In this talk, we discuss the performance of disturbance-feedback policies in robust models of multi-period, linear dynamical systems. For the one-dimensional case, using geometric ideas from polyhedral theory, we prove the optimality of policies that are affine in the history of disturbances. The result underscores a key distinction between robust and stochastic models for dynamic optimization, with the former resulting in qualitatively simpler problems than the latter. For the case of a general system, we provide a hierarchy of polynomial policies that are also directly parameterized in observed disturbances, and that can be efficiently computed using semi-definite optimization methods. Empirical results in several applications are very encouraging, suggesting that policies based on quadratic or cubic polynomials are near-optimal. This is joint work with Dimitris Bertsimas and Pablo Parrilo.
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