Optimization of Linear Multi-Agent Dynamical Systems via Feedback Distributed Gradient Descent Methods

Feedback optimization is a control paradigm for optimizing dynamical systems at steady-state. Existing methods rely on centralized architectures, limiting scalability and privacy in large-scale systems. We propose a distributed feedback optimization approach inspired by the Distributed Gradient Descent method, where each agent updates its control variable using local gradients and average of neighbors. Under convexity and smoothness assumptions, we establish convergence to a critical optimization point, and under restricted strong convexity, we prove linear convergence to a neighborhood of the optimum, with its size dependent on the stepsize. Simulations corroborate the theoretical results.