A novel approach for the numerical investigation of optimal control problems containing multiple delays. (20th July 2017)

• Record Type: Journal Article
• Authors: Marzban, Hamid Reza; Pirmoradian, Hoda
• Is Part Of: Optimal control applications and methods. Volume 39:Number 1(2018)
• Page Start: 302
• Page End: 325
• Publication Date: 2017-07-20
• Subjects: block‐pulse functions -- hybrid functions -- Lagrange interpolating polynomials -- mathematical programming problem -- multidelay systems -- optimal control; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2349
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: This paper deals with the numerical solution of optimal control problems with multiple delays in both state and control variables. A direct approach based on a hybrid of block‐pulse functions and Lagrange interpolating polynomials is used to convert the original problem into a mathematical programming one. The resulting optimization problem is then solved numerically by the Lagrange multipliers method. The operational matrix of delay for the presented framework is derived. This matrix plays an imperative role to transfer information between 2 consecutive switching points. Furthermore, 2 upper bounds on the error with respect to the L 2 ‐norm and infinity norm are established. Several optimal control problems containing multiple delays are carried out to illustrate the various aspects of the proposed approach. The simulation results are compared with either analytical or numerical solutions available in the literature.