Approximation of controllable set by semidefinite programming for open-loop unstable systems with input saturation

In order to test the efficiency of recently developed semidefinite programming (SDP), we apply SDP software package to the solution of our optimization problems. And we compare the ease of programming and the execution time for solving the problem between the classical approach (which applies a nonlinear equation solver to the Kuhn-Tucker conditions) and the SDP approach (which exploits interior-point algorithms). It is also shown that, for certain types of optimization problems, SDP is indeed very efficient. However, our examples show that SDP has limitations in solving non-convex optimization problems. It is also shown that the controllable set approximated by SDP is very efficient, however, the resulting controllable set is somewhat smaller than the set approximated under Lyapunov descent criteion.