:56 ,  Issue: 12 )