A Novel Prescribed-Time Control Approach Under Unknown Control Gain and Mismatched Disturbance

Area of Science:

• Control Theory
• Nonlinear Systems
• Robotics

Background:

• Existing prescribed-time output feedback control struggles with unknown control coefficients and mismatched nonvanishing disturbances.
• These challenges limit the applicability of current control strategies in complex uncertain systems.

Purpose of the Study:

• To propose a novel prescribed-time output feedback controller for uncertain nonlinear systems.
• To address challenges posed by unknown control coefficients and mismatched nonvanishing disturbances.
• To achieve prescribed-time stability and unified prescribed performance (UPP).

Main Methods:

• Development of a new prescribed-time control criterion incorporating Nussbaum functions.
• Design of a state observer and a prescribed-time output feedback controller.
• Rigorous mathematical proofs for convergence of system output and observer errors.

Main Results:

• Prescribed-time stability is achieved for the uncertain nonlinear systems.
• System output and observer errors converge to zero within a specified time.
• Unified prescribed performance (UPP) and output constraint satisfaction are simultaneously realized.

Conclusions:

• The proposed control design effectively handles unknown control coefficients and mismatched disturbances.
• The controller guarantees convergence and constraint satisfaction within a prescribed time.
• Numerical simulations and experimental results validate the controller's effectiveness.