Fixed-Time Adaptive Fuzzy Control for Nonstrict Feedback High-Order Stochastic Nonlinear Systems With State...

Area of Science:

• Control Theory
• Nonlinear Systems
• Stochastic Systems

Background:

• Stochastic high-order nonlinear systems (HONSs) present challenges due to state constraints and uncertainties.
• Existing control methods often struggle with asymmetric full-state constraints and stochastic disturbances.

Purpose of the Study:

• To develop an adaptive fixed-time tracking control strategy for stochastic HONSs with full state constraints.
• To address asymmetric state constraints using a fractional Barrier Lyapunov function (BLF).
• To handle stochastic disturbances and unknown nonlinearities via fuzzy logic systems.

Main Methods:

• Employing a fractional Barrier Lyapunov function (BLF) to manage asymmetric full-state constraints.
• Utilizing fuzzy logic systems to approximate unknown nonlinearities and stochastic disturbances.
• Applying the adding a power integrator technique and backstepping method for controller design.
• Leveraging fixed-time Lyapunov stability theory to guarantee probabilistic fixed-time boundedness.

Main Results:

• An adaptive fixed-time fuzzy state feedback controller was designed, ensuring all signals remain bounded.
• All system states were proven to stay within the constrained interval.
• The nonlinear system demonstrated fixed-time boundedness in probability.
• The proposed BLF approach is adaptable to unconstrained high-order systems.

Conclusions:

• The developed control strategy effectively manages stochastic HONSs with full state constraints.
• The fractional BLF offers a robust solution for asymmetric state limitations.
• Simulation results, including a spring-mass damper system, validate the control strategy's performance.