Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Nonlinear Programming Methods

Abstract

We discuss nonlinear programming (NLP) methods for solving optimal control problems with control and state inequality constraints. Suitable discretizations of control and state variables are used to transform the optimal control into a finite dimensional NLP problem. In [8] we have proposed numerical methods for the post-optimal calculations of parameter sensitivity derivatives of optimal solutions to NLP problems. The purpose of this paper is to extend the methods of post-optimal sensitivity analysis and real-time optimization to discretized control problems. The dimension of the discretized control problem should be kept small to obtain accurate sensitivity results. This can be achieved by taking only the discretized control variables as optimization variables whereas the state variables are computed recursively through an appropriate integration routine. We discuss the implications of this approach for the calculations of parameter sensitivity derivatives with respect to optimal control, state and adjoint functions. The efficiency of the proposed methods are illustrated by two numerical examples.