In this paper we first present a full order $H_{\infty }$ controller for a multi- input, multi-output (MIMO) adaptive optics system. We apply model reduction techniques to the full order $H_{\infty }$ controller and demonstrate that the closed-loop (CL) system with the reduced order $H_{\infty }$ controller achieves the same high level of performance. Upon closer examination of the structure of the reduced order $H_{\infty }$ controller it is found that the dynamical behavior of the reduced order $H_{\infty }$ controller can be accurately approximated by...

Effective, simulation-based trajectory optimization algorithms adapted to heterogeneous computers are studied with reference to the problem taken from alpine ski racing (the presented solution is probably the most general one published so far). The key idea behind these algorithms is to use a grid-based discretization scheme to transform the continuous optimization problem into a search problem over a specially constructed finite graph, and then to apply dynamic programming to find an approximation...