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On Stability of Perturbed Nonlinear Switched Systems with Adaptive Reinforcement Learning

Author

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  • Phuong Nam Dao

    (Department of Automatic Control, Hanoi University of Science and Technology, 1 Dai Co Viet Road, Hanoi 100000, Vietnam)

  • Hong Quang Nguyen

    (Department of Automation, Thai Nguyen University of Technology, 666, 3/2 Street, Tich Luong Ward, Thai Nguyen City 251750, Vietnam)

  • Minh-Duc Ngo

    (Department of Automation, Thai Nguyen University of Technology, 666, 3/2 Street, Tich Luong Ward, Thai Nguyen City 251750, Vietnam)

  • Seon-Ju Ahn

    (Department of Electrical Engineering, Chonnam National University, Gwangju 61186, Korea)

Abstract

In this paper, a tracking control approach is developed based on an adaptive reinforcement learning algorithm with a bounded cost function for perturbed nonlinear switched systems, which represent a useful framework for modelling these converters, such as DC–DC converter, multi-level converter, etc. An optimal control method is derived for nominal systems to solve the tracking control problem, which results in solving a Hamilton–Jacobi–Bellman (HJB) equation. It is shown that the optimal controller obtained by solving the HJB equation can stabilize the perturbed nonlinear switched systems. To develop a solution to the translated HJB equation, the proposed neural networks consider the training technique obtaining the minimization of square of Bellman residual error in critic term due to the description of Hamilton function. Theoretical analysis shows that all the closed-loop system signals are uniformly ultimately bounded (UUB) and the proposed controller converges to optimal control law. The simulation results of two situations demonstrate the effectiveness of the proposed controller.

Suggested Citation

  • Phuong Nam Dao & Hong Quang Nguyen & Minh-Duc Ngo & Seon-Ju Ahn, 2020. "On Stability of Perturbed Nonlinear Switched Systems with Adaptive Reinforcement Learning," Energies, MDPI, vol. 13(19), pages 1-19, September.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:19:p:5069-:d:420484
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    References listed on IDEAS

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    1. Abualkasim Bakeer & Andrii Chub & Dmitri Vinnikov, 2020. "Step-Up Series Resonant DC–DC Converter with Bidirectional-Switch-Based Boost Rectifier for Wide Input Voltage Range Photovoltaic Applications," Energies, MDPI, vol. 13(14), pages 1-14, July.
    2. Manoharan Premkumar & Umashankar Subramaniam & Hassan Haes Alhelou & Pierluigi Siano, 2020. "Design and Development of Non-Isolated Modified SEPIC DC-DC Converter Topology for High-Step-Up Applications: Investigation and Hardware Implementation," Energies, MDPI, vol. 13(15), pages 1-27, August.
    3. Hermes Loschi & Robert Smolenski & Piotr Lezynski & Douglas Nascimento & Galina Demidova, 2020. "Aggregated Conducted Electromagnetic Interference Generated by DC/DC Converters with Deterministic and Random Modulation," Energies, MDPI, vol. 13(14), pages 1-9, July.
    4. Oleksandr Korkh & Andrei Blinov & Dmitri Vinnikov & Andrii Chub, 2020. "Review of Isolated Matrix Inverters: Topologies, Modulation Methods and Applications," Energies, MDPI, vol. 13(9), pages 1-30, May.
    5. Bi-Ying Chen & Xing-Chen Shangguan & Li Jin & Dan-Yun Li, 2020. "An Improved Stability Criterion for Load Frequency Control of Power Systems with Time-Varying Delays," Energies, MDPI, vol. 13(8), pages 1-14, April.
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