Discrete-Time Distributed Optimal Formation Algorithms for Multiagent Systems With Nonlinear Inequality Constraints

This article studies the distributed optimal formation problems for multiagent systems subject to nonlinear inequality constraints. This problem can be formulated into a nonlinear mixed-integer programming (NMIP) problem. We first decompose the NMIP problem into a formation optimal matching problem, which is actually an integer linear programming (ILP) problem, and an optimal formation reference center problem described as a constrained quadratic optimization problem. Subsequently, we develop a discrete-time perturbation-based distributed dual consensus ADMM (PDC-ADMM) algorithm, which achieves an optimal integer solution to the ILP problem and eliminates the unmatched phenomenon. In addition, we propose a distributed optimistic gradient descent ascent (D-OGDA) algorithm with a constant step size, which guarantees exact convergence to the optimal formation reference center. Finally, three simulation examples are carried out to demonstrate the effectiveness of the developed algorithms.