Minimal-Approximation-Based Decentralized Backstepping Control of Interconnected Time-Delay Systems

Area of Science:

• Control Systems Engineering
• Nonlinear System Dynamics
• Adaptive Control Theory

Background:

• Decentralized control is crucial for large-scale nonlinear systems.
• Existing methods often require complex controllers with multiple function approximators.
• Handling unknown time-varying delays and hysteresis poses significant challenges.

Purpose of the Study:

• To develop a simplified decentralized adaptive backstepping control.
• To address nonlinear large-scale systems with unknown unmatched time-varying delayed interactions.
• To incorporate unknown backlash-like hysteresis nonlinearities into the control design.

Main Methods:

• A decentralized adaptive backstepping control design is proposed.
• Minimal function approximators are utilized for each subsystem.
• A simple local control law is designed using one adaptive function approximator per subsystem.
• Lyapunov stability theorem is employed to analyze system stability.

Main Results:

• A novel control law is designed with a single adaptive function approximator per subsystem.
• The proposed method eliminates the need for multiple function approximators and subsystem order considerations.
• Effective estimation of lumped unknown functions, including nonlinearities and hysteresis, is achieved.
• The stability of the closed-loop system is rigorously proven.

Conclusions:

• The proposed decentralized adaptive control offers a simplified and efficient approach.
• It effectively manages complex nonlinear dynamics, time-varying delays, and hysteresis.
• This method reduces computational complexity compared to existing techniques.