Consensus of Nonlinear Uncertain Delayed Multiagent Systems Modeled by PDEs via Adaptive Boundary Control

Area of Science:

• Control theory
• Systems engineering
• Applied mathematics

Background:

• Consensus problems in multiagent systems are complex due to nonlinearity, time-varying delays, and uncertainties.
• Partial differential equations (PDEs) model agents whose dynamics involve both time and space variables.
• Existing control strategies may face challenges with boundary control and cost-effectiveness.

Purpose of the Study:

• To develop an adaptive boundary control strategy for consensus in PDE-based multiagent systems.
• To reduce control costs by utilizing dynamic gains and minimal boundary actuators/sensors.
• To establish robust consensus conditions ensuring exponential stability.

Main Methods:

• Development of an adaptive boundary controller using boundary measurements.
• Application of directed graph theory for system interconnection.
• Derivation of linear matrix inequality (LMI)-based consensus conditions.
• Utilization of inequality techniques and Lyapunov direct approach for stability analysis.

Main Results:

• An adaptive boundary controller effectively reduces control costs.
• LMI-based conditions guarantee exponential stability of consensus error systems.
• The proposed control protocols demonstrate effectiveness in numerical simulations.

Conclusions:

• The study successfully presents an adaptive boundary control approach for PDE-based multiagent systems.
• The method achieves consensus and exponential stability under challenging conditions.
• Numerical examples validate the efficacy of the developed control protocols.