SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control

• Published in: Journal of computational and applied mathematics Vol. 120; no. 1; pp. 85 - 108
• Main Authors: Büskens, Christof, Maurer, Helmut
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2000
• Subjects: Adjoint variables; Control-state constraints; Nonlinear programming methods; Optimal control problems; Real-time control; Second-order sufficient conditions; Sensitivity analysis; Control-state constraints; Sensitivity analysis; Optimal control problems; Second-order sufficient conditions; Adjoint variables; Real-time control; Nonlinear programming methods
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/S0377-0427(00)00305-8

Parametric nonlinear optimal control problems subject to control and state constraints are studied. Two discretization methods are discussed that transcribe optimal control problems into nonlinear programming problems for which SQP-methods provide efficient solution methods. It is shown that SQP-methods can be used also for a check of second-order sufficient conditions and for a postoptimal calculation of adjoint variables. In addition, SQP-methods lead to a robust computation of sensitivity differentials of optimal solutions with respect to perturbation parameters. Numerical sensitivity analysis is the basis for real-time control approximations of perturbed solutions which are obtained by evaluating a first-order Taylor expansion with respect to the parameter. The proposed numerical methods are illustrated by the optimal control of a low-thrust satellite transfer to geosynchronous orbit and a complex control problem from aquanautics. The examples illustrate the robustness, accuracy and efficiency of the proposed numerical algorithms.