Adaptive output-feedback control for switched stochastic uncertain nonlinear systems with time-varying delay

Area of Science:

• Control Theory
• Nonlinear Systems
• Stochastic Systems

Background:

• Adaptive control is crucial for systems with unknown dynamics.
• Stochastic time-delay nonlinear systems present significant control challenges.
• Uncertainty in output functions complicates controller design.

Purpose of the Study:

• To develop an adaptive output-feedback controller for switched stochastic time-delay nonlinear systems.
• To address unknown control coefficients, time-varying delays, and uncertain output functions.
• To ensure stability and state regulation for the closed-loop system.

Main Methods:

• Utilizing the power integrator technique for controller design.
• Developing an adaptive control strategy for systems with unknown drift and diffusion terms.
• Employing Lyapunov stability theory to prove system boundedness and convergence.

Main Results:

• The proposed adaptive controller guarantees the closed-loop system is bounded in probability.
• The state of the switched stochastic nonlinear system is regulated to the origin almost surely.
• A numerical example validates the effectiveness of the developed control method.

Conclusions:

• The adaptive output-feedback control strategy is effective for the studied class of systems.
• The method provides robust performance under significant system uncertainties and delays.
• This work contributes to the advancement of control theory for complex nonlinear systems.