Prescribed‐Time Event‐Triggered Distributed Optimization With Privacy Protection Over Directed Networks

ABSTRACT This paper focuses on privacy‐preserving distributed convex optimization across directed graphs within a prescribed‐time. To reduce the communication cost and achieve fast convergence, we propose a novel event‐triggered and prescribed‐time convergent distributed optimization algorithm built upon an extended Zero‐Gradient‐Sum method with free initialization. Specifically, we formulate event‐triggering conditions for each agent, ensuring that inter‐agent communication occurs solely upon meeting these conditions, thus significantly reducing communication costs. By the Lyapunov stability theory, the proposed algorithm is proven to achieve an accurate convergence to the optima within a prescribed‐time. Moreover, we establish the absence of Zeno behavior throughout any arbitrary period except the specified convergence time. When the environment exists, eavesdropping attacks, we further provide a privacy‐preserving prescribed‐time event‐triggered distributed algorithm based on state and objective decomposition. Finally, two comprehensive simulations demonstrate the performance of our proposed algorithm.