Geometric control of patterned linear systems

Hamilton, Sarah C.; Broucke, Mireille E.

doi:10.1109/cdc.2010.5717513

Cited by 10 publications

(2 citation statements)

References 6 publications

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“…Remark 3. Linear spatio-temporally symmetric systems are related to patterned systems, introduced in Hamilton and Broucke [2012a] and Hamilton and Broucke [2012b]. In fact, if Γ = Σ = Θ and A,B,C,D are constant, conditions (6a)-(6d) imply that A, B, C, D commute with Γ.…”

Section: Stabilization Of Spatio-temporally Symmetric Trajectoriesmentioning

confidence: 99%

Spatio-temporal symmetries in control systems: an application to formation control

Consolini

Tosques

2013

IFAC Proceedings Volumes

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Section: Stabilization Of Spatio-temporally Symmetric Trajectoriesmentioning

confidence: 99%

Spatio-temporal symmetries in control systems: an application to formation control

Consolini

Tosques

2013

IFAC Proceedings Volumes

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“…In particular, this paper addresses the problem of ensuring that each output component comprises a preassigned set of closed-loop modes, possibly including the invariant zeros of the system. In order to prove this result, a new framework is introduced which links classical results of geometric control theory [30,3,28,6,10] with the theory of combinatorics [24,23,14] that enables the solvability conditions to be expressed in terms of specific and easily computable controlled invariant subspaces which are completely defined in terms of the parameters of the problem. It is also worth mentioning that the methodology developed in this paper is constructive in nature, because it allows to immediately compute the suitable feedback matrix that solves the problem whenever such matrix exists.…”

Section: Introductionmentioning

confidence: 99%

A Structural Approach to State-to-Output Decoupling

Garone¹,

Ntogramatzidis²,

Padula³

2018

SIAM J. Control Optim.

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In this paper, we address a general eigenstructure assignment problem where the objective is to distribute the closed-loop modes over the components of the system outputs in such a way that, if a certain mode appears in a given output, it is unobservable from any of the other output components. By linking classical geometric control results with the theory of combinatorics, we provide necessary and sufficient conditions for the solvability of this problem, herein referred to as state-to-output decoupling, under very mild assumptions.We propose solvability conditions expressed in terms of the dimensions of suitably defined controlled invariant subspaces of the system. In this way, the solvability of the problem can be evaluated a priori, in the sense that it is given in terms of the problem/system data.Finally, it is worth mentioning that the proposed approach is constructive, so that when a controller that solves the problem indeed exists, it can be readily computed by using the machinery developed in this paper. structure assignment.will be referred to as state-to-output decoupling.This property appears to be a particularly important feature of the problem considered in this paper. For example, it links with some problems of security in large-scale complex systems, see [22], [29] and the references cited therein. Indeed, the idea behind the state-to-output decoupling is the fact that, from each output component, only a certain subset of the system modes is observable; this means that, in the context of secure control, an attacker needs to have access to the information originating from all the sensors in order to reconstruct the state of the system. In this way, if the information coming from a sensor is compromised, it is not possible to reconstruct the entire state of the system, but only a portion of it.Furthermore, the machinery developed in this paper can be used as a building block to solve a variety of other important control problems. For instance it allows to drastically reduce the computational burden in the calculation of the matrix exponential of the closed-loop system. Other applications arise in the context of the fault detection and non-interacting control literature, see e.g. [31]. Indeed, a number of those problems, for which only a posteriori solvability conditions are currently available in the literature, can be viewed as reformulations of the state-to-output decoupling problem. Thus, the methodology provided in this paper provides a solution to the aforementioned problems in terms of the problem data, which is therefore a priori.Among the problems that can be dealt with as state-to-output decoupling, one that stands out is the monotonic tracking control for those systems for which the necessary and sufficient conditions of [20] do not hold. Indeed, such systems may still exhibit a non-overshooting and non-undershooting response, and the shape and size of the set of initial conditions for which this is the case depends on the number of closed-loop modes appearing in each output component.More...

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Input and Output Symmetric Dynamical Systems: Features and Control Design

Kőnigsmarková,

Schlegel

2022

Lecture Notes in Control and Information Sciences - Proceedings

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Geometric control of patterned linear systems

Cited by 10 publications

References 6 publications

Spatio-temporal symmetries in control systems: an application to formation control

Spatio-temporal symmetries in control systems: an application to formation control

A Structural Approach to State-to-Output Decoupling

Input and Output Symmetric Dynamical Systems: Features and Control Design

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