Suboptimal control of discrete stochastic amplitude constrained systems

Abstract

Abstract Optimal control of linear discrete time stochastic systems with an amplitude constraint on the input is considered. A suboptimal controller is obtained by considering linear feedback laws with saturation. The variances of the closed-loop system are evaluated by approximating the stationary probability distribution of the state with a gaussian distribution. The gradient of the loss with respect to the feedback gain is evaluated, and an iterative algorithm to optimize the regulator parameters is given. Numerical examples are used to evaluate the control performance of the suboptimal strategy. The obtained loss is compared with a lower bound on the minimum of the loss which is achievable in amplitude constrained control. The results show that the suboptimal strategy may give near-optimal control performance