Algebraic Methods for Nonlinear Control Systems

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

doi:10.1007/978-1-84628-595-0

Cited by 131 publications

(84 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Roughly speaking, (42) is controllable if one can steer it from any point x 0 ∈ M to any other point x 1 ∈ M by choosing u from a set of admissible controls U, which is a subset of functions mapping R + to U. The controllability of nonlinear systems has been extensively studied since the early 1970s (Brockett, 1972;Conte et al, 2007;Elliot, 1970;de Figueiredo and Chen, 1993;Haynes and Hermes, 1970;Hermann and Krener, 1977;Isidori, 1995;Lobry, 1970;Nijmeijer and van der Schaft, 1990;Rugh, 1981;Sontag, 1998;Sussmann and Jurdjevic, 1972). The goal was to derive results of similar reach and generality as obtained for linear time-invariant systems.…”

Section: Controllability Of Nonlinear Systemsmentioning

confidence: 99%

See 1 more Smart Citation

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

536

349

View full text Add to dashboard Cite

A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: it requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

show abstract

Section: Controllability Of Nonlinear Systemsmentioning

confidence: 99%

“…Mathematically, we can quantify observability from either an algebraic viewpoint (Conte et al, 2007;Diop and Fliess, 1991a,b) or a differential geometric viewpoint (Hermann and Krener, 1977). Here we focus on the former.…”

Section: Nonlinear Systemsmentioning

confidence: 99%

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

536

349

View full text Add to dashboard Cite

show abstract

“…Below we give a brief exposition of the linear algebraic approach based on differential forms [5]. Let K denote the field of meromorphic functions in a finite number of independent system variables from the infinite set C = y,ẏ, .…”

Section: Algebraic Frameworkmentioning

confidence: 99%

“…Once a system is in the observer form, the design of the nonlinear observer with linearizable error dynamics is relatively easy. The earliest methods, relying on a state transformation only (see [2,5,10,15]), provide restrictive conditions for the existence of the observer form for a nonlinear control system. This fact motivates various extensions and generalizations to enlarge the class of systems for which the observer with linear error dynamics can be constructed.…”

Section: Introductionmentioning

confidence: 99%

Transformation of nonlinear state equations into the observer form: Necessary and sufficient conditions in terms of one-forms

Kaparin¹,

Kotta²

2015

Kybernetika

View full text Add to dashboard Cite

“…Here we will consider the observability problem based on algebra. Some basic notations and terminologies we refer readers to reference [12]. Definition 4.1: The element of quotient field K of the ring of analytic functions is called meromorphic function.…”

Section: Algebraic Criterion On Structural Observability Condition mentioning

confidence: 99%

Structural Conditions on Observability of Nonlinear Systems

Ma¹

2011

IJITCS

View full text Add to dashboard Cite

Abstract-In this paper parameter space and Lebesgue measurement are introduced into analysis of nonlinear systems. Structural observability rank condition is defined and together with the distinguishabililty the structural observability criterions of nonlinear systems are obtained. It proves that when the parameters are not identifiable the solutions with the same time but different parameters are also indistinguishable. Differential geometry and algebraic methods are used to investigate the observability problem, and it is proved that there are some relations between these two methods. Finally, examples are used to illustrate applications of the structural observability criterions.

show abstract

Algebraic Methods for Nonlinear Control Systems

Abstract: Algebraic methods for nonlinear control systems. -2nd ed. -(Communications and control engineering) 1. Nonlinear control theory I.

Cited by 131 publications

References 0 publications

Control principles of complex systems

Control principles of complex systems

Transformation of nonlinear state equations into the observer form: Necessary and sufficient conditions in terms of one-forms

Structural Conditions on Observability of Nonlinear Systems

Contact Info

Product

Resources

About