Set-Membership Estimation for T–S Fuzzy Complex Networks: A Dynamic Coding-Decoding Mechanism

Computer Science Information Science Engineering Electrical Engineering Artificial Intelligence
T-S fuzzy complex networks set-membership estimation dynamic coding-decoding mechanism optimization algorithm network communication state estimation unknown but bounded noise

Academic Background

In today’s complex network systems, state estimation is a critical issue, especially when dealing with uncertainties and noise. Complex networks typically consist of multiple interconnected nodes, and the dynamic behavior of each node may be influenced by nonlinear factors. The Takagi-Sugeno (T-S) fuzzy model has demonstrated significant advantages in modeling complex networks due to its ability to effectively capture uncertain information and describe the nonlinear dynamic characteristics of complex networks. However, traditional state estimation methods usually require detailed statistical properties of noise, whereas in practical applications, noise is often unknown but bounded (UBB). The set-membership estimation (SME) method offers a new solution in such scenarios, providing deterministic error bounds without precise noise statistical information.

This study aims to explore the set-membership estimation problem for T-S fuzzy complex networks (TSFCNs) under unknown but bounded noise conditions and proposes a dynamic coding-decoding mechanism (CDM) to optimize data transmission and the robustness of state estimation.

Source of the Paper

This paper was co-authored by Changzhen Hu, Sanbo Ding, and Nannan Rong from the School of Artificial Intelligence at Hebei University of Technology and Tiangong University, respectively. The paper was accepted by the journal Nonlinear Dynamics on February 18, 2025, and published by Springer Nature in 2025.

Research Process and Results

1. Research Process

a) T-S Fuzzy Complex Network Modeling

The study first constructs a T-S fuzzy complex network model, which consists of multiple coupled nodes. The dynamic behavior of each node is described through a set of fuzzy rules based on the premise variables and fuzzy sets of the system states. The process noise and measurement noise in the model are assumed to be unknown but bounded and are constrained by ellipsoidal sets.

b) Design of the Dynamic Coding-Decoding Mechanism

To optimize data transmission, the study proposes a dynamic coding-decoding mechanism that introduces a dynamic auxiliary variable to adjust the coding interval. This mechanism dynamically adjusts the frequency and precision of data transmission under limited network resources, thereby reducing network congestion and delay.

c) Design of the Fuzzy Estimator

A fuzzy estimator based on relative measurement outputs is designed for each node. The estimator uses the measurement outputs from the node itself and its neighboring nodes to determine the system state and constructs an ellipsoidal set to encapsulate the system state at each time instant. In this way, the estimator can provide deterministic error bounds under unknown noise conditions.

d) Optimization Problem Solving

The study proposes two optimization problems to ensure that the performance requirements of the estimator are met. The first optimization problem aims to minimize the size of the ellipsoidal set to improve estimation accuracy. The second optimization problem uses the sparrow search algorithm (SSA) to optimize the bit rate allocation protocol, reducing decoding errors and improving communication efficiency.

2. Main Results

a) Effectiveness of the Fuzzy Estimator

Through numerical simulations, the study verifies the effectiveness of the proposed fuzzy estimator in complex networks. The simulation results show that the system state is successfully encapsulated within the ellipsoidal set constructed by the estimator at each time instant, demonstrating the robustness of the set-membership estimation method.

b) Performance of the Dynamic Coding-Decoding Mechanism

The dynamic coding-decoding mechanism demonstrates significant performance advantages under limited network resources. By dynamically adjusting the coding interval, the mechanism effectively reduces the frequency and quantity of data transmission, thereby lowering network congestion and delay.

c) Application of the Optimization Algorithm

The sparrow search algorithm shows high efficiency and accuracy in optimizing bit rate allocation. Compared to traditional average allocation protocols, the optimized bit rate allocation scheme significantly reduces decoding errors and improves communication efficiency.

3. Conclusion

This study introduces the set-membership estimation method into T-S fuzzy complex networks for the first time and proposes a dynamic coding-decoding mechanism to optimize data transmission and state estimation. By combining the fuzzy estimator with optimization algorithms, the study achieves robust state estimation under unknown but bounded noise conditions. This method has significant scientific value and engineering implications, especially in high-dynamic and resource-constrained scenarios.

4. Research Highlights

  • Innovation: The first exploration of the set-membership estimation problem in T-S fuzzy complex networks, filling a research gap in this field.
  • Dynamic Coding-Decoding Mechanism: Improves the efficiency and reliability of data transmission through dynamic adjustment of the coding interval.
  • Optimization Algorithm: Uses the sparrow search algorithm to optimize bit rate allocation, significantly reducing decoding errors.
  • Practical Application Value: This method has broad application prospects in high-dynamic and resource-constrained network environments.

5. Other Valuable Information

The study also explores the potential of this method in other application scenarios, such as synchronization control of complex networks and set-membership filtering/estimation in sensor networks. These applications further demonstrate the generality and extensibility of the method.

Significance and Value

This study not only provides a new solution for state estimation in T-S fuzzy complex networks but also offers important theoretical support for data transmission and resource optimization in complex network environments. By combining the dynamic coding-decoding mechanism with optimization algorithms, the study has made significant progress in improving estimation accuracy and communication efficiency, with broad application prospects and important engineering value.