A Novel Approach for Adaptive Tracking Control of Nonlinear Systems Subject to Long-Range-Dependent Stochastic...

Area of Science:

• Control Theory
• Stochastic Systems
• Nonlinear Dynamics

Background:

• Existing adaptive control research primarily addresses standard Brownian motion (sBm).
• Fractional Brownian motion (fBm) disturbances, common in batteries, vehicles, and robotics, are under-researched in adaptive control.
• Long-range dependence and nonsemimartingale properties of fBm pose challenges for current control schemes.

Purpose of the Study:

• To develop an adaptive tracking control scheme for unmeasured stochastic nonlinear systems (SNSs) driven by fBm.
• To establish novel stability criteria for nonlinear systems influenced by fBm.
• To adapt existing observer-based control methods for systems with fBm characteristics.

Main Methods:

• Development of new stability criteria, including stochastic and practical stochastic stability, for fBm-driven systems.
• Application of the Bolzano-Weierstrass and Heine theorems for proving observer stability.
• Design of an observer-based adaptive tracking control scheme tailored for fBm disturbances.

Main Results:

• Novel stability criteria were successfully developed for nonlinear systems with fBm.
• The proposed adaptive tracking control scheme ensures all closed-loop signals remain bounded in the mean-square sense.
• The effectiveness of the control strategy was validated using a vehicle model.

Conclusions:

• The study provides a robust adaptive control solution for stochastic nonlinear systems affected by fractional Brownian motion.
• The developed stability criteria and control scheme address key limitations of existing methods for fBm-driven systems.
• The findings have significant implications for enhancing control performance in applications like electric vehicles and robotics.