Premium
A novel approach for the numerical investigation of optimal control problems containing multiple delays
Author(s) -
Marzban Hamid Reza,
Pirmoradian Hoda
Publication year - 2017
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2349
Subject(s) - lagrange multiplier , optimal control , mathematical optimization , mathematics , norm (philosophy) , lagrange polynomial , h infinity methods in control theory , state (computer science) , computer science , control (management) , control theory (sociology) , polynomial , algorithm , mathematical analysis , artificial intelligence , political science , law
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.