A Distributed Event-Triggered Neurodynamic Approach for Lyapunov Matrix Equation

In this article, a neurodynamic approach based on event-triggered mechanism for solving Lyapunov matrix equation is established. First, employing matrix decomposition technique, the Lyapunov matrix equation is reformulated as a distributed optimization problem. Then, a distributed neurodynamic approach is constructed to solve the corresponding distributed optimization problem owing to its better-parallel computing ability. In order to protect the privacy of agents and fulfill the distributed communication, a primal-dual method with auxiliary variables is introduced. Agents collaborate to solve distributed optimization problem by interacting with auxiliary variables rather than decision variables. Besides, to reduce the communication cost and frequency between agents, the neurodynamic approach incorporates an event-triggered mechanism for Lyapunov matrix equation for the first time. Through theoretical analysis, it is proved that the state solution of the proposed neurodynamic approach converges exponentially and no Zeno behavior occurs. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed event-triggered neurodynamic approach.