LQR-based coupling gain for synchronization of linear systems

By S. E. Tuna. 2008

275 citations recorded by the source corpus.

Synchronization control of coupled continuous-time linear systems is studied. For identical systems that are stabilizable, a linear feedback law obtained via algebraic Riccati equation is shown to synchronize any fixed directed network of any number of coupled systems provided that the coupling is strong enough. The strength of coupling is determined by the smallest distance of a nonzero eigenvalue of the coupling matrix to the imaginary axis. A dual problem where detectable systems that are coupled via their outputs is also considered and solved.

Subfields: Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/795a148092f9115350553243ab1570b3c5438f7f

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In Computer Networks and Communications

Citations in the corpus

Conditions for Synchronizability in Arrays of Coupled Linear Systems (2008, background): “4.1], is: Given , all detectable pairs are synchronizable with respect to . (For this case, an explicit formulation of a synchronizing feedback law is available; see, for instance, [ 11 ].) We can also make the following trivial statements.”
Constructing consensus controllers for networks with identical general linear agents (2010, background): “Very recently, a few researchers have begun to consider consensus control among agents with general identical linear internal dynamics, see [8, 9, 10, 11].”
Consensus of Multi-Agent Systems With General Linear and Lipschitz Nonlinear Dynamics Using Distributed Adaptive Protocols (2011, methodology): “Therefore, the consensus protocols given in Lemma 1 and [14], [15] cannot be implemented by each agent in a fully distributed fashion, i.”
Cooperative Optimal Control for Multi-Agent Systems on Directed Graph Topologies (2014, methodology): “It is shown in [7], [8] that, using the distributed state feedback derived from a local algebraic Riccati equation, synchronization can be achieved for a broad class of communication graphs.”
Stability of a Class of Linear Switching Systems with Applications to Two Consensus Problems (2011, background): “The first type consensus problem, i.e., the leaderless consensus problem was first studied for the fixed network in [11], [14], [17], [ 19 ], [20], and for the switching network in [8], [10], [14], [15], [17], [21].”
Designing Fully Distributed Consensus Protocols for Linear Multi-Agent Systems With Directed Graphs (2013, background): “The consensus protocol (5) can also be designed by solving the algebraic Ricatti equ ation:ATQ+QA+I−QBBTQ = 0, as in [23], [10].”
Necessary and Sufficient Conditions for Consensusability of Linear Multi-Agent Systems (2010, background): “in the context of fixed topologies and switching topologies, respectively. In [ 6 ], for linear MASs, output feedback”
Adaptive Event-Triggered Consensus of Multiagent Systems on Directed Graphs (2021, methodology): “It is only required that the communication graph contains a spanning tree, a condition similar to that for the celebrated continuous-time state-feedback protocols in [7]–[9] and [12].”
Lyapunov, Adaptive, and Optimal Design Techniques for Cooperative Systems on Directed Communication Graphs (2012, background): “[32] and Tuna [33] where the cooperative regulator problems were considered.”
Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback (2011, methodology): “In [18], linear quadratic regulator (LQR) based optimal control approach was used for leaderless consensus and only full state feedback was considered.”