Optimal control and stabilisation for large‐scale systems with imposed constraints

This study mainly concerns the linear quadratic optimal control and stabilisation problems for large‐scale systems with constraint, the constraint is imposed on the weighted control and state, which arises from coordination problem for multi‐agent systems. The main contributions of this study are: first, the optimal controller is developed via using the maximum principle and decoupling the forward and backward difference equations (FBDEs); secondly, by defining the Lyapunov function with the optimal cost function, the necessary and sufficient stabilisation conditions for the large‐scale systems are derived. The main techniques adopted in this study are the maximum principle and the solution to the FBDEs. It is noted that the optimal control strategy involves the centralised information of the weighted state average, but this can be easily accessed for the large‐scale‐system network.