Decentralized control for linear systems with multiple input channels

In this paper, we consider the decentralized optimal control problem for linear discrete-time systems with multiple input channels. First, under centralized control, the optimal feedback gains are given in terms of two algebraic Riccati equations. A reduced order observer is then designed using only the local input and output information. By selecting an appropriate initial value for the observer, we derive an observer-based decentralized optimal controller where the feedback gain is the same as that obtained in the centralized optimal control problem. Last but not least, we study the optimal control problem of non-homogeneous multi-agent systems as an application. A suboptimal decentralized controller is obtained and the difference between the suboptimal cost and the optimal one is given.