Model Reference Adaptive Control of Networked Systems with State and Input Delays

Abstract: Adaptive control strategies have progressively advanced to accommodate increasingly uncertain, delayed, and interconnected systems. This paper addresses the model reference adaptive control (MRAC) of networked, heterogeneous, and unknown dynamical agents subject to both state and input delays. The objective is to ensure that all follower agents asymptotically track the trajectory of a stable leader system, despite system uncertainties and communication constraints. Two communication topologies are considered, full connectivity between each agent and the leader, and partial connectivity wherein agents rely on both neighboring peers and the leader. The agent-to-agent and agent-to-leader interactions are encoded using a Laplacian-like matrix and a diagonal model-weighting matrix, respectively. To compensate for the delays, a predictor-based control structure and an auxiliary dynamic system are proposed. The control framework includes distributed adaptive parameter laws derived via Lyapunov-based analysis, ensuring convergence of the augmented tracking error. Stability conditions are established through a carefully constructed Lyapunov Krasovskii functional, under minimal assumptions on connectivity and excitation. Numerical simulations of both network structures validate the proposed method, demonstrating that exact leader tracking is achieved under appropriately designed learning rates and initializations. This work lays a foundation for future studies on fault-resilient distributed adaptive control incorporating data-driven or reinforcement learning techniques.