Cooperative robust output regulation of heterogeneous Lur'e networks

Abstract

In this paper, we study robust cooperative output regulation problems for a directed network of Lur'e systems that consist of a nominal linear dynamics with an unknown static nonlinearity around it through negative feedback. We assume that the linear part of each agent is identical, but the nonlinearities are allowed to be different for distinct agents. In this sense, the network is heterogeneous. As is common in the context of Lur'e systems, the unknown nonlinearities are assumed to be sector bounded within one given sector. The interconnection graph among these agents is assumed to contain a directed spanning tree. Similar to classical output regulation problems, there is a virtual exosystem generating a reference signal in which all the agents are required to track cooperatively. Our designed distributed dynamic state/output feedback protocol makes a copy of the reference signal at each agent asymptotically, and then the robust cooperative output regulation problem becomes a robust tracking problem that can be handled by each agent via local information. It turns out that our cooperative protocols are fully distributed. Sufficient conditions on the existence of output synchronization protocols are given along with some discussions on these conditions. Finally, two simulation examples illustrate our design.where w i .t / 2 R s and v i .t / 2 R n c are the states of the dynamic protocol for agent i, T is a matrix such that S TR is Hurwitz, A D OEa ij is the adjacency matrix associated with the graph G, and A c , B c , C c , D c , and K are gain matrices to be determined. The dimension n c is also a crucial parameter to be chosen. For the later dynamic output feedback protocol design, H is assumed to have full row rank (Theorems 3 and 4).

On Input-to-Output Stability and Robust Synchronization of Generalized Persidskii Systems

“…The last assumption assumes that all unbounded nonlinearities possess a kind of symmetry that 𝐶 𝑓 𝑗 takes zero on the set where 𝑦 = 0 only. Such a restriction is satisfied if, for example, 𝑓 𝑗 𝑖 (𝑠) = 𝑓 𝑗 1 (𝑠) for all 𝑖 ∈ 2, 𝑛 and 𝑗 ∈ 1, 𝑚, and 𝐶 = Γ as in (15), under which Assumption 2 is essentially an incremental passivity condition for all nonlinearities [31], [32].…”

Robust cooperative output regulation of heterogeneous Lur'e networks

“…In our present paper, only the condition of sector boundedness is imposed. For the passivity case, the reader is referred to the conference version , where only dynamic state feedback protocols were designed. In the present paper, the dynamic output feedback protocol design will be discussed as well.…”