Sample-Based Continuous Approximation for Computing Probabilistic Boundary of Future State Trajectory in Uncertain Dynamical Systems

Xun Shen

Abstract: The probabilistic boundary is necessary for robust control design in uncertain dynamical systems. The problem of computing the tightest ellipsoidal boundary of the future trajectory with a given probability is intractable. This paper proposes a sample-based continuous approximation of the original problem. The approximate problem is solvable by a general nonlinear programming algorithm. We prove that the approximate problem's optimal solution and objective value converge to those of the original problem. The feasibility of the approximate solution by finite samples is also investigated. A numerical example has been implemented to compare the proposed and existing methods. The results show that the proposed method increases the approximate solution's robustness and reduces the computational complexity to obtain the approximate solution.