Computing probabilistic bounds on state trajectories for uncertain systems

Xun Shen, Tinghui Ouyang, Yahui Zhang, Xingguo Zhang

Abstract: Bounds for the evolution of state trajectories of systems with uncertainty are important for various applications such as safety assessment, experimental design, and robust control design. While computing the bounds for nonlinear systems with uncertainties of arbitrary distributions is still a challenging task due to the NP-hard issue. This paper proposes a scenario approach-based method to compute probabilistic ellipsoidal bounds for discrete-time nonlinear systems with uncertain initial state, disturbances, and uncertain parameters. First, a probabilistic constrained problem is formulated for the probabilistic ellipsoidal bound computation of discrete-time nonlinear systems. Then, the solution of the original probabilistic constrained problem is approximated by solving a robust convex program with N samples of uncertain variables extracted from the sample space. The feasibility and optimality of the approximate solution are discussed with proofs. For validation, a numerical example is implemented. The results show that the proposed method will have improved performance on feasibility if a slight loss on optimality is permitted.