A multiobjective dynamic programming approach to constrained discrete-time optimal control

• Published in: Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207) Vol. 5; pp. 3077 - 3083 vol.5
• Main Authors: Driessen, B.J., Kwok, K.S.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 1998
• Subjects: Convergence of numerical methods; Cost function; Dynamic programming; Heuristic algorithms; History; Iterative algorithms; Laboratories; Linear matrix inequalities; Optimal control; Time factors
• ISBN: 0780345304; 9780780345300
• ISSN: 0743-1619
• DOI: 10.1109/ACC.1998.688424

This paper presents a multiobjective differential dynamic programming approach to constrained discrete-time optimal control. In the backward sweep of the dynamic programming in the quadratic sub-problem, the sub-problem input at a stage or time step is solved in terms of the sub-problem state entering that stage so as to minimize the summed immediate and future cost subject to minimizing the summed immediate and future constraint violations, for all such entering states. The method differs from previous dynamic programming methods, which used penalty methods, in that the constraints of the sub-problem, which may include terminal constraints and path constraints, are solved exactly if they are solvable; otherwise, their total violation is minimized. Again, the resulting solution of the sub-problem is an input history that minimizes the quadratic cost function subject to being a minimizer of the total constraint violation. The expected quadratic convergence of the proposed algorithm is demonstrated on a numerical example.