An LMI approach to structured sparse feedback design in linear control systems

Polyak, B. T.; Khlebnikov, M. V.; Shcherbakov, Pavel

doi:10.23919/ecc.2013.6669578

Cited by 92 publications

(65 citation statements)

References 14 publications

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“…Alternatively, suboptimal solutions (in the sense that are based only on sufficient conditions) have been proposed (e.g. [23], [14], [18], [15]) where This work was supported in part by NSF grants ECCS-1404163 and DGE-0654176. ; AFOSR grant FA9559-12-1-0271; and DHS grant 2008-ST-061-ED0001.…”

Section: Introductionmentioning

confidence: 99%

Sparse static output feedback controller design via convex optimization

Wang

López

Sznaier

2014

53rd IEEE Conference on Decision and Control

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We consider the problem of designing a stabilizing static output feedback controller subject to a pre-specified sparsity pattern. While this problem is known to be NP-hard, our main result shows that a sequence of convergent convex relaxations can be obtained by recasting the problem into a polynomial optimization through the use of polyhedral Lyapunov functions. Moreover, as shown in the paper, combining these ideas with rank minimization tools leads to a computationally attractive algorithm. These results are illustrated with an example, where we show the effectiveness of the proposed approach vis-a-vis existing techniques.

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Section: Introductionmentioning

confidence: 99%

Sparse static output feedback controller design via convex optimization

Wang

López

Sznaier

2014

53rd IEEE Conference on Decision and Control

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“…Therefore, it is not very feasible to manually find a subset of all available components to meet a specific control objective. Hence, the problem of selecting a configuration of actuators (sensors) from the set of all available actuators (sensors), while the control performance remains at an acceptable level compared to the non-sparse performance, is a well-known problem in the literature of control theory; see for example Joshi and Boyd (2009) ;Polyak, Khlebnikov, and Shcherbakov (2013); Rogers (2000); Roy, Chepuri, and Leus (2013); Savkin and Evans (2002) ;Savkin, Evans, and Skafidas (2001).…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the problem of simultaneous sensor and actuator placement is considered in Güney and Eşkinat (2008) ;Nestorović and Trajkov (2013) employing heuristic optimisation-based methods. In Polyak et al (2013), an LMI approach is utilised for addressing this problem by incorporating certain forms of sparsity in the feedback gain. Further, an ADMM algorithm based method is proposed in Dhingra et al (2014) which addresses the problems of sensor and actuator selection separately.…”

Section: Introductionmentioning

confidence: 99%

A framework for optimal actuator/sensor selection in a control system

Argha

Savkin

et al. 2017

International Journal of Control

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When dealing with large-scale systems, manual selection of a subset of components (sensors/actuators), or equivalently identification of a favourable structure for the controller, that guarantees a certain closedloop performance, is not very feasible. This paper is dedicated to the problem of concurrent optimal selection of actuators/sensors which can equivalently be considered as the structure identification for the controller. In the context of a multi-channel ℋ 2 dynamic output feedback controller synthesis, we formulate and analyse a framework in which we incorporate two extra terms for penalising the number of actuators and sensors into the variational formulations of controller synthesis problems in order to induce a favourable controller structure. We then develop an explicit scheme as well as an iterative process for the purpose of dealing with the multiobjective problem of controller structure and control law co-design. It is also stressed that the immediate application of the proposed approach lies within the fault accommodation stage of a fault tolerant control scheme. By two numerical examples, we demonstrate the remarkable performance of the proposed approach.keywords Simultaneous actuator/sensor selection, regularisation, row/columnwise sparsification, linear matrix inequality, dynamic output feedback.

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“…Sparsity-promoting optimization has been applied to networked control in (Nagahara et al, 2014), where quantization errors and data rate can be reduced at the same time by sparse representation of control packets. Other examples of control applications include optimal controller placement by (Casas et al, 2012;Clason and Kunisch, 2012;Fardad et al, 2011), design of feedback gains by (Lin et al, 2013;Polyak et al, 2013), state estimation by (Charles et al, 2011), to name a few.…”

Section: Introductionmentioning

confidence: 99%

Continuous Hands-off Control by CLOT Norm Minimization

2017

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In this paper, we consider hands-off control via minimization of the CLOT (Combined L-One and Two) norm. The maximum hands-off control is the L 0 -optimal (or the sparsest) control among all feasible controls that are bounded by a specified value and transfer the state from a given initial state to the origin within a fixed time duration. In general, the maximum hands-off control is a bang-off-bang control taking values of ±1 and 0. For many real applications, such discontinuity in the control is not desirable. To obtain a continuous but still relatively sparse control, we propose to use the CLOT norm, a convex combination of L 1 and L 2 norms. We show by numerical simulation that the CLOT control is continuous and much sparser (i.e. has longer time duration on which the control takes 0) than the conventional EN (elastic net) control, which is a convex combination of L 1 and squared L 2 norms.

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An LMI approach to structured sparse feedback design in linear control systems

Cited by 92 publications

References 14 publications

Sparse static output feedback controller design via convex optimization

Sparse static output feedback controller design via convex optimization

A framework for optimal actuator/sensor selection in a control system

Continuous Hands-off Control by CLOT Norm Minimization

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