Towards rigorous robust optimal control via generalized high-order moment expansion - Houska,B; Li,JC; Chachuat,B (Optimal Control Applications & Methods, 2017)
This paper is concerned with the rigorous solution of worst-case robust optimal control problems havingbounded time-varying uncertainty and nonlinear dynamics with affine uncertainty dependence. We proposean algorithm that combines existing uncertainty set-propagation and moment-expansion approaches.Specifically, we consider a high-order moment expansion of the time-varying uncertainty, and we bound theeffect of the infinite-dimensional remainder term on the system state, in a rigorous manner, using ellipsoidalcalculus. We prove that the error introduced by the expansion converges to zero as more moments are added.Moreover, we describe a methodology to construct a conservative, yet more computationally tractable, robustoptimization problem, whose solution values are also shown to converge to those of the original robustoptimal control problem. We illustrate the applicability and accuracy of this approach with the robust time-optimal control of a motorized robot arm.