Full-state-feedback minimal cost variance control on an infinite time horizon: the risk-sensitive approach

Abstract

The idea of minimal cost variance (MCV) control, which is a part of stochastic control based upon constrained cost means and minimized cost variances, may be viewed as a generalization of linear quadratic Gaussian (LQG) and of risk-sensitive control strategies, the former when a cost mean is constrained to be minimum and the latter when the risk-sensitive cost function is considered as a denumerable linear combination of cost cumulants. The paper finds the solutions of the infinite time horizon MCV control problem. In the solutions of infinite time horizon MCV control problems, a pair of coupled Riccati equations arises. The paper considers the existence and uniqueness of a positive semidefinite solution pair for the steady-state version of these equations, where one entry of the pair corresponds to cost mean, while the other entry of the pair corresponds to cost variance. From this result it is established that the MCV feedback controller stabilizes the closed loop system under special conditions. Furthermore, the algorithm to find the solutions of the coupled algebraic Riccati equations is presented with an example. The MCV control method is illustrated by applying it to simulations of satellite attitude control.