Patterned linear systems

Hamilton, Sarah C.; Broucke, Mireille E.

doi:10.1016/j.automatica.2011.07.004

Cited by 13 publications

(7 citation statements)

References 12 publications

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“…Hamilton and Broucke proposed a new class of linear system called patterned linear systems [12]. For a square matrix M ∈ R d×d , they called a matrix written by 1 , a 0 , a 1 , . .…”

Section: B Block Patterned Systemsmentioning

confidence: 99%

An algebraic approach to hierarchical LQR synthesis for large-scale dynamical systems

Tsubakino

Yoshioka

Hara

2013

2013 9th Asian Control Conference (ASCC)

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This paper considers a linear quadratic optimal hierarchical control problem for large-scale dynamical systems modeled by an interconnected system under multi-scale information exchange networks. We first propose an algebraic characterization of hierarchies by using semigroups the Kronecker product. The multiplication rule of the Kronecker product quite fits to the property of semigroups. As a result, a condition under which the stabilizing solution of the Riccati equation inherits the hierarchy is obtained with the aid of the previous result. Furthermore, the proposed framework makes it possible to understand several previous results on decentralized optimal control from a unified viewpoint.

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“…Hamilton and Broucke proposed a new class of linear system called patterned linear systems [12]. For a square matrix M ∈ R d×d , they called a matrix written by 1 , a 0 , a 1 , . .…”

Section: B Block Patterned Systemsmentioning

confidence: 99%

An algebraic approach to hierarchical LQR synthesis for large-scale dynamical systems

Tsubakino

Yoshioka

Hara

2013

2013 9th Asian Control Conference (ASCC)

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“…2 PROOF By projecting both sides of (2) into the direction f , we obtain (13). Then by subtracting (13) for all , 1 ≤ ≤ d from (2) according to the definitions of the auxiliary state and the auxiliary control in (11), we obtain (12).…”

Section: A Decoupled Dynamicsmentioning

confidence: 99%

“…pinning control [5], ensemble control [8]), low-rank (e.g. mean field) coupling [9]- [11], or patterned coupling [12].…”

Section: Introductionmentioning

confidence: 99%

Optimal and Approximate Solutions to Linear Quadratic Regulation of a Class of Graphon Dynamical Systems

Gao

Caines

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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In this paper we study the linear quadratic regulation (LQR) problem for dynamical systems coupled over largescale networks and obtain locally computable low-complexity solutions. The underlying large or even infinite networks are represented by graphons and the couplings appear in both the dynamics and the quadratic cost. The optimal solution is obtained first for graphon dynamical systems for the special case where the graphons are exactly characterized by finite spectral summands. The complexity of generating these control solutions involves solving d+1 scalar Riccati equations where d is the number of non-zero eigenvalues in the spectral representation. Based on this, we provide a suboptimal low-complexity solution for problems with general graphon couplings via spectral approximations and analyze the performance under the approximate control. Finally, a numerical example is given to illustrate the explicit solution and demonstrate the simplicity of the solution.

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“…A key theme for investigating large-scale networked control systems is to identify conditions under which the optimal control laws may be synthesized and implemented with low-complexity. Such conditions include simplified control objectives (e.g., consensus [7]- [11] and synchronization [16]), simplified control inputs (e.g., pinning control [17]- [19] and ensemble control [20]), simplified coupling between subsystems (e.g., symmetric interconnections [4], [12], [13], [21], [22], exchangeable or anonymous subsystems [23]- [26] and patterned systems [27]), approximate optimality (e.g., mean-field games [28]- [31], control based on approximate aggregations [32], approximate distributed control [33], and graphon control [34]).…”

Section: A Motivationmentioning

confidence: 99%

Networked control of coupled subsystems: Spectral decomposition and low-dimensional solutions

Gao

Mahajan

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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In this paper, we investigate optimal networked control of coupled subsystems where the dynamics and the cost couplings depend on an underlying undirected weighted graph. The graph coupling matrix may be the adjacency matrix, the Laplacian matrix, or any other symmetric matrix corresponding to the underlying graph. We use the spectral decomposition of the graph coupling matrix to decompose the overall system into (L + 1) systems with decoupled dynamics and cost, where L is the rank of the coupling matrix. Consequently, the optimal control input at each subsystem can be computed by solving at most (L + 1) decoupled Riccati equations. A salient feature of the result is that the solution complexity depends on the rank of the coupling matrix rather than the size of the network (i.e., the number of nodes). Therefore, the proposed solution framework provides a scalable method for synthesizing and implementing optimal control laws for large-scale networked control systems.

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Patterned linear systems

Cited by 13 publications

References 12 publications

An algebraic approach to hierarchical LQR synthesis for large-scale dynamical systems

An algebraic approach to hierarchical LQR synthesis for large-scale dynamical systems

Optimal and Approximate Solutions to Linear Quadratic Regulation of a Class of Graphon Dynamical Systems

Networked control of coupled subsystems: Spectral decomposition and low-dimensional solutions

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