Hierarchical Decentralized Stabilization for Networked Dynamical Systems by LQR Selective Pole Shift

Nguyễn, Đình Hòa; Hara, Shinji

doi:10.3182/20140824-6-za-1003.00925

Cited by 17 publications

(9 citation statements)

References 14 publications

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“…and K is any stabilizing controller for Ḡ parameterized by Theorem 3.1. By (17), the problem ( 16) becomes an unconstrained H 2 design for Ḡ, which yields the optimal controller Kopt as in (13). The optimal hierarchical controller, therefore, follows as K opt = P T u Kopt P y .…”

Section: Convex Reformulation By Quadratic Invariancementioning

confidence: 99%

“…The recent paper [12] also addresses similar goals as ours using receding-horizon control, but the scalability of their controller is subject to the sparsity structure of the open-loop network. Related hierarchical designs have been proposed in [13], [14], however, they do not exploit the convex reformulation provided by quadratic invariance.…”

Section: Introductionmentioning

confidence: 99%

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Hierarchical $\mathcal{H}_{2}$ Control of Large-Scale Network Dynamic Systems

Xue

Chakrabortty

2018

2018 Annual American Control Conference (ACC)

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Standard H2 optimal control of networked dynamic systems tend to become unscalable with network size. Structural constraints can be imposed on the design to counteract this problem albeit at the risk of making the solution nonconvex. In this paper, we present a special class of structural constraints such that the H2 design satisfies a quadratic invariance condition, and therefore can be reformulated as a convex problem. This special class consists of structured and weighted projections of the input and output spaces. The choice of these projections can be optimized to match the closedloop performance of the reformulated controller with that of the standard H2 controller. The advantage is that unlike the latter, the reformulated controller results in a hierarchical implementation which requires significantly lesser number of communication links, while also admitting model and controller reduction that helps the design to scale computationally. We illustrate our design with simulations of a 500-node network.

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Section: Convex Reformulation By Quadratic Invariancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hierarchical $\mathcal{H}_{2}$ Control of Large-Scale Network Dynamic Systems

Xue

Chakrabortty

2018

2018 Annual American Control Conference (ACC)

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“…LQR-based consensus designs for leader-follower MASs was presented in [7] in which only local LQR problems were solved and no global LQR problem was considered. Next, in our previous research [8], we introduced an LQR-based method to design a distributed consensus controller for general linear MASs but the obtained controller is only sub-optimal. Recently, we have proposed an approach in [9] to achieve a consensus design with a non-conservative coupling strength where an alternative MAS model namely edge dynamics was presented that helps transforming the consensus design into an equivalent stability synthesis which can be derived by LQR method.…”

Section: Introductionmentioning

confidence: 99%

Minimum-Rank Dynamic Output Consensus Design for Heterogeneous Nonlinear Multi-Agent Systems

Nguyễn

2018

IEEE Trans. Control Netw. Syst.

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In this paper, we propose a new and systematic design framework for output consensus in heterogeneous MultiInput Multi-Output (MIMO) general nonlinear Multi-Agent Systems (MASs) subjected to directed communication topology. First, the input-output feedback linearization method is utilized assuming that the internal dynamics is Input-to-State Stable (ISS) to obtain linearized subsystems of agents. Consequently, we propose local dynamic controllers for agents such that the linearized subsystems have an identical closed-loop dynamics which has a single pole at the origin whereas other poles are on the open left half complex plane. This allows us to deal with distinct agents having arbitrarily vector relative degrees and to derive rank-1 cooperative control inputs for those homogeneous linearized dynamics which results in a minimum rank distributed dynamic consensus controller for the initial nonlinear MAS. Moreover, we prove that the coupling strength in the consensus protocol can be arbitrarily small but positive and hence our consensus design is non-conservative. Next, our design approach is further strengthened by tackling the problem of randomly switching communication topologies among agents where we relax the assumption on the balance of each switched graph and derive a distributed rank-1 dynamic consensus controller. Lastly, a numerical example is introduced to illustrate the effectiveness of our proposed framework.

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“…Linear Quadratic Regulator (LQR), a classical control design method, has been proven to be an effective approach for developing consensus algorithms [15][16][17][18][19][20][21], which usually results in solving structured Riccati equations. As previously shown, e.g., in [19,21] and references therein, low-rank consensus design can reduce the computational cost and possibly increases the consensus speed.…”

Section: Introductionmentioning

confidence: 99%

Distributed Consensus Design for a Class of Uncertain Linear Multiagent Systems under Unbalanced Randomly Switching Directed Topologies

Nguyễn

2018

Mathematical Problems in Engineering

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This paper proposes a novel approach to design fully distributed consensus controllers for heterogeneous linear Multiagent Systems subjected to randomly switching directed topologies and model uncertainties. The appealing features of this approach are as follows. First, it uses the mildest assumption for the randomly switching topologies that the union of switched graphs has a spanning tree. Second, the consensus is achieved under a class of state multiplicative uncertainties. Moreover, the proposed consensus controllers are low-rank and have nonconservative coupling strengths. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical approach.

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Hierarchical Decentralized Stabilization for Networked Dynamical Systems by LQR Selective Pole Shift

Cited by 17 publications

References 14 publications

Hierarchical $\mathcal{H}_{2}$ Control of Large-Scale Network Dynamic Systems

Hierarchical $\mathcal{H}_{2}$ Control of Large-Scale Network Dynamic Systems

Minimum-Rank Dynamic Output Consensus Design for Heterogeneous Nonlinear Multi-Agent Systems

Distributed Consensus Design for a Class of Uncertain Linear Multiagent Systems under Unbalanced Randomly Switching Directed Topologies

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