Consensus-Based Event-Triggered Distributed Optimization for a Network of Agents With Cubic Objective Functions

The conventional resource allocation methods, using a central node, are not resilient, owing to the failure of the central unit. An advanced solution is to apply distributed optimization by integrating intelligent nodes across a network. This paper deals with distributed optimization via the event-triggered (ET) consensus approach for nodes over a directed graph. An optimality condition for solving the optimization problem of a collective cubic objective function is provided. An optimization protocol for solving the optimization problem in a distributed manner by application of a nonlinear incremental cost (IC) consensus method is proposed. The analysis for the proposed optimization protocol has been attained by the Lyapunov function and the Lyapunov-Krasovskii functional to attain IC consensus and balance of supply-demand mismatch. In contrast to the existing works, the proposed approach (i) deals with an optimization problem for a combined cubic objective function, (ii) considers an ET mechanism for bandwitdth management, (iii) deals with a directed network topology (rather than an undirected graph), and (iv) incorporates the communication delay. Moreover, the elimination of Zeno behavior is ensured through the resultant approach. Finally, simulation experiments for the resource allocation in distributed generators of cubic objective functions are provided by considering the comparison with existing works and analysis of the presented methodology.