Prescribed-Time Impulsive Control of High-Order Integrator Systems

Area of Science:

• Control Systems Engineering
• Robotics
• Nonlinear Dynamics

Background:

• High-order integrator systems present challenges in control due to potential singularities.
• Achieving stability within a predefined time frame (prescribed-time stability) is crucial for many real-world applications.

Purpose of the Study:

• To design novel prescribed-time impulsive controllers for high-order integrator systems.
• To address the singularity issue in control input matrices for enhanced stability.
• To develop a prescribed-time impulsive observer for systems with sampled outputs.

Main Methods:

• Stability analysis using the algebraic Riccati equation to derive explicit parametric control gains.
• Design of prescribed-time impulsive control by adjusting gains at impulsive instants.
• Convergence of the state transition matrix to a nilpotent matrix.

Main Results:

• Explicit parametric control gains for impulsive control are derived.
• Prescribed-time stability (PTS) is achieved for high-order integrator systems.
• A prescribed-time impulsive observer is proposed and validated.

Conclusions:

• The proposed controllers and observer effectively achieve prescribed-time stability for high-order systems.
• The method is validated through trajectory tracking of omnidirectional mobile robots.
• This work offers a robust approach for time-constrained control in complex systems.