DMCN Nash Seeking Based on Distributed Approximate Gradient Descent Optimization Algorithms for MASs

A key problem in multiagent multitask systems is optimizing conflict-free strategies, especially when task-assignment is coupled with path-planning. Incomplete information exacerbates this complexity, leading to frequent conflicts, such as redundant agents performing the same task. Different from the existing single-type game model, this article introduces a distributed mixed cooperative-noncooperative (DMCN) model that considers nondifferentiable constraints. In order to deal with nondifferentiable task layer constraints, we use approximation operators and splitting schemes to transform the original optimization function into the primal-dual differentiable function. In order to obtain more stable solutions, a distributed approximate gradient descent optimization algorithm and conflict resolution mechanism are proposed, which enhances the convergence of our method. We use Lyapunov theory to verify the exponential convergence of the algorithm in the time range. Simulation and experiments demonstrate the superiority of this method and its applicability in engineering applications.