Distributed continuous-time algorithm for time-varying optimization with desired shape constraints

This paper focuses on a time-varying distributed convex optimization problem for multi-agent systems, with the objective of preserving their desired rigid formation. The core challenge is driving all agents to minimize the global objective function cooperatively with limited information each agent can share. To tackle the dual objective problem, here we propose a single-integrator and a double-integrator dynamic systems to solve the distributed optimization problem with desired shape achievement. It is proved that all agents can achieve the rigid formation while optimizing the global objective function asymptotically in two algorithms by using the Lyapunov theorem. Finally, the good performance of the control algorithms is demonstrated through numerical experiments and computer simulations.