Continuous-Time Algorithms for Distributed Optimization Problem on Directed Digraphs

This paper has proposed continuous-time algorithms to address a distributed optimization problem for the multi-agent system with parametric uncertainties over directed digraphs. Firstly, an virtual vector was introduced to generate reference signal. Then, a continuous-time distributed adaptive optimization algorithm with dynamic coupling gains and updating the coupling gains using relative information of system outputs and virtual vector was designed. Under this algorithm, the virtual vector can track the optimal solution asymptotically. Thirdly, an output feedback tracking protocol was designed to track the reference signal under strongly connected and directed graphs. Finally, convergence proofs were given with Lyapunov arguments and simulation results have illustrated the theoretical results.