Decentralized Design for LQ Consensus in Multi-Agent Systems

Consensus control of multi-agent systems (MAS) with integrator dynamics is a canonical and well-studied problem in the literature. In contrast, the optimal distributed linear quadratic (LQ) consensus problem minimizing an appropriate quadratic cost is less studied. For this problem, most of the available design methods require global information on the interconnection graph and/or global (initial) state information. In this paper, we propose a suboptimal solution to the LQ-based distributed consensus control problem by approximating the quadratic cost function in a way that allows for decentralized design of the control gains. The resulting control protocol only uses information from neighboring agents for both control design and implementation. It has the additional benefit that the information can be exchanged periodically, reducing the communication requirements of the agent. Despite the suboptimality, asymptotic consensus is guaranteed for our control law, as we will formally prove. We illustrate by numerical simulations on a 6-agent system the effectiveness of our design and compare it to other approaches.