Approximation-based adaptive tracking control of pure-feedback nonlinear systems with multiple unknown time-varying
Min Wang1, Shuzhi Sam Ge, Keum-Shik Hong
1College of Automation and the Center for Control and Optimization, South China University of Technology, Guangzhou, China. auwangmin@scut.edu.cn
IEEE Transactions on Neural Networks
|September 23, 2010
Summary
This study introduces adaptive neural control for complex systems with unknown time delays. The novel approach ensures system stability and accurate tracking performance, overcoming significant control design challenges.
Area of Science:
- Control Systems Engineering
- Artificial Intelligence
- Nonlinear Dynamics
Background:
- Non-affine pure-feedback systems present significant control design challenges due to their complex structure.
- Unknown state time-varying delays further complicate the stability analysis and control of these systems.
- Existing control methods often struggle with the inherent nonlinearities and delays.
Purpose of the Study:
- To develop an adaptive neural tracking control strategy for non-affine pure-feedback systems with multiple unknown state time-varying delays.
- To address the design difficulties arising from the non-affine structure and time-varying delays.
- To ensure uniform ultimate boundedness of all closed-loop system signals and achieve accurate tracking.
Main Methods:
- Exploiting the mean value theorem to transform non-affine terms into an affine form for virtual and actual controls.
- Employing separation techniques to decompose unknown functions of delayed states into series of continuous functions.
- Utilizing novel Lyapunov-Krasovskii functionals to compensate for unknown functions of current delayed states.
- Introducing novel continuous functions to manage adaptive parameter complexities.
- Modifying control gains dynamically using even functions for stability analysis.
Main Results:
- Successfully designed an adaptive neural control scheme for the targeted system class.
- Demonstrated the ability to handle unknown state time-varying delays without restrictions on delay functions.
- Achieved uniformly ultimate boundedness of all signals within the closed-loop system.
- Validated the effectiveness of the proposed control strategy through simulation studies.
Conclusions:
- The proposed adaptive neural tracking control scheme effectively addresses the challenges posed by non-affine pure-feedback systems with multiple unknown time-varying delays.
- The novel methodologies employed overcome inherent design difficulties, ensuring system stability and tracking performance.
- Simulation results confirm the practical applicability and robustness of the developed control strategy.
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