Nonlinear optimal control synthesis via occupation measures

Details Nonlinear optimal control synthesis via occupation measures Nonlinear optimal control synthesis via occupation measures

2008-03-11

arxiv.org/abs/0803.1570v1

Mathematics

Optimization and Control

Scientific paper

We consider nonlinear optimal control problems (OCPs) for which all problem data are polynomial. In the first part of the paper, we review how occupation measures can be used to approximate pointwise the optimal value function of a given OCP, using a hierarchy of linear matrix inequality (LMI) relaxations. In the second part, we extend the methodology to approximate the optimal value function on a given set and we use such a function to constructively and computationally derive an almost optimal control law. Numerical examples show the effectiveness of the approach.

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