Optimal Control Computation for Nonlinear Fractional Time-Delay Systems with State Inequality Constraints

In this paper, a numerical method is developed for solving a class of delay fractional optimal control problems involving nonlinear time-delay systems and subject to state inequality constraints. The fractional derivatives in this class of problems are described in the sense of Caputo, and they can...

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Vydáno v:Journal of optimization theory and applications Ročník 191; číslo 1; s. 83 - 117
Hlavní autoři: Liu, Chongyang, Gong, Zhaohua, Yu, Changjun, Wang, Song, Teo, Kok Lay
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.10.2021
Springer Nature B.V
Témata:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Computation
Control systems
Engineering
Inequality
Integral equations
Interpolation
Mathematics
Mathematics and Statistics
Methods
Nonlinear control
Nonlinear systems
Numerical analysis
Numerical integration
Numerical methods
Operations Research/Decision Theory
Optimization
Optimization techniques
Taylor series
Theory of Computation
Time delay systems
Time optimal control
Fractional optimal control
Numerical integration
Numerical optimization
90C55
Inequality constraint
34K37
49M37
Fractional time-delay system
ISSN:0022-3239, 1573-2878
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Shrnutí:In this paper, a numerical method is developed for solving a class of delay fractional optimal control problems involving nonlinear time-delay systems and subject to state inequality constraints. The fractional derivatives in this class of problems are described in the sense of Caputo, and they can be of different orders. First, we propose a numerical integration scheme for the fractional time-delay system and prove that the convergence rate of the numerical solution to the exact one is of second order based on Taylor expansion and linear interpolation. This gives rise to a discrete-time optimal control problem. Then, we derive the gradient formulas of the cost and constraint functions with respect to the decision variables and present a gradient computation procedure. On this basis, a gradient-based optimization algorithm is developed to solve the resulting discrete-time optimal control problem. Finally, several example problems are solved to demonstrate the effectiveness of the developed solution approach.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-021-01926-8