Consistent approximation of a nonlinear optimal control problem with uncertain parameters |
| |
Affiliation: | 1. Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA, United States;2. Department of Operations Research, Naval Postgraduate School, Monterey, CA, United States;3. Department of Mechanical and Astronautical Engineering, Naval Postgraduate School, Monterey, CA, United States;1. Faculty of Sciences and Technology, University Abbes Laghrour Khenchela, Algeria;2. University of Picardie Jules Verne, MIS (EA 4029), 33 rue Saint-Leu, 80039 Amiens, France;3. Department of Engineering, Faculty of Engineering and Science, University of Agder, N-4898 Grimstad, Norway |
| |
Abstract: | This paper focuses on a non-standard constrained nonlinear optimal control problem in which the objective functional involves an integration over a space of stochastic parameters as well as an integration over the time domain. The research is inspired by the problem of optimizing the trajectories of multiple searchers attempting to detect non-evading moving targets. In this paper, we propose a framework based on the approximation of the integral in the parameter space for the considered uncertain optimal control problem. The framework is proved to produce a zeroth-order consistent approximation in the sense that accumulation points of a sequence of optimal solutions to the approximate problem are optimal solutions of the original problem. In addition, we demonstrate the convergence of the corresponding adjoint variables. The accumulation points of a sequence of optimal state-adjoint pairs for the approximate problem satisfy a necessary condition of Pontryagin Minimum Principle type, which facilitates assessment of the optimality of numerical solutions. |
| |
Keywords: | Optimal control Computational methods Optimization Nonlinear system Search theory |
本文献已被 ScienceDirect 等数据库收录! |
|