2608004953
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Dynamic-Coding-Based SMC with Multi-Node Protocol under Gilbert-Elliott Channel: An Intelligent Bit-Rate Pre-Allocation Method

  • Pengcheng Zhang,   
  • Zhiru Cao *,   
  • Chen Peng *

Received: 02 Apr 2026 | Revised: 03 Jun 2026 | Accepted: 25 Jul 2026 | Published: 17 Aug 2026

Abstract

This paper is concerned with a dynamic-coding-based sliding mode control and intelligent bit-rate pre-allocation method for networked control systems under Gilbert-Elliott channels. To alleviate limited communication bandwidth and packet-length-dependent packet dropout, a channel-guided multi-node round-robin-like protocol is proposed. This protocol allows the sensor side to utilize previous channel mode information to dynamically determine the number of accessing nodes, thereby effectively preventing a surge in packet dropout probability when network conditions deteriorate. Furthermore, a dynamic quantization encoding-decoding mechanism is designed to encapsulate channel modes, zoomed state to be quantized, and dynamic quantization parameters into a binary packet, while an input-holding strategy at the receiver precisely compensates for potential state losses. Crucially, to maximize steady-state control precision, the minimization of the convergent upper bound is transformed into a mixed-integer programming problem. An intelligent optimization scheme combining the simulated annealing algorithm with linear matrix inequalities is proposed to optimally allocate bit rates among different nodes subject to total bandwidth constraints. Theoretical analysis proves that the closed-loop system achieves exponential ultimate boundedness in mean square and ensures the reachability of the sliding domain. Finally, simulation results verify the effectiveness of the proposed strategy.

References 

  • 1.

    Zou, L.; Wang, Z.; Shen, B.; et al. Encryption-Decryption-Based State Estimation with Multirate Measurements against Eavesdroppers: A Recursive Minimum-Variance Approach. IEEE Trans. Autom. Control 2023, 68, 8111–8118.

  • 2.

    Song, B.; Shang, Z.; Wang, Z. Trajectory tracking control of omni-directional mobile robots: A HOFA-LESO based approach. Robot. Auton. Syst. 2026, 202, 105492.

  • 3.

    Peng, S.; Zhang, Z.; Deng, R.; et al. Localizing False Data Injection Attacks in Smart Grid: A Spectrum-Based Neural Network Approach. IEEE Trans. Smart Grid 2023, 14, 3723–3737.

  • 4.

    Lou, X.; Yang, X.; Sun, J.; et al. Optimization Scheduling Strategy for Coal Railway Integrated Energy Systems. Energies 2025, 18, 4534.

  • 5.

    Li, C.; Liu, Y.; Gao, M.; et al. Fault-tolerant formation consensus control for time-varying multi-agent systems with stochastic communication protocol. Int. J. Netw. Dyn. Intell. 2024, 3, 100004.

  • 6.

    Song, B.; Zhao, S.; Wang, Z.; et al. DAF-DETR: A dynamic adaptation feature transformer for enhanced object detection in unmanned aerial vehicles. Knowl.-Based Syst. 2025, 323, 113760.

  • 7.

    Wang, X.; Sun, Y.; Ding, D. Adaptive Dynamic Programming for Networked Control Systems under Communication Constraints: A Survey of Trends and Techniques. Int. J. Netw. Dyn. Intell. 2022, 1, 85–98.

  • 8.

    Zhang, X.M.; Han, Q.L.; Ge, X. A novel approach to H∞ performance analysis of discrete-time networked systems subject to network-induced delays and malicious packet dropouts. Automatica 2022, 136, 110010.

  • 9.

    Zhang, D.; Han, Q.L.; Zhang, X.M. Network-Based Modeling and Proportional-Integral Control for Direct-Drive-Wheel Systems in Wireless Network Environments. IEEE Trans. Cybern. 2020, 50, 2462–2474.

  • 10.

    Wu, J.; Peng, C.; Zhang, J.; et al. A Sampled-Data-Based Secure Control Approach for Networked Control Systems under Random DoS Attacks. IEEE Trans. Cybern. 2024, 54, 4841–4851.

  • 11.

    Liu, D.; Wang, Z.; Liu, Y.; et al. Recursive State Estimation for Stochastic Complex Networks under Round-Robin Communication Protocol: Handling Packet Disorders. IEEE Trans. Netw. Sci. Eng. 2021, 8, 2455–2467.

  • 12.

    Liu, J.; Gong, E.; Zha, L.; et al. Observer-Based Security Fuzzy Control for Nonlinear Networked Systems under Weighted Try-Once-Discard Protocol. IEEE Trans. Fuzzy Syst. 2023, 31, 3853–3864.

  • 13.

    Zou, L.; Wang, Z.; Hu, J.; et al. On H∞ finite-horizon filtering under stochastic protocol: Dealing with high-rate communication networks. IEEE Trans. Autom. Control 2017, 62, 4884–4890.

  • 14.

    Chen, H.; Wang, Z.; Liang, J.; et al. State Estimation for Stochastic Time-Varying Boolean Networks. IEEE Trans. Autom. Control 2020, 65, 5480–5487.

  • 15.

    Chen, H.; Wang, Z.; Shen, B.; et al. Distributed Recursive Filtering over Sensor Networks with Nonlogarithmic Sensor Resolution. IEEE Trans. Autom. Control 2022, 67, 5408–5415.

  • 16.

    Zhao, H.; Wang, W.; He, W. Dynamic event-triggered sliding mode control for T-S fuzzy switched systems with multi-node stochastic communication protocols. Appl. Math. Comput. 2026, 523, 130024.

  • 17.

    Yang, S.; Caballero-Aguila, R.; Hu, J.; et al. Secure Tobit filtering for multi-rate nonlinear systems under multi-node random access protocol: A Paillier encryption-decryption mechanism. Inf. Fusion 2026, 130, 104146.

  • 18.

    Hu, Y.; Kwon, O.M.; Lee, S.H. H∞ control for interval type-2 fuzzy singularly perturbed systems with multi-node round-robin protocol and packet dropouts. Fuzzy Sets Syst. 2025, 500, 109202.

  • 19.

    Zhang, P.; Kao, Y.; Hu, J.; et al. Robust observer-based sliding mode H∞ control for stochastic Markovian jump systems subject to packet losses. Automatica 2021, 130, 109665.

  • 20.

    Wu, Y.; Zhao, X.; Shen, Z.; et al. Stability Analysis of Connected Vehicle Platoons with Markovian Packet Losses. IEEE Trans. Intell. Transp. Syst. 2025, 26, 3155–3169.

  • 21.

    Ding, D.; Wang, Z.; Han, Q.L.; et al. Recursive Secure Filtering Over Gilbert-Elliott Channels in Sensor Networks: The Distributed Case. IEEE Trans. Signal Inf. Process. Netw. 2021, 7, 75–86.

  • 22.

    Gilbert, E.N. Capacity of a Burst-Noise Channel. Bell Syst. Tech. J. 1960, 39, 1253–1265.

  • 23.

    Song, H.; Chen, S.C.; Yam, Y. Sliding Mode Control for Discrete-Time Systems with Markovian Packet Dropouts. IEEE Trans. Cybern. 2017, 47, 3669–3679.

  • 24.

    Shen, Y.; Wang, Z.; Shen, B.; et al. Nonfragile H∞ filtering for discrete multirate time-delayed systems over sensor networks characterized by Gilbert-Elliott models. Int. J. Robust Nonlinear Control 2020, 30, 3194–3214.

  • 25.

    Brockett, R.W.; Liberzon, D. Quantized Feedback Stabilization of Linear Systems. IEEE Trans. Autom. Control 2000, 45, 1279–1289.

  • 26.

    Kang, X.; Ishii, H. Coarsest quantization for networked control of uncertain linear systems. Automatica 2015, 51, 1–8.

  • 27.

    Yan, Y.; Yu, S.; Yu, X. Quantized super-twisting algorithm based sliding mode control. Automatica 2019, 105, 43–48.

  • 28.

    Li, J.; Niu, Y.; Ho, D.W.C. Limited Coding-Length-Based Sliding-Mode Control with Adaptive Quantizer’s Parameter. IEEE Trans. Autom. Control 2022, 67, 6248–6255.

  • 29.

    Zhou, S.; Song, J.; Lam, H.K.; et al. Coding-Decoding-Based Sliding Mode Control for Markovian Jump Systems under Constrained Bit Rate: An Adaptive Quantizer Approach. IEEE Trans. Control Netw. Syst. 2024, 11, 255–269.

  • 30.

    Li, J.; Niu, Y.; Ho, D.W.C. Dynamic Coding-Based Control Scheme under Lossy Digital Network: An Optimized Time-Varying Packet Length Approach. IEEE Trans. Cybern. 2024, 54, 2955–2965.

  • 31.

    Zhou, W.; Wang, Y.; Liang, Y. Sliding mode control for networked control systems: A brief survey. ISA Trans. 2022, 124, 249–259.

  • 32.

    Liu, X.; Ling, Z.; Zhang, Y. Torus-Event-Based Sliding Mode Control for Networked Interval Type-2 Fuzzy Systems under Deception Attacks. Int. J. Netw. Dyn. Intell. 2025, 4, 100003.

  • 33.

    Zhang, M.; Ding, D.; Shen, B.; et al. Integral Sliding Mode Control for Automated Vehicles under Coding-Decoding Mechanisms with Constrained Bit Rate. IEEE Internet Things J. 2025, 12, 16214–16226.

  • 34.

    Zhang, H.; Yang, S.; Song, J.; et al. Sliding Mode Control for Persistent Dwell-Time Switched System under Multi-Node Round-Robin Protocol and Replay Attacks. Int. J. Robust Nonlinear Control 2026, 36, 4760–4774.

  • 35.

    Xu, J.; Niu, Y. Sliding mode consensus control for multi-agent systems under multi-node round-robin protocol. Franklin Open 2023, 5, 100052.

  • 36.

    Zhang, P.; Cao, Z.; Peng, C.; et al. Dynamic-Coding-Based Sliding Mode Control under Gilbert-Elliott Networks with FlexRay Protocol: The High-Rate Case. IEEE Internet Things J. 2026, 13, 12051–12063.

  • 37.

    Cao, Z.; Niu, Y.; Peng, C. Finite-Time Stabilization of Uncertain Markovian Jump Systems: An Adaptive Gain-Scheduling Control Method. IEEE Trans. Autom. Control 2024, 69, 3531–3543.

  • 38.

    Lou, H.; Jiang, B.; Kao, Y.; et al. A GA-based dynamic event-triggered adaptive sliding mode control of networked Markov jump systems. Nonlinear Dyn. 2025, 113, 18453–18468.

  • 39.

    Zhang, L.; Jiang, Y.; Chen, G.; et al. Heading control of variable configuration unmanned ground vehicle using PID-type sliding mode control and steering control based on particle swarm optimization. Nonlinear Dyn. 2023, 111, 3359–3376.

  • 40.

    Vijay, D.; Jayashree, R. Sliding Mode Controller Based on Genetic Algorithm and Simulated Annealing for Assured Crew Reentry Vehicle. J. Aerosp. Eng. 2023, 36, 04023039.

  • 41.

    Ke, H.; Yang, Y.; Xu, Y.; et al. Simulated Annealing-Driven Event-Triggered Neural Sliding Mode Control for Networked Nonlinear Markov Jump Systems. Electronics 2026, 15, 1220.

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How to Cite
Zhang, P.; Cao, Z.; Peng, C. Dynamic-Coding-Based SMC with Multi-Node Protocol under Gilbert-Elliott Channel: An Intelligent Bit-Rate Pre-Allocation Method. International Journal of Network Dynamics and Intelligence 2026, 5 (3), 18. https://doi.org/10.53941/ijndi.2026.100018.
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