Distributed Optimization Algorithms for Heterogeneous Linear Multi-agent Systems With Inequality Constraints

Abstract

In this paper, for heterogeneous linear multi-agent systems, a distributed constrained optimization problem about digraphs is studied. Every agent only utilizes local interaction and information such that all agents can achieve the global objective function. The state of each agent is limited to a local inequality constraint set. First, this paper proposes a distributed continuous-time optimization algorithm by designing a left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix, which removes the imbalance of the communication graph. Next, the asymptotical convergence about the algorithm is demonstrated using Lyapunov stability. Finally, two numerical examples are given to illustrate the effectiveness of the algorithm.