Distributed Lebesgue Approximation Model for Distributed Continuous-Time Nonlinear Systems.

Area of Science:

• Control Systems Engineering
• Applied Mathematics
• Nonlinear Dynamics

Background:

• Approximation models are vital for enhancing accuracy and computational efficiency in model-based control.
• Distributed continuous-time nonlinear systems with coupled subsystems require effective approximation techniques.

Purpose of the Study:

• To propose and analyze two novel Lebesgue approximation models (LAMs) for distributed, asynchronous, and discretized approximation of continuous-time nonlinear systems.
• To reduce computational load through aperiodic triggering mechanisms and importance conditions.

Main Methods:

• Development of two Lebesgue approximation models: unconditionally triggered LAM (CT-LAM) and an importance-based CT-LAM.
• Analysis via a distributed event-triggered system demonstrating equivalent state trajectories to linear interpolation.
• Derivation of conditions for quantization sizes to ensure stability, bounded errors, and prevent Zeno behavior.

Main Results:

• The proposed LAMs effectively approximate distributed continuous-time nonlinear systems.
• Aperiodic triggering reduces iterations, especially for slow dynamics.
• The importance condition in CT-LAM further optimizes computational effort.

Conclusions:

• The developed LAMs offer an efficient and accurate method for approximating complex distributed nonlinear systems.
• The analysis provides guarantees for stability, error bounds, and avoidance of Zeno phenomena.
• Simulations on a quarter-car suspension system validate the practical advantages of the proposed approaches.