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Dissipative control for nonlinear singularly perturbed systems with dynamic quantization and actuator failure.

Xue Jin1, Xiao-Heng Chang1

  • 1School of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan, 430081, People's Republic of China.

ISA Transactions
|April 28, 2024
PubMed
Summary

This study addresses dissipative control for nonlinear singularly perturbed systems (SPSs) facing dynamic quantization and actuator failure. The research develops an ϵ-independent controller ensuring system stability and performance despite network constraints.

Keywords:
Actuator failureDissipative controlDynamic quantizationSingularly perturbed systemsT–S fuzzy model

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Area of Science:

  • Control Theory
  • Systems Engineering
  • Fuzzy Systems

Background:

  • Nonlinear singularly perturbed systems (SPSs) present significant control challenges.
  • Dynamic quantization and actuator failures complicate control system design due to network bandwidth limitations and potential component malfunctions.
  • Takagi-Sugeno (T-S) fuzzy models are effective for representing nonlinear systems.

Purpose of the Study:

  • To investigate the dissipative control problem for nonlinear SPSs with dynamic quantization and actuator failure.
  • To design an ϵ-independent state feedback controller that guarantees asymptotic stability and dissipative performance.
  • To develop a method for determining the maximum stability bound (ϵ̄).

Main Methods:

  • Utilizing Takagi-Sugeno (T-S) fuzzy models to represent the nonlinear plant.
  • Employing linear matrix inequalities (LMIs) for controller design.
  • Incorporating dynamic quantization and considering actuator failure in the control framework.
  • Developing a search algorithm to find the maximum stability bound (ϵ̄).

Main Results:

  • Sufficient design conditions for an ϵ-independent state feedback controller were derived.
  • The proposed controller ensures the closed-loop system is asymptotically stable.
  • The controller guarantees the system achieves a predefined dissipative performance.
  • A search algorithm was presented to find the maximum stability bound (ϵ̄).

Conclusions:

  • The developed method effectively addresses the dissipative control problem for nonlinear SPSs with dynamic quantization and actuator failure.
  • The proposed controller design is feasible and effective, as demonstrated by two examples.
  • The approach provides a robust solution for systems operating under network constraints and potential component failures.