Nonsmooth Distributed Resource Allocation Over Second-Order Nonlinear Multiagent Systems

The rapid development of cyber-physical systems technique has promoted the development of autonomous systems. To perform the distributed task autonomously, this study delves into the problem of distributed resource allocation over second-order multiple autonomous physical systems. It aims to minimize the global cost function while allocating plenty of resources to finite distributed second-order agents. Since exogenous disturbances in the control channel are unavoidable, and the nonlinear dynamical system can more accurately describe the physical behavior of the system, i.e., Euler-Lagrange systems. The nonlinear term in the control channel is considered, including the exogenous disturbances and nonlinear dynamics. Unlike most existing results, the nonlinear term is assumed to be bounded by a known constant. To this end, the bounded nonlinear term is handled using a sign function-based discontinuous nonlinear control scheme. Based on this, a distributed method with an adjustable dual Lagrange multiplier is designed using the modified primal-dual scheme for achieving the optimal allocation result. In addition, its convergence proof is completed in view of the fixed-time stability and the set-valued LaSalle invariance principle. With our designed method, the agent state asymptotically converges to the exact solution for the undirected and weighted-balanced directed connected networks. Last, we adopt some case studies to certify the effectuality of the developed analytical outcomes.