Optimal $H_2$ Decentralized Control of Cone Causal Spatially Invariant Systems
For control theorists and engineers working on spatially invariant systems, this paper offers an explicit formula for decentralized control, which is a novel theoretical contribution but incremental in terms of practical impact.
This paper provides an explicit solution to the optimal H2 decentralized control problem for cone causal spatially invariant systems, deriving a closed-form expression for the decentralized controller for the first time. The method is shown to be effective through a numerical example compared with previous works.
This paper presents an explicit solution to decentralized control of a class of spatially invariant systems. The problem of optimal $H_2$ decentralized control for cone causal systems is formulated. Using Parseval's identity, the optimal $H_2$ decentralized control problem is transformed into an infinite number of model matching problems with a specific structure that can be solved efficiently. In addition, the closed-form expression (explicit formula) of the decentralized controller is derived for the first time. In particular, it is shown that the optimal decentralized controller is given by a specific positive feedback scheme. A constructive procedure to obtain the state-space representation of the decentralized controller is provided. A numerical example is given and compared with previous works which demonstrate the effectiveness of the proposed method.