Handling Asynchronous Scheduling Functions in Periodic Event-Triggered Gain-Scheduled Control With Guaranteed...

Area of Science:

• Control Systems Engineering
• Nonlinear System Dynamics
• Optimization Theory

Background:

• Periodic event-triggered control (PETC) is applied to nonlinear systems using quasi-linear parameter-varying (quasi-LPV) representations.
• Gain-scheduling controllers offer improved performance but face challenges with asynchronous scheduling functions in PETC, leading to conservative results.
• Existing methods for handling asynchronous functions rely on bounding assumptions that may not hold during closed-loop operation.

Purpose of the Study:

• To develop a novel PETC scheme that effectively manages asynchronous scheduling functions in nonlinear systems.
• To co-design an event-triggering mechanism and a gain-scheduled controller for improved system stabilization.
• To maximize the region of attraction and minimize data transmissions within the PETC framework.

Main Methods:

• Utilizing a looped-functional approach and a nonquadratic Lyapunov function.
• Deriving linear matrix inequality (LMI)-based conditions for controller and event-trigger design.
• Formulating a multiobjective optimization problem to balance performance and transmission efficiency.

Main Results:

• The proposed PETC scheme successfully addresses the asynchronous scheduling phenomenon.
• Guaranteed convergence of closed-loop trajectories to the origin from the estimated region of attraction.
• Demonstrated avoidance of mismatched scheduling function boundedness violations during operation.
• Validation through two numerical examples showcasing the methodology's effectiveness.

Conclusions:

• The novel PETC scheme provides a robust solution for controlling nonlinear systems with asynchronous scheduling.
• The co-design approach optimizes performance by maximizing the region of attraction and minimizing transmissions.
• This work advances the field of event-triggered control for complex nonlinear systems.