Adaptive learning nonsynchronous control of nonlinear hidden Markov jump systems with limited mode information

Chao Ma; Hang Gao; Wei Wu; Chao Ma; Hang Gao; Wei Wu

doi:10.3934/era.2023340

Electronic Research Archive

2023, Volume 31, Issue 11: 6746-6762. doi: 10.3934/era.2023340

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Research article

Adaptive learning nonsynchronous control of nonlinear hidden Markov jump systems with limited mode information

Chao Ma ^1,2,
Hang Gao ¹,
Wei Wu ^{2
,
,}

1.
School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China
2.
State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China

Academic Editor: Bin Liu

Received: 14 May 2023 Revised: 14 September 2023 Accepted: 25 September 2023 Published: 19 October 2023

In this paper, an adaptive neural network learning based nonsynchronous control method is developed for hidden Markov jump systems with unmodeled nonlinear dynamics. In particular, the system modes are not directly accessible and the limited mode information can be partly estimated by the nonsynchronous controller. More precisely, the mode information with partly accessible transition rates is utilized based on the transition probability matrix. Moreover, the unmodeled nonlinear dynamics are more general in practical applications. Based on the designed mode-dependent controllers with mode observation, sufficient conditions are first exploited by means of the Lyapunov method, such that the desired control performance could be ensured in the mean-square sense. Then, the nonsynchronous mode-dependent controllers are further determined in terms of convex optimization. In the end, our proposed control strategy is applied to a robotic manipulator with varying loads to validate the feasibility with simulation results.
- adaptive control,
- nonsynchronous control,
- hidden Markov jump system,
- limited mode information
Citation: Chao Ma, Hang Gao, Wei Wu. Adaptive learning nonsynchronous control of nonlinear hidden Markov jump systems with limited mode information[J]. Electronic Research Archive, 2023, 31(11): 6746-6762. doi: 10.3934/era.2023340

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Abstract

In this paper, an adaptive neural network learning based nonsynchronous control method is developed for hidden Markov jump systems with unmodeled nonlinear dynamics. In particular, the system modes are not directly accessible and the limited mode information can be partly estimated by the nonsynchronous controller. More precisely, the mode information with partly accessible transition rates is utilized based on the transition probability matrix. Moreover, the unmodeled nonlinear dynamics are more general in practical applications. Based on the designed mode-dependent controllers with mode observation, sufficient conditions are first exploited by means of the Lyapunov method, such that the desired control performance could be ensured in the mean-square sense. Then, the nonsynchronous mode-dependent controllers are further determined in terms of convex optimization. In the end, our proposed control strategy is applied to a robotic manipulator with varying loads to validate the feasibility with simulation results.

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