Abstract
This paper is focused on a distributed optimal control design for a class of nonlinear time-delay systems with delayed measurements and communication disruptions. The innovation lies in three aspects. The distributed optimal control method which includes an optimal controller and a bounded controller is designed based on Lyapunov function. The availability of data transmitted through the communication channel depends on a feasibility problem. And a sufficient condition to guarantee ultimate boundedness of the system is given based on appropriate assumptions. The significance of this paper is that this distributed optimal control method is applied to time-delay system. Finally, a simulation example is given to verify the effectiveness of the proposed method.
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References
Bao L P, Fei S M, and Yu L, Exponential stability of linear distributed parameter switched systems with time-delay, Journal of Systems Science and Complexity, 2014, 27(2): 263–275.
Sun W, Yuan W X, Shao Y, et al., Adaptive fuzzy control of strict-feedback nonlinear time-delay systems with full-state constraints, International Journal of Fuzzy Systems, 2018, 20(8): 2556–2565.
Teng L, Wang Y Y, Cai W J, et al., Efficient robust fuzzy model predictive control of discrete nonlinear time-delay systems via Razumikhin approach, IEEE Transactions on Fuzzy Systems, 2019, 27(2): 262–272.
Li J Y, Zhang L, and Wang Z H, Two effective stability criteria for linear time-delay systems with complex coefficients, Journal of Systems Science and Complexity, 2011, 24(5): 835–849.
He Y, Sun X M, Liu J, et al., Stability analysis for homogeneous hybrid systems with delays, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, DOI: https://doi.org/10.1109/TSMC.2018.2872045.
Sun Z Y, Liu Y G, and Xie X J, Global stabilization for a class of high-order time-delay nonlinear systems, International Journal of Innovative Computing Information and Control, 2019, 7(12): 7119–7130.
Mayne D Q, Model predictive control: Recent developments and future promise, Automatica, 2014, 50: 2967–2986.
Ma Z X, Zhang X, Huang J J, et al., Stability-constraining-dichotomy-solution-based model predictive control to improve the stability of power conversion system in the MEA, IEEE Transactions on Industrial Electronics, 2019, 66(7): 5696–5706.
Wu S and Shu L, Maximum principle for partially-observed optimal control problems of stochastic delay systems, Journal of Systems Science and Complexity, 2017, 30(2): 316–328.
Song Y, Wang Z D, Ding D, et al., Robust model predictive control for linear systems with polytopic uncertainties under weighted MEF-TOD protocol, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 7(49): 1470–1481.
Lima P F, Pereira goncalo collares and martensson jonas, experimental validation of model predictive control stability for autonomous driving, Control Engineering Practice, 2018, 81: 244–255.
Liu X H and Han C Y, Rubust model predictive control of continuous uncertain systems, Journal of Systems Science and Complexity, 2008, 21(2): 267–275.
Mazen A, Stability proof for nonlinear MPC design using monotonically increasing weighting profiles without terminal constraints, Automatica, 2018, 87(1): 455–459.
Ma X, Qi Q Y, and Zhang H S, Optimal output feedback control and stabilization for NCSs with packet dropout and delay: TCP Case, Journal of Systems Science and Complexity, 2018, 31(1): 147–160.
Heidarinejad M, Liu J F, and Christofides P D, Economic model predictive control of switched nonlinear systems, Systems and Control Letters, 2013, 62(1): 77–84.
Liu J F, David Muñoz de la Peña, and Christofides P D, Distributed model predictive control of nonlinear process systems, American Institute of Chemical Engineers Journal, 2009, 55: 1171–1184.
Liu J F, David Muñoz de la Peña, and Christofides P D, Distributed model predictive control of nonlinear systems subject to asynchronous and delayed measurements, Automatica, 2010, 46: 52–61.
Heidarinejad M, Liu J F, David Muñoz de la Peña, Davis J F, et al., Handling communication disruptions in distributed model predictive control, Journal of Process Control, 2011, 21: 173–181.
Heidarinejad M, Liu J F, and Christofides P D, Distributed model predictive control of switched nonlinear systems, American Control Conference, 2012, 3198–3203.
Frédéric M and Silviu-Iulian N, Lyapunov stability analysis for nonlinear delay systems, Systems and Control Letters, 2001, 42: 245–251.
Su B L and Chunyu D D, Finite-time optimization stabilization for a class of constrained switched nonlinear systems, Mathematical Problems in Engineering, 2018, DOI: https://doi.org/10.1155/2018/6824803.
Su B L, Li S Y, and Zhu Q M, The design of predictive control with characterized set of initial condition for constrained switched nonlinear system, Science in China Series E: Technological Sciences, 2009, 52(2): 456–466.
Song Y, Hu J, Chen D Y, et al., Recursive approach to networked fault estimation with packet dropouts and randomly occurring uncertainties, Neurocomputing, 2016, 214(19): 340–349.
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This paper was supported by the National Natural Science Foundation of China under Grant Nos. 61374004, 61773237, 61473170 and Rizhao Science and Technology Innovation Special Plan (2019cxzx2212).
This paper was recommended for publication by Editor SUN Jian.
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Su, B., Duan, Y. Distributed Optimal Control of Nonlinear Time-Delay System Subject to Delayed Measurements and Communication Disruptions. J Syst Sci Complex 34, 1426–1437 (2021). https://doi.org/10.1007/s11424-020-9302-x
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DOI: https://doi.org/10.1007/s11424-020-9302-x