This paper presents a new approach to distributed controller design that exploits a partial-structure representation of linear time invariant systems to characterize the structure of a system. This partial-structure representation, called the dynamical structure function, characterizes the signal structure , or open-loop causal dependencies among manifest variables, capturing a significantly richer notion of structure than the sparsity pattern of the transfer function. The design technique sequentially constructs each link in an arbitrary controller signal structure, and the main result proves that the resulting controller is either stabilizing or no controller with the desired structure can stabilize the system.
A different type of distributed controller design has been proposed in @cite_3 . The approach taken in this paper enforces the controller to have the same network structure as the plant. The structure in this paper is defined as the constraint on the interconnection of sub-systems, or the subsystem structure. Hence, the plant and the controller can share the same communication network reducing the implementation cost. An algorithm to synthesize a sub-optimal controller with such structure is also provided in this paper.
@cite_3
2146378835
We consider the problem of designing stabilizing distributed output-feedback controllers that achieve H 2 and H ∞ performance objectives for a group of sub-systems dynamically interconnected via an arbitrary directed communication network. For a particular class of discrete-time linear time-invariant interconnected systems that are characterized by a structural property of their state-space matrices, we design stabilizing distributed controllers which can use the available network along with the sub-systems of the interconnected system. This is achieved by means of a parameterization for the output-feedback linear controllers that linearizes the closed-loop H 2 and H ∞ norm conditions and provide equivalent linear matrix inequalities (LMIs). Using these LMIs, we formulate the minimization of H 2 and H ∞ norms as semi-definite programs (SDPs) that can be efficiently solved using well-established techniques and tools. The solutions of these SDPs allow us to synthesize the corresponding controllers that are realizable over the given network. Even though we provide only sufficiency conditions for the design of stabilizing distributed controllers, simulations show that the synthesized controllers we obtain provide good performance in spite of being suboptimal compared to the centralized controller. In essence, we gain the advantage of designing realizable distributed controllers at the expense of slight performance degradation compared to the centralized solutions.