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Output covariance tracking of linear stochastic systems

The idea of covariance control is to construct the state covariance matrix (P) to assign this P to the closed-loop stochastic system. In this paper the main idea is output covariance control based on converting the conventional differential equations governing the temporal behavioral of the covariance matrix into the state space vector equations. We derived the closed-form of the covariance transfer equations based on the model of the original stochastic system. This paper tends to force some elements of the covariance matrix P as the output of the covariance system to track desired values by some stabilizing PID controller. In this sense, the proposed algorithm is essentially different from other approaches because it does not involve Lyapunov or Riccati equations.