Dynamics-Aware Distributed Optimization over a Network of Input-Saturated Linear Agents

This paper discusses a dynamics-aware distributed optimization over a network of linear agents subject to input saturations, which commonly affect actuators in various physical plants. We formulate a coupled optimization problem and design a novel distributed controller that guarantees every agent asymptotically converges to the unique optimizer of the problem in a cooperative manner. We analyze local synchronizability by using local sector conditions, and derive a sufficient condition for solvability of the dynamics-aware distributed optimization problem under the input saturation in terms of the linear matrix inequalities. Furthermore, we derive a possible alternative that does not require any prior information about the optimizer, albeit with increased conservativeness. Through a numerical simulation, we validate the effectiveness of the proposed criteria.