Approximate Optimal Control for Nonlinear Systems With Periodic Event-Triggered Mechanism.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Artificial Intelligence

Background:

• Optimal control problems are crucial for nonlinear systems.
• Traditional control methods often require continuous data transmission.
• Event-triggered control (ETC) reduces communication load but can impact performance.

Purpose of the Study:

• To investigate the approximate optimal control problem for nonlinear affine systems using Periodic Event-Triggered Control (PETC).
• To theoretically compare PETC with continuous and traditional ETC regarding stability and convergence.
• To introduce a novel application of PETC for optimal control in nonlinear systems.

Main Methods:

• A critic network, based on reinforcement learning (RL), is employed to approximate the optimal value function.
• The discrete time series from PETC are utilized for updating the learning network.
• Gradient-based weight estimation is adapted for discrete-time systems.
• Uniformly ultimately bounded (UUB) analysis is performed to ensure system stability.

Main Results:

• PETC demonstrates comparable convergence rates to traditional ETC for optimal control.
• The study presents the first application of PETC for achieving optimal control targets in nonlinear systems.
• The discrete updating mechanism of PETC effectively supports the learning network's weight estimation.

Conclusions:

• PETC is a viable and effective strategy for approximate optimal control in nonlinear systems.
• The proposed method ensures system stability through UUB analysis.
• The findings validate the efficiency of PETC in reducing data transmission while maintaining control performance.