Numerical solution of free final time fractional optimal control problems

•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...

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Veröffentlicht in:Applied mathematics and computation Jg. 405; S. 126270
Hauptverfasser: Gong, Zhaohua, Liu, Chongyang, Teo, Kok Lay, Wang, Song, Wu, Yonghong
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.09.2021
Schlagworte:
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
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Zusammenfassung:•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.
ISSN:0096-3003
DOI:10.1016/j.amc.2021.126270