Linear conic optimization for nonlinear optimal control
Résumé
In this chapter, we discuss infinite-dimensional conic linear optimization (CLO) for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, where as the dual linear problem consists of finding the largest lower bound on the value function of the optimal control problem. We develop various approximation results relating the original optimal control problem and its conic linear formulations. These results are relevant in the context of finite-dimensional semidefinite programming relaxations used to numerically approximate the solutions of the infinite-dimensional conic linear problems.
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