Performance Guaranteed Robust Tracking Control of MIMO Nonlinear Systems With Input Delays: A Global and...

Area of Science:

• Control Theory
• Nonlinear Systems
• Robotics

Background:

• Designing controllers for multi-input and multi-output (MIMO) nonlinear systems with unknown dynamics and time delays is challenging.
• Existing methods often require specific initial conditions or detailed system knowledge, limiting their practical application.

Purpose of the Study:

• To develop a global performance-guaranteed tracking control method for general strict-feedback MIMO nonlinear systems.
• To address unknown nonlinearities and unknown time-varying input delays.
• To relax stringent conditions on initial values and system knowledge.

Main Methods:

• Introduction of a novel error transformation integrated with a Lyapunov-Krasovskii functional (LKF).
• Development of a control scheme that compensates for unknown input delays and gain matrices.
• Relaxation of traditional controllability conditions.

Main Results:

• Achieved global prescribed performance tracking for uncertain MIMO systems with delayed inputs.
• Eliminated constraints on initial values for tracking/virtual errors and performance functions.
• Designed a simpler, computationally less expensive controller requiring no prior knowledge of system nonlinearities or trajectory derivatives.
• Introduced a differentiable time-varying feedback term to handle unknown delays and gain matrices.
• Demonstrated enlarged applicability due to relaxed controllability conditions.

Conclusions:

• The proposed control method offers a robust and efficient solution for tracking control in complex nonlinear systems.
• The strategy successfully handles uncertainties and input delays, enhancing control system reliability.
• The method's relaxed conditions and simplified structure make it suitable for a broader range of applications, as shown in the robotic manipulator example.