Covariance control for stochastic uncertain multivariable systems via sliding mode control strategy

Abstract

The main idea proposed in this study is based on converting continuous-time covariance matrix differential equations of a multivariable system into a new uncertain deterministic linear system. The closed-loop form of the new state covariance equations is derived by converting the covariance matrix Riccati equation to a new linear deterministic vector state space system. Since the new covariance system is linear and deterministic, all conventional and well-defined control strategies can be applied to it. Using a sliding mode control strategy, the uncertain interconnection terms satisfying a matching condition are nullified and the closed-loop covariance system is asymptotically stable. This is accomplished by applying a control strategy composed of sliding mode and covariance feedback control for each local subsystem.