A NUMERICAL ALGORITHM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS

Abstract

In this paper, we consider a general class of discrete-time optimal control problems subject to all-time-step constraints on the state and control variables. The derivations of the gradient formulas for the cost and constraint functions for this constrained discrete-time optimal control problem are rather involved. We present a simple approach to the derivations of these gradient formulas based on reversed automatic differentiation. On this basis, a numeri- cal algorithm is developed to solve this all-time-step constrained discrete-time optimal control problem. We then consider a class of continuous-time optimal control problems subject to continuous state inequality constraints. This con- strained continuous-time optimal control problem is discretized into a discrete- time optimal control problem with all-time-step constraints using the Euler discretization method. Then, the algorithm developed for constrained discrete- time optimal control problem is applied to solve this discretized optimal control problem. Numerical examples are presented to verify the applicability of the proposed methods.