Descent algorithms for optimal periodic output feedback control

Periodic output feedback is investigated in the context of linear-quadratic regulation for finite-dimensional time-invariant linear systems. Discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control. The optimal solution is obtained in two steps by separating the continuous-time from the discrete-time structure. First, the optimal pole placement problem under periodic output feedback is solved explicitly under the assumption that the behavior at the sample times has been specified in terms of a gain matrix G. Then the minimum value, which depends on G, is substituted into the overall objective. This results in a finite-dimensional nonlinear programming problem over all admissible gain matrices G. The solution defines the optimal periodic output feedback control via the formulas of the optimal pole placement problem. A steepest descent and a direct iterative method for solving this problem are formulated and compared. Numerical examples show that the performance using periodic output feedback is almost equivalent to that using optimal continuous-state feedback