Algebraic Methods for Nonlinear Control Systems

Conte, G.; Moog, Claude H.; Perdon, Anna Maria

doi:10.1109/tac.2007.911476

Cited by 89 publications

(141 citation statements)

References 5 publications

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“…Characterizing the structural accessibility of G requires us to define the notion of autonomous element for impulsive control systems for the first time (Definitions 3 in SI-2), since this notion has been studied only for systems with continuous control inputs [33]. We then characterized the conditions for the absence of autonomous elements for a given pair {f, g}, finding that, surprisingly, such conditions are identical for systems with continuous and impulsive control (Theorem 2 and Remark 3 in SI-2).…”

Section: Structural Accessibilitymentioning

confidence: 99%

“…Note that the zero-nonzero patterns of the matrices A ∈ R n×n and B ∈ R m×n are fully determined by G c . Note also that, for linear systemsẋ = Ax + Bu, the absence of autonomous elements is equivalent to their (linear) controllability [33] -the intrinsic ability to steer these linear systems between two arbitrary states, which can be verified by the famous Kalman's rank condition:…”

Section: -Structural Accessibilitymentioning

confidence: 99%

See 1 more Smart Citation

Controlling complex microbial communities: a network-based approach

Angulo

Moog

Liu

2017

Preprint

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Microbes comprise nearly half of all biomass on Earth. Almost every habitat on Earth is teeming with microbes, from hydrothermal vents to the human gastrointestinal tract. Those microbes form complex communities and play critical roles in maintaining the integrity of their environment or the well-being of their hosts. Controlling microbial communities can help us restore natural ecosystems and maintain healthy human microbiota. Yet, our ability to precisely manipulate microbial communities has been fundamentally impeded by the lack of a systematic framework to control them. Here we fill this gap by developing a control framework based on the new notion of structural accessibility. This framework allows identifying minimal sets of “driver species” through which we can achieve feasible control of the entire microbial community. We numerically validate our control framework on large microbial communities, and then we demonstrate its application for controlling the gut microbiota of gnotobiotic mice infected with Clostridium difficile and the core microbiota of the sea sponge Ircinia oros.

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Section: Structural Accessibilitymentioning

confidence: 99%

Section: -Structural Accessibilitymentioning

confidence: 99%

Controlling complex microbial communities: a network-based approach

Angulo

Moog

Liu

2017

Preprint

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“…Conditions for the transformation of nonlinear systems into more general forms than exact linear systems have been explored. These classes of systems consists in systems which are made up of a particular linear part and a nonlinear part satisfying some Keywords and phrases: homogeneity, approximations, local observer conditions, and are characterized using algebro-geometric tools, see [3,5,10,21,24] for example. The common point in all these approaches is that the output function is always linearized, hence, this still restrict the class of systems considered while it allows to obtain global or semi-global convergence.…”

Section: Introductionmentioning

confidence: 99%

Homogeneous approximations and local observer design

2013

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Abstract. This paper is concerned with the construction of local observers for nonlinear systems without inputs, satisfying an observability rank condition. The aim of this study is, rst, to dene an homogeneous approximation that keeps the observability property unchanged at the origin. This approximation is further used in the synthesis of a local observer which is proven to be locally convergent for Lyapunov-stable systems. We compare the performance of the homogeneous approximation observer with the classical linear approximation observer on an example.

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“…Several ways of investigation have been borrowed. Linearization of nonlinear system with algebraic methods have been investigated in [1] and [2]. The high-gain observer approach which is closely related to triangular structure has been developped by Gauthier et al (see [3] and [4]) and is derived from the uniform observability of nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%