Multiple-interval pseudospectral approximation for nonlinear optimal control problems with time-varying delays

• Published in: Applied Mathematical Modelling Vol. 68; pp. 137 - 151
• Main Authors: Tang, Xiaojun, Xu, Heyong
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.04.2019; Elsevier BV
• Subjects: Control theory; Delay; Domain decomposition methods; Economic models; Graphs; Nonlinear control; Nonlinear time-delay systems; Optimal control; Pseudospectral methods; Pseudospectral methods; Nonlinear time-delay systems; Optimal control
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2018.09.039

•A multiple-interval pseudospectral scheme is developed for solving nonlinear optimal control problems with time-varying delays.•The size of mesh intervals in the multiple-interval approach can be various and the location of mesh points can be placed freely.•A novel and smart approach is presented for computing the values of state delay efficiently and stably. A multiple-interval pseudospectral scheme is developed for solving nonlinear optimal control problems with time-varying delays, which employs collocation at the shifted flipped Jacobi-Gauss–Radau points. The new pseudospectral scheme has the following distinctive features/abilities: (i) it can directly and flexibly solve nonlinear optimal control problems with time-varying delays without the tedious quasilinearization procedure and the uniform mesh restriction on time domain decomposition, and (ii) it provides a smart approach to compute the values of state delay efficiently and stably, and a unified framework for solving standard and delay optimal control problems. Numerical results on benchmark delay optimal control problems including challenging practical engineering problems demonstrate that the proposed pseudospectral scheme is highly accurate, efficient and flexible.