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Volume 9 Issue 3
Mar.  2022

IEEE/CAA Journal of Automatica Sinica

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L. N. Xia, Q. Li, R. Z. Song, and H. Modares, “Optimal synchronization control of heterogeneous asymmetric input-constrained unknown nonlinear MASs via reinforcement learning,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 3, pp. 520–532, Mar. 2022. doi: 10.1109/JAS.2021.1004359
Citation: L. N. Xia, Q. Li, R. Z. Song, and H. Modares, “Optimal synchronization control of heterogeneous asymmetric input-constrained unknown nonlinear MASs via reinforcement learning,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 3, pp. 520–532, Mar. 2022. doi: 10.1109/JAS.2021.1004359

Optimal Synchronization Control of Heterogeneous Asymmetric Input-Constrained Unknown Nonlinear MASs via Reinforcement Learning

doi: 10.1109/JAS.2021.1004359
Funds:  This work was supported in part by the National Natural Science Foundation of China (61873300, 61722312), the Fundamental Research Funds for the Central Universities (FRF-MP-20-11), and Interdisciplinary Research Project for Young Teachers of University of Science and Technology Beijing (Fundamental Research Funds for the Central Universities) (FRFIDRY-20-030)
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  • The asymmetric input-constrained optimal synchronization problem of heterogeneous unknown nonlinear multiagent systems (MASs) is considered in the paper. Intuitively, a state-space transformation is performed such that satisfaction of symmetric input constraints for the transformed system guarantees satisfaction of asymmetric input constraints for the original system. Then, considering that the leader’s information is not available to every follower, a novel distributed observer is designed to estimate the leader’s state using only exchange of information among neighboring followers. After that, a network of augmented systems is constructed by combining observers and followers dynamics. A nonquadratic cost function is then leveraged for each augmented system (agent) for which its optimization satisfies input constraints and its corresponding constrained Hamilton-Jacobi-Bellman (HJB) equation is solved in a data-based fashion. More specifically, a data-based off-policy reinforcement learning (RL) algorithm is presented to learn the solution to the constrained HJB equation without requiring the complete knowledge of the agents’ dynamics. Convergence of the improved RL algorithm to the solution to the constrained HJB equation is also demonstrated. Finally, the correctness and validity of the theoretical results are demonstrated by a simulation example.

     

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    Highlights

    • A state space transformation method is presented to solve the optimal synchronization control problem for heterogeneous nonlinear MASs with asymmetric input constraints. In addition, it implies that the symmetric input constraints in relevant work can be regarded as a special case of our research work
    • An improved data-based RL algorithm is employed to learn the solution to the non-quadratic HJB equations without requiring system’s dynamics information
    • To implement this algorithm, the critic NN and the actor factor NN are established respectively to estimate the cost function and the control policy for agents, such that input constraint is encoded into the framework of the proposed algorithm

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