A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization

作者：Bertsimas Dimitris^*; Iancu Dan Andrei; Parrilo Pablo A

来源：IEEE Transactions on Automatic Control, 2011, 56(12): 2803-2818.

DOI：10.1109/TAC.2011.2162878

• Constrained control
• optimization
• robust adaptive control
• semidefinite programming
• sums-of-squares
• uncertain systems

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.

• 出版日期2011-12