Note on a change of coordinates for nonlinear SISO systems with singular points

Research output: Contribution to conferencePaperResearch

Abstract

In the paper titled `Asymptotic Output Tracking Through Singular Points for a class of Uncertain SISO Nonlinear Systems', a transformation T:Rn×R+→Rn+β which takes (x,t)qq(Z,ζ,Φ) defined by Z1 = h(x) Z2 = Lfh(x)qqZα = Lfα-1h(x) ζα+1 = a0(x)+b0(x)u ζα+2 = a1(x,u)+b0(x)u′+b1(x,u)u ζα+3 = a2(x,u,u′)+b2(x,u,u′)u+2b1(x,u)u′+ b0( x)u″qqζα+β = aβ-1(x,u,qq,u(β-2))+bβ-1(x,u, qq,u( β-2))u+qq+b0(x)u(β-1) {Φi(x)}i = α+1n was proposed in order to get rid of the singularity and being able to compute an admissible control u. There was also discussed that T was formed by at least n linearly independent functions as long as x≠xs i.e., no singular points, (this was assumed when x = xs). The main purpose of this paper is to present a proof where it is shown that T given by (1) provides us with a set of at least n linearly independent functions in case of having singular points.
Original languageAmerican English
Pages2973-2974
Number of pages2675
StatePublished - 1 Jan 1993
Externally publishedYes
EventAmerican Control Conference -
Duration: 1 Jan 1993 → …

Conference

ConferenceAmerican Control Conference
Period1/01/93 → …

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SISO (control systems)
nonlinear systems
output

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Retchkiman, Z. (1993). Note on a change of coordinates for nonlinear SISO systems with singular points. 2973-2974. Paper presented at American Control Conference, .
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abstract = "In the paper titled `Asymptotic Output Tracking Through Singular Points for a class of Uncertain SISO Nonlinear Systems', a transformation T:Rn×R+→Rn+β which takes (x,t)qq(Z,ζ,Φ) defined by Z1 = h(x) Z2 = Lfh(x)qqZα = Lfα-1h(x) ζα+1 = a0(x)+b0(x)u ζα+2 = a1(x,u)+b0(x)u′+b1(x,u)u ζα+3 = a2(x,u,u′)+b2(x,u,u′)u+2b1(x,u)u′+ b0( x)u″qqζα+β = aβ-1(x,u,qq,u(β-2))+bβ-1(x,u, qq,u( β-2))u+qq+b0(x)u(β-1) {Φi(x)}i = α+1n was proposed in order to get rid of the singularity and being able to compute an admissible control u. There was also discussed that T was formed by at least n linearly independent functions as long as x≠xs i.e., no singular points, (this was assumed when x = xs). The main purpose of this paper is to present a proof where it is shown that T given by (1) provides us with a set of at least n linearly independent functions in case of having singular points.",
author = "Zvi Retchkiman",
year = "1993",
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Retchkiman, Z 1993, 'Note on a change of coordinates for nonlinear SISO systems with singular points' Paper presented at American Control Conference, 1/01/93, pp. 2973-2974.

Note on a change of coordinates for nonlinear SISO systems with singular points. / Retchkiman, Zvi.

1993. 2973-2974 Paper presented at American Control Conference, .

Research output: Contribution to conferencePaperResearch

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