A novel approach for the numerical investigation of optimal control problems containing multiple delays

作者：Marzban Hamid Reza^*; Pirmoradian Hoda

来源：Optimal Control Applications and Methods, 2018, 39(1): 302-325.

DOI：10.1002/oca.2349

• block-pulse functions
• hybrid functions
• Lagrange interpolating polynomials
• mathematical programming problem
• multidelay systems
• optimal control

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 optimizaion 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.

• 出版日期2018-2