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Reliability-based anti-disturbance control for systems with parametric stochastic uncertainty: A probabilistic LMI
Jianchun Zhang1, Hao Lu1, Jianliang Wang1
1Hangzhou Innovation Institute, Beihang University, Zhejiang, 310052, China.
ISA Transactions
|April 13, 2024
Summary
This study introduces a reliability-based anti-disturbance control (RADC) method to manage systems with uncertainty. The RADC method ensures system stability and performance robustness by considering parametric stochastic uncertainty.
Area of Science:
- Control Systems Engineering
- Stochastic Systems Analysis
- Robust Control Theory
Background:
- Existing anti-disturbance control methods often overlook parametric stochastic uncertainty.
- Stochastic uncertainty in both the system and disturbance dynamics poses significant challenges for control design.
- Ensuring system stability and performance robustness under uncertainty is critical for reliable operation.
Purpose of the Study:
- To develop a novel reliability-based anti-disturbance control (RADC) method for systems with parametric stochastic uncertainty.
- To incorporate uncertainty into both the system and exogenous disturbance dynamics for a comprehensive approach.
- To enable flexible and reliable controller design at various prescribed reliability levels.
Main Methods:
- Utilizing linear matrix inequality (LMI) and limit state function for control design.
- Formulating stability and robustness conditions as a stochastic LMI holding with a certain probability (reliability).
- Transforming the stochastic LMI into two probabilistic LMIs using the limit state function method.
Main Results:
- The proposed probabilistic LMIs quantify the impact of parametric stochastic uncertainty using reliability indexes.
- Controllers with adjustable reliability can be designed based on specified reliability indexes.
- Demonstrated feasibility and effectiveness through two illustrative examples and Monte-Carlo verification.
Conclusions:
- The developed RADC method effectively addresses parametric stochastic uncertainty in control systems.
- The approach allows for the design of controllers with tailored reliability.
- The method provides a robust framework for enhancing system stability and performance robustness.
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