Optimal Consensus Control for Multi-Agent Systems with Input Constraints: A State Decomposition Approach

This paper presents optimal consensus control for multi-agent systems with input constraints by using a state decomposition approach. The state decomposition approach is to divide the state space into consensus subspace and its orthonormal complement subspace. The proposed equality condition ensures that consensus subspace is consensus. Therefore, if we design the gain K that orthonormal subspace converges to zero, the consensus is achieved. Solving the proposed optimization problem that minimizes global cost function guarantees consensus control with input constraints of states. To solve the optimization problem, linear matrix inequality (LMI) formulation is used. The simulation results of numerical examples show that the proposed condition achieves multi-agent systems consensus.