Minimal Actuator Placement With Bounds on Control Effort

Tzoumas, Vasileios; Rahimian, Mohammad Amin; Pappas, George J.; Jadbabaie, Ali

doi:10.1109/tcns.2015.2444031

Cited by 185 publications

(161 citation statements)

References 32 publications

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“…is far from solved although several different approaches have been tried. It is for instance formulated as an optimization problem in Tzoumas et al (2016) and Summers et al (2016). Another way to approach the problem is to quantify the importance of the different nodes for controllability with network centrality measures (Bof et al, 2017;Pasqualetti et al, 2014), see also Papers B and C.…”

Section: Minimum Energy Control Of Complex Networkmentioning

confidence: 99%

“…It could for instance be the case that completely unreasonable amounts of control energy are required to steer the network in some directions. In the context of large-scale networks, the need to achieve a "practical degree of controllability" is much more pressing than in classical (small-scale) control systems (Bof et al, 2017;Chen et al, 2016;Li et al, 2016;Nacher and Akutsu, 2014;Olshevsky, 2016;Pasqualetti et al, 2014;Summers et al, 2016;Tzoumas et al, 2016;Yan et al, 2012Yan et al, , 2015.…”

Section: Introductionmentioning

confidence: 99%

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Methods and algorithms for control input placement in complex networks

Lindmark¹

2018

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The control-theoretic notion of controllability captures the ability to guide a systems behavior toward a desired state with a suitable choice of inputs. Controllability of complex networks such as traffic networks, gene regulatory networks, power grids etc. brings many opportunities. It could for instance enable improved efficiency in the functioning of a network or lead to that entirely new applicative possibilities emerge. However, when control theory is applied to complex networks like these, several challenges arise. This thesis consider some of these challenges, in particular we investigate how control inputs should be placed in order to render a given network controllable at a minimum cost, taking as cost function either the number of control inputs or the energy that they must exert. We assume that each control input targets only one node (called a driver node) and is either unconstrained or unilateral.A unilateral control input is one that can assume either positive or negative values but not both. Motivated by the many applications where unilateral controls are common, we reformulate classical controllability results for this particular case into a more computationally-efficient form that enables a large scale analysis. We show that the unilateral controllability problem is to a high degree structural and derive theoretical lower bounds on the minimal number of unilateral control inputs from topological properties of the network, similar to the bounds that exists for the minimal number of unconstrained control inputs. Moreover, an algorithm is developed that constructs a near minimal number of control inputs for a given network. When evaluated on various categories of random networks as well as a number of real-world networks, the algorithm often achieves the theoretical lower bounds.A network can be controllable in theory but not in practice when completely uneasonable amounts of control energy are required to steer it in some direction. For unconstrained control inputs we show that the control energy depends on the time constants of the modes of the network, and that the closer the eigenvalues are to the imaginary axis of the complex plane, the less energy is required for control. We also investigate the problem of placing driver nodes such that the control energy requirements are minimized (assuming that theoretical controllability is not an issue). For the special case with networks having all purely imaginary eigenvalues, several constructive algorithms for driver node placement are developed. In order to understand what determines the control energy in the general case with arbitrary eigenvalues, we define two centrality measures for the nodes based on energy flow considerations: the first centrality reflects the network impact of a node and the second the ability to control it indirectly. It turns out that whether a node is suitable as driver node or not largely depends on these two qualities. By combining the centralities into node rankings we obtain driver node placements that signific...

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Section: Minimum Energy Control Of Complex Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Methods and algorithms for control input placement in complex networks

Lindmark¹

2018

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“…Exact solutions to MCP are explored in [5], and in [6], using graph theoretical constructions, the minimal controllability problem is shown to be polynomially solvable for almost all numerical realizations of the dynamic matrix, satisfying a predefined pattern of zeros/nonzeros. Alternatively, in [7], [8], [9], [10] the configuration of actuators is sought to ensure certain performance criteria; more precisely, [7], [8], [10] focus on optimizing properties of the controllability Grammian, whereas [9] studies leader selection problems, in which leaders are viewed as inputs to the system, and the selection criteria aims to speed up convergence. In addition, in [9], [7], [8] the submodularity properties of functions of the controllability Grammian are explored, and design algorithms are proposed that achieve feasible placement with certain guarantees on the optimality gap.…”

Section: Related Workmentioning

confidence: 99%

“…Alternatively, in [7], [8], [9], [10] the configuration of actuators is sought to ensure certain performance criteria; more precisely, [7], [8], [10] focus on optimizing properties of the controllability Grammian, whereas [9] studies leader selection problems, in which leaders are viewed as inputs to the system, and the selection criteria aims to speed up convergence. In addition, in [9], [7], [8] the submodularity properties of functions of the controllability Grammian are explored, and design algorithms are proposed that achieve feasible placement with certain guarantees on the optimality gap. The I/O selection problem considered in the present paper differs from the aforementioned problems in the following two aspects: first, the selection of the inputs is restricted to belong to a specific given set of possible inputs, i.e., we study constrained input placement, and, hence, differing from [4], [5], [6] in which unconstrained input placement is studied.…”

Section: Related Workmentioning

confidence: 99%

Minimum cost constrained input-output and control configuration co-design problem: A structural systems approach

Pequito

Kar

Pappas

2015

2015 American Control Conference (ACC)

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In this paper, we study the minimal cost constrained input-output (I/O) and control configuration co-design problem. Given a linear time-invariant plant, where a collection of possible inputs and outputs is known a priori, we aim to determine the collection of inputs, outputs and communication among them incurring in the minimum cost, such that desired control performance, measured in terms of arbitrary poleplacement capability of the closed-loop system, is ensured. We show that this problem is NP-hard in general (in the size of the state space). However, the subclass of problems, in which the dynamic matrix is irreducible, is shown to be polynomially solvable and the corresponding algorithm is presented. In addition, under the same assumption, the same algorithm can be used to solve the minimal cost constrained I/O selection problem, and the minimal cost control configuration selection problem, individually. In order to illustrate the main results of this paper, some simulations are also provided.

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“…For example, its nonsingularity indicates that the network is controllable; its eigenvalues quantify the minimum control energy required to steer the network state along the eigenvectors [Yan et al 2012, Pasqualetti et al 2014, Cortesi et al 2014, Kumar et al 2015, Yan et al 2015, Bof et al 2016, Zhao and Cortes 2016, Tzoumas et al 2016; and its trace measures how robust the network state is against external disturbance [Summers et al 2016, Zhou et al 1995. It is of great interest to identify the connections from these properties to the network structure and weights.…”

Section: Introductionmentioning

confidence: 99%