SYNTHESIS OF OPTIMAL CONTROL SYSTEMS WITH STABLE FEEDBACK
Doctor of Philosophy
In this thesis, the question of optimal control system design when constrained to using a stable controller is addressed. The performance index that is minimized is H$\sp\infty$-norm of the sensitivity of the closed-loop system to external disturbances. It is shown that the resulting feedback associated with the minimum value of the optimality criterion is irrational. A design algorithm is developed to find an approximation whose deviation from a sub-optimal controller lies within a pre-specified error bound, thus guaranteeing internal stability. For multivariable systems, a characterization is provided of all sensitivity functions that result from a stable controller; and two important special cases are solved for optimality. Next, the problem of finding the H$\sp 2$-optimal stable feedback controller for a general optimality criterion is considered. It is shown that this optimization reduces to finding the "best" function in RH$\sp 2$ (i.e. of minimum norm) that satisfies an avoidance constraint. A design procedure is proposed for obtaining an optimal stable controller that minimizes the performance index and maintains internal stability. Given an initial point, this is achieved by minimizing a nonlinear objective function subject to nonlinear inequality constraints via a sequential gradient programming method.
Electronics; Electrical engineering