A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations

Abstract

In this paper a class of optimal control problems with distributed parameters is considered. The governing equations are nonlinear first order partial differential equations that arise in the study of heterogeneous reactors and control of chemical processes. The main focus of the present paper is the mathematical theory underlying the algorithm. A conditional gradient method is used to devise an algorithm for solving such optimal control problems. A formula for the Frgchet derivative of the objective function is obtained, and its properties are studied. A necessary condition for optimality in terms of the Fr6chet derivative is presented, and then it is shown that any accumulation point of the sequence of admissible controls generated by the algorithm satisfies this necessary condition for optimality.

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter System

“…9 Kazemi obtained adjoint equations for a degenerate hyperbolic equation. 10 Adjoint method is well-known in optimal control and optimization theories as it provides an indirect method for solving optimization problems. For a transport system governed by hyperbolic equations, two types of adjoint formulation are used: discrete adjoint and continuous adjoint.…”