Disturbance observer based fixed-time control of stochastic systems.

Area of Science:

• Control Theory
• Stochastic Systems Analysis
• Fault-Tolerant Control

Background:

• Stochastic systems are susceptible to various disturbances and faults, impacting their stability and performance.
• Existing control methods may not guarantee convergence within a fixed time or effectively handle multiple simultaneous disturbances and faults.
• Derivative-bounded disturbances and multiplicative noise pose significant challenges in control system design.

Purpose of the Study:

• To propose a novel fixed-time anti-disturbance control scheme for stochastic systems.
• To address systems subjected to multiple disturbances (derivative-bounded and multiplicative noise) and time-varying faults.
• To ensure system state convergence to equilibrium within a pre-specified fixed time.

Main Methods:

• Design of a fixed-time disturbance observer (Fixed-time DO) using pole placement to estimate derivative-bounded disturbances.
• Employment of an adaptive law to approximate time-varying faults.
• Construction of a composite fixed-time controller integrating disturbance estimation and fault adaptation.

Main Results:

• The proposed fixed-time disturbance observer effectively estimates derivative-bounded disturbances.
• The adaptive law successfully approaches time-varying faults.
• The composite fixed-time controller ensures system convergence to equilibrium within a pre-specified time.
• Simulation results validate the controller's effectiveness and demonstrate convergence time independence from initial states.

Conclusions:

• The developed fixed-time anti-disturbance control scheme is effective for stochastic systems with multiple disturbances and faults.
• The proposed approach guarantees finite-time convergence, offering enhanced performance and robustness.
• The controller's convergence time is independent of the system's initial conditions, providing predictable performance.