Some Fundamental Control Theory II: Feedback Linearization of Single Input Nonlinear Systems

Terrell, William J.

doi:10.2307/2589614

Cited by 5 publications

(3 citation statements)

References 6 publications

(18 reference statements)

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“…We have made extensive use of inverse systems, and these play an important role in feedback linearization (Terrell 1999b; Isidori 1995), i.e., linearization of nonlinear input–output systems by means of a state feedback, where, with the aid of the above normal forms, the inverse system is used (often implicitly) to cancel out the nonlinearities. The stability of the inverse system is important in this context and is determined by the stability of the internal dynamics of the system under consideration.…”

Section: The Second Subsystem Is Given (From Transmitter Release To Nmentioning

confidence: 99%

“…The relative degree is also sometimes called the relative order (Tsinias and Kalouptsidis 1983) or the characteristic number (Nijmeijer and van der Schaft 1990). For more on the relative degree, see, e.g., Terrell (1999b); Isidori (1995); Tsinias and Kalouptsidis (1983); Henson and Seborg (1997); Nijmeijer and van der Schaft (1990). …”

Section: The Second Subsystem Is Given (From Transmitter Release To Nmentioning

confidence: 99%

“…In this paper, we have made use of results in the literature on nonlinear control systems (see, e.g., Terrell ( 1999a , b ) and Khalil ( 2002 ) for some of the fundamentals). For instance, both the form ( 37 ) above and the form ( 41 ) below are normal forms for systems with the same number of inputs as outputs, so-called square systems (with uniform relative degree one, to be more specific, as we explain shortly).…”

Section: The Second Subsystem Is Given (From Transmitter Release To Nmentioning

confidence: 99%

See 2 more Smart Citations

Synapse fits neuron: joint reduction by model inversion

Scheer

Doelman

2017

Biol Cybern

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In this paper, we introduce a novel simplification method for dealing with physical systems that can be thought to consist of two subsystems connected in series, such as a neuron and a synapse. The aim of our method is to help find a simple, yet convincing model of the full cascade-connected system, assuming that a satisfactory model of one of the subsystems, e.g., the neuron, is already given. Our method allows us to validate a candidate model of the full cascade against data at a finer scale. In our main example, we apply our method to part of the squid’s giant fiber system. We first postulate a simple, hypothetical model of cell-to-cell signaling based on the squid’s escape response. Then, given a FitzHugh-type neuron model, we derive the verifiable model of the squid giant synapse that this hypothesis implies. We show that the derived synapse model accurately reproduces synaptic recordings, hence lending support to the postulated, simple model of cell-to-cell signaling, which thus, in turn, can be used as a basic building block for network models.

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Section: The Second Subsystem Is Given (From Transmitter Release To Nmentioning

confidence: 99%

Section: The Second Subsystem Is Given (From Transmitter Release To Nmentioning

confidence: 99%

Section: The Second Subsystem Is Given (From Transmitter Release To Nmentioning

confidence: 99%

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Synapse fits neuron: joint reduction by model inversion

Scheer

Doelman

2017

Biol Cybern

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Introduction

Ungureanu¹

2018

Pareto-Nash-Stackelberg Game and Control Theory

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On the outputs of linear control systems

Shapiro

2008

Journal of Mathematical Analysis and Applications

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This paper studies autonomous, single-input, single-output linear control systems on finite time intervals. The object of interest is the output operator O, which associates to each input function and initial state vector the corresponding system output. Main result: If the system has relative degree r < ∞, then for any "admissible" Banach space U of inputs, O is a bounded operator taking U × C n onto the "Sobolev space" of complex functions f ∈ C (r−1) ([0, T ]) for which the (r − 1)-order derivative f (r−1) is absolutely continuous, with f (r) ∈ U . This completes recent results of Jönsson and Martin [Ulf Jönsson, Clyde Martin, Approximation with the output of linear control systems, J. Math. Anal. Appl. 329 (2007) 798-821] who showed that if the system is minimal and U is either L 2 ([0, T ]) or C([0, T ]), then O : U × C n → U has dense range.

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Some Fundamental Control Theory II: Feedback Linearization of Single Input Nonlinear Systems

Cited by 5 publications

References 6 publications

Synapse fits neuron: joint reduction by model inversion

Synapse fits neuron: joint reduction by model inversion

Introduction

On the outputs of linear control systems

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