Constraint-Coupled Distributed Coordination Control for Nonlinear Stochastic Multiagent Systems: Application to Power Resource Allocation

This article studies the distributed coordination control problem of the nonlinear stochastic multiagent system, which involves multiple inequality constraints, as well as random disturbances. The communication network is modeled as an undirected and connected graph, where each node has a cost function that is considered to be strongly convex. First, an algorithm is developed that utilizes state feedback and projection operations, along with auxiliary variables, to precisely estimate the optimal state and its derivatives in a distributed manner. Furthermore, the decision variable is subject to several inequality constraints, and there are no restrictions on the initial value. Taking into account the impact of nonlinearity resulting from drift coefficients, diffusion coefficients, and external disturbances on the system’s stability, the existing works cannot be directly applied to this study. Through the utilization of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm It}\hat{\rm o}$</tex-math></inline-formula> formula and convex analysis, a novel analytical approach has been demonstrated to establish the asymptotic convergence of decision variable to the optimal value in mean square. This method distinguishes itself from the conventional convergence analysis techniques. Finally, the algorithm is utilized for the allocation of energy resources, resulting in the attainment of the optimal regulating method for power resource allocation.