Optimal Control for Fractional-Order Nonlinear Systems Using Fractional-Order Online Policy Iteration

In this paper, a fractional-order online policy iteration (FOOPI)-based optimal control strategy is developed for a class of fractional-order nonlinear systems (FONSs). The fractional Taylor expansion and the property of Hadamard product are utilized to derive the fractional Hamilton-Jacobi-Bellman...

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Bibliographic Details
Published in2024 43rd Chinese Control Conference (CCC) pp. 2558 - 2563
Main Authors Kong, Jie, Zhao, Bo
Format Conference Proceeding
LanguageEnglish
Published Technical Committee on Control Theory, Chinese Association of Automation 28.07.2024
Subjects
Adaptive dynamic programming
Approximation algorithms
Artificial neural networks
Cost function
fractional-order nonlinear systems
Heuristic algorithms
neural networks
Optimal control
reinforcement learning
Simulation
Taylor series
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Summary:In this paper, a fractional-order online policy iteration (FOOPI)-based optimal control strategy is developed for a class of fractional-order nonlinear systems (FONSs). The fractional Taylor expansion and the property of Hadamard product are utilized to derive the fractional Hamilton-Jacobi-Bellman equation, which is solved by a FOOPI method consisting of policy evaluation and policy improvement. Through constructing a critic neural network (NN), whose weight vector is adjusted by the gradient descent algorithm, the cost function and the fractional control policy are obtained approximately. Then, the state trajectories of closed-loop FONSs and the critic NN weight vector approximation error dynamics are guaranteed to be uniformly ultimately bounded. Simulation results illustrate the effectiveness of the presented fractional optimal control scheme.
ISSN:1934-1768
DOI:10.23919/CCC63176.2024.10662444