Sparse feedback in linear control systems

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

doi:10.1134/s0005117914120029

Cited by 35 publications

(14 citation statements)

References 7 publications

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“…Lastly, note that a similar procedure to Algorithm 1 can be formulated for actuator selection by considering the relative norm of rows in F n , each corresponding to an actuator represented as a column of the input matrix B in (3.1). These ideas are closely related to sparse controller synthesis techniques based on convex optimization, which can be used to explicitly promote sparsity and design controller gains with many columns or rows of all zeros (Lin et al 2013;Polyak et al 2014).…”

Section: Sensor Selection By Column-norm Evaluation (Ce)mentioning

confidence: 99%

Feedback control of transitional shear flows: Sensor selection for performance recovery

Yao¹,

Sun²,

Hemati³

2020

Preprint

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The choice and placement of sensors and actuators is an essential factor determining the performance that can be realized using feedback control. This determination is especially important, but difficult, in the context of controlling transitional flows. The highly non-normal nature of the linearized Navier-Stokes equations makes the flow sensitive to small perturbations, with potentially drastic performance consequences on closed-loop flow control performance. Full-information controllers, such as the linear quadratic regulator (LQR), have demonstrated some success in reducing transient energy growth and suppressing transition; however, sensor-based output feedback controllers with comparable performance have been difficult to realize. In this study, we propose two methods for sensor selection that enable sensor-based output feedback controllers to recover full-information control performance: one based on a sparse controller synthesis approach, and one based on a balanced truncation procedure for model reduction. Both approaches are investigated within linear and nonlinear simulations of a sub-critical channel flow with blowing and suction actuation at the walls. We find that sensor configurations identified by both approaches allow sensor-based static output feedback LQR controllers to recover full-information LQR control performance, both in reducing transient energy growth and suppressing transition. Further, our results indicate that both the sensor selection methods and the resulting controllers exhibit robustness to Reynolds number variations.

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Section: Sensor Selection By Column-norm Evaluation (Ce)mentioning

confidence: 99%

Feedback control of transitional shear flows: Sensor selection for performance recovery

Yao¹,

Sun²,

Hemati³

2020

Preprint

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“…More recent work in dynamical systems [81] resumes again 1 -minimization emphasizing its sparsifying power. We also refer to the recent and very appropriate paper [71] on sparse stabilization of linear dynamical systems. Also in optimal control with partial differential equation constraints it became rather popular to use L 1 -minimization to enforce sparsity of controls, for instance in the modeling of optimal placing of actuators or sensors [20,23,24,49,75,82].…”

Section: Sparse Controllability Of Multi-agent Systemsmentioning

confidence: 99%

Learning and sparse control of multiagent systems

Fornasier

2018

European Congress of Mathematics

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“…If the system has a single input, this problem is exactly the same as the conventional sparse control problem. However, if this is not the case, the problem is somewhat different from the conventional problems, [1][2][3][4][5] in which sparsity is maximized in the elementwise sense.…”

Section: Introductionmentioning

confidence: 99%

Maximum turn‐off control for discrete‐time linear systems

Iwata

Azuma

Ariizumi

et al. 2022

Intl J Robust & Nonlinear

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We aim to address the problem of finding a control input maximizing the time instants when all control channels take a zero‐value (are turned off) while stabilizing the system to zero over a given horizon length. This problem is called the maximum turn‐off control problem. To solve it, we reduce the problem into a block‐sparse optimization problem with respect to the control input sequence, where the ℓ2false/ℓ0$$ {\ell}_2/{\ell}_0 $$ norm of the control input sequence is the objective function that must be minimized. Because the problem is not convex, we introduce a relaxed problem based on the ℓ2false/ℓ1$$ {\ell}_2/{\ell}_1 $$ norm, which is a convex function, and characterize the equivalence relation between the original and relaxed problems using the so‐called block restricted isometry property (block‐RIP). Based on the equivalence, the solution can be obtained by solving the convex relaxed problem. However, the block‐RIP is not easy to interpret and verify. Thus, we propose the notion of sparse controllability Gramians, which is an extension of the controllability Gramians, and show that the block‐RIP can be interpreted by the eigenvalues of the sparse controllability Gramian. This study presents an easy‐to‐check condition of the block‐RIP. Moreover, the above control framework is extended to a model predictive control scheme. These results are demonstrated using numerical examples.

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Sparse feedback in linear control systems

Cited by 35 publications

References 7 publications

Feedback control of transitional shear flows: Sensor selection for performance recovery

Feedback control of transitional shear flows: Sensor selection for performance recovery

Learning and sparse control of multiagent systems

Maximum turn‐off control for discrete‐time linear systems

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