Optimal consensus control of multi-agent systems based on the state-dependent riccati equation

This paper is concerned with optimal consensus control of a multi-agent system, leaderless or leader-follower control. The hierarchical state-dependent Riccati equation (SDRE) controller was the main framework. The Lyapunov-based method is used for solving time-varying systems. Not only positive definite solution of the related algebraic Riccati equation is realized by the SDRE method based on Lyapunov, but also the negative definite solution is realized. Furthermore, the leader-follower tracking structure is developed based on two nonlinear differential equations; the feedforward differential equation and the state-dependent Riccati differential equation, which consider the error in the cost function through the co-sate equation. The application of the proposed controller structure in controlling the lifting system of multiple 3D cranes is studied. The theoretical results have been verified by simulating the leaderless and leader-follower consensus control problem.