Minimized coupling in probability sense for a class of multivariate dynamic stochastic control systems

This paper presents a novel concept which is firstly established to describe the probabilistic property of the couplings among system states. Based on this concept, a new algorithm is presented to minimize the elements of the states covariance matrix for a class of multivariate dynamic stochastic nonlinear systems, which are represented by a set of Ito̅ stochastic differential equations. Since the measurable covariance matrix is dynamically related to the control inputs, this controller combines feedback linearization, covariance control and LQR can thus attenuate the pairwise dependence of the states. Moreover, decoupling in probability sense can be realized. The mean square stability is proved for the closed loop systems. To evaluate the performance of the closed loop systems with different controllers, the assessment criterion is proposed. An illustrative example is utilized to demonstrate the use of the control algorithm, and desired results have been obtained.