Consistent approximation of a nonlinear optimal control problem with uncertain parameters

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 aswell 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-evadingmoving 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 PontryaginMinimumPrinciple type,which facilitates assessment of the optimality of numerical solutions. © 2014 Elsevier Ltd. All rights reserved.