Observer-based Distributed Optimization for Linear Multi-agent Systems

This paper investigates the observer-based distributed optimization of multi-agent systems under undirected and connected interaction topology. Different from state-based multi-agent distributed optimization problem, it is assumed that the states of all agents can not be available directly. To solve the problem, a distributed adaptive observer-based distributed optimization algorithm is presented for the multi-agent systems. A state observer is adopted to estimate agent’s state, and the gradient-based optimization term make the agent state converge to the optimal solution. Based on theory of Riccati equation and Lyapunov method, a distributed approach is proposed to construct the gain matrices, by which the constructed algorithm can make the system reach a consensus and minimize the team performance function. Finally, a simulation example is provided to illustrate our established result.