Numerical solution of free final time fractional optimal control problems

• Published in: Applied mathematics and computation Vol. 405; p. 126270
• Main Authors: Gong, Zhaohua, Liu, Chongyang, Teo, Kok Lay, Wang, Song, Wu, Yonghong
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.09.2021
• Subjects: Constrained optimal control; Fractional-order system; Free final time; Numerical optimization; Time-scaling transformation; Constrained optimal control; Fractional-order system; Numerical optimization; Free final time; Time-scaling transformation
• ISSN: 0096-3003
• DOI: 10.1016/j.amc.2021.126270

•A constrained fractional optimal control problem with free terminal time is considered.•The problem is transformed based on time-scaling transformation and numerical integration scheme.•A novel gradient-based optimization is developed to solve the transformed optimization problem. The main purpose of this work is to develop a numerical solution method for solving a class of nonlinear free final time fractional optimal control problems. This problem is subject to equality and inequality constraints in canonical forms, and the orders in the fractional system can be different. For this problem, we first show that, by a time-scaling transformation, the problem can be transformed into an equivalent fractional optimal control problem with fixed final time. We then discretize the transformed fractional optimal control problem by a second-order one-point numerical integration scheme and the trapezoidal rule. Furthermore, we derive the gradient formulae of the cost and constraint functions with respect to decision variables and propose a numerical procedure for calculating these gradients. On this basis, a gradient-based optimization algorithm is developed for solving the resulting problem. Finally, numerical simulations of three example problems illustrate the effectiveness of the developed algorithm.