Approximate Confidence Region of State Prediction in Stochastic Dynamical Discrete-Time Systems *

The confidence region of state prediction is necessary for anomaly detection and robust control design in stochastic dynamical systems. This paper addresses the problem of computing the tightest ellipsoidal region of state prediction with a required probability confidence level for stochastic dynamical discrete-time systems. This problem is not directly tractable. In this paper, a sample-based method is proposed to construct a solvable approximate problem of the original problem. By solving the approximate problem, the approximate confidence region can be obtained. We prove that the approximate confidence region converges to the optimal confidence region with probability 1 when the number of sample data increases to infinite. Numerical simulations have been implemented to validate the effectiveness of the proposed method.