Distributed Time-Varying Convex Optimization Problem with Affine Formation Constraints for Multi-Agent System
Piaoyi Su, Zhexin Shi, Jianglong Yu, Pengfei Shi, Xiwang Dong, Zhang Ren · 2023
In this work, a distributed time-varying convex optimization problem with affine formation constraints is studied for nonlinear system subject to parametric uncertainties. Each agent has a local time-varying cost function known to only itself, and minimize the team cost functions through local interaction when satisfying affine formation constraints to complete the task. First, a novel problem considering affine formation constraints with more practical general Laplacians is discusseded. Second, distributed continuous-time optimization protocols are designed to generate optimal reference signals and adaptive controllers are constructed to track the optimal reference signals. Third, based on the Lyapunov theory, the bounded convergence to the optimal solution is proved. Finally, numerical simulation example is presented to demonstrate the theoretical results.