Suboptimal closed-loop controller design for minimum probability of inequality constraints violation

When a dynamic system is perturbed by random disturbances, the system responses deviate from their nominal values, in general. Because of physical reasons, the deviations are required to satisfy certain inequality constraints. When a closed-loop controller is designed to minimize the deviations, the control efforts are also subject to some inequality constraints. In this paper, a suboptimal closed-loop controller is developed for a linear time-varying process subject to additive random disturbances and additive measurement noises. The controller minimizes the probability that the system responses and the control inputs violate given inequality constraints. The method is based on the quadratic equivalence. The problem is formulated in the normed function space so that Dem'yanov and Rubinov's algorithm can be applied. The convergence conditions are also given. As an illustration, the method is used to design a closed-loop controller for a Saturn-class missile modeled by a tenth-order linear time-varying system.