Distributed Resilient Initialization-Free Jacobi Descent Algorithm for Constrained Optimization Against DoS Attacks

This paper investigates one type of distributed constrained optimization problem, e.g., the economic dispatch problem, in the presence of DoS attacks. Therein, multiple DoS attackers are collaborative to impede the communication transmission and change the communication topology at will. Consequently, the convergence and/or optimality of distributed algorithm may be compromised. To reduce the effect of this kind of DoS attacks, a distributed resilient initialization-free Jacobi descent algorithm is proposed. It is designed with three switched control protocols which enable the proposed algorithm reasonably employing the estimations to replace the missing information when attacks occur. Meanwhile, the proposed method is embedded with second order information, resulting in faster convergence speed. Moreover, theoretical analysis results are provided to show that the proposed algorithm can exponentially converge to the global optimal solution of the studied problem. Finally, simulation results tested in IEEE 30-bus system validate its effectiveness and flexibility. Note to Practitioners-The economic dispatch is a key issue in smart grid, which can be formulated as a kind of distributed constrained optimization problem. Since the distributed algorithms work under distributed sensor networks, they are easier to undergo DoS attacks. To address this issue, this paper presents a distributed resilient initialization-free Jacobi descent algorithm, which features strong robustness to resist DoS attacks and faster convergence. Meanwhile, the proposed method is shaped for common constrained optimization problem with better expansibility. We conduct the global convergence and optimality proofs, which benefits the practitioners to estimate the convergence performance, e.g., the convergence rate. Simulations further show the correctness and effectiveness of the proposed method. In future, we will pay more attention on the non-convex constrained optimization problem.