Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays

This paper considers an optimal control problem governed by nonlinear fractional-order systems with multiple time-varying delays and subject to canonical constraints, where the fractional-order derivatives are expressed in the Caputo sense. To solve the problem by discretization scheme, an explicit...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 193; no. 1-3; pp. 856 - 876
Main Authors: Liu, Chongyang, Gong, Zhaohua, Teo, Kok Lay, Wang, Song
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2022
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Approximation
Boundary value problems
Calculus of Variations and Optimal Control; Optimization
Control systems
Discretization
Engineering
Fractional calculus
Functionally gradient materials
Functionals
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear control
Nonlinear systems
Numerical integration
Operations Research/Decision Theory
Optimal control
Optimization
Optimization algorithms
Optimization techniques
Theory of Computation
Time varying control
Time-varying delay
Optimal control
Gradient computation
90C55
34K37
Fractional-order system
49M37
Discretization scheme
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:This paper considers an optimal control problem governed by nonlinear fractional-order systems with multiple time-varying delays and subject to canonical constraints, where the fractional-order derivatives are expressed in the Caputo sense. To solve the problem by discretization scheme, an explicit numerical integration technique is proposed for solving the fractional-order system, and the trapezoidal rule is introduced to approximate the cost functional. Then, the gradients of the resulting cost and constraint functions are derived. On the basis of this result, we develop a gradient-based optimization algorithm to numerically solve the discretized problem. Finally, numerical results of several non-trivial examples are provided to illustrate the applicability and effectiveness of the proposed algorithm.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-021-01935-7