Adaptive Fixed-Time Control for High-Order Stochastic Nonlinear Time-Delay Systems: An Improved Lyapunov-Krasovskii
IEEE Transactions on Cybernetics
|December 21, 2023
Summary
This study introduces a novel adaptive tracking control for high-order stochastic nonlinear time-delay systems, achieving fixed-time stability. The method ensures all signals remain bounded and tracking errors converge rapidly.
Area of Science:
- Control Systems Engineering
- Nonlinear Dynamics
- Stochastic Systems
Background:
- Adaptive tracking control is crucial for complex systems.
- High-order stochastic nonlinear systems with time delays present significant control challenges.
- Achieving fixed-time stability is desirable for predictable system performance.
Purpose of the Study:
- To develop an adaptive tracking control strategy for high-order stochastic nonlinear time-delay systems.
- To ensure semi-globally practical fixed-time stability (SGPFS).
- To guarantee boundedness of all closed-loop signals (CLSs) within a fixed-time interval.
Main Methods:
- Design of an improved Lyapunov-Krasovskii function to handle time delays and high-order terms.
- Application of L'Hopital's rule for boundedness analysis of the Lyapunov-Krasovskii function.
- Utilization of the fixed-time Lyapunov stability theorem for stability proof.
Main Results:
- The proposed control scheme guarantees semi-globally practical fixed-time stability (SGPFS).
- All closed-loop signals (CLSs) are proven to be bounded within the fixed-time interval.
- Tracking errors converge to a small region around zero within a fixed time.
Conclusions:
- The developed adaptive tracking control effectively addresses challenges in high-order stochastic nonlinear time-delay systems.
- The improved Lyapunov-Krasovskii function and fixed-time stability analysis are key contributions.
- Simulation results validate the efficacy and robustness of the proposed control scheme.
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