Category:Chattering - Revision history

JonasSchulze: Text replacement - "" to ""

2016-01-23T10:10:58Z

Text replacement - "<bibreferences/>" to "<biblist />"

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	== References ==		== References ==
	<~~bibreferences~~/>		<biblist />

	[[Category:Solution characterization]]		[[Category:Solution characterization]]

JonasSchulze: Text replacement - "\(.*)\<\/bibref\>" to ""

2016-01-20T17:54:24Z

Text replacement - "\<bibref\>(.*)\<\/bibref\>" to "<bib id="$1" />"

← Older revision		Revision as of 17:54, 20 January 2016
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	This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching.		This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching.

	If an optimal control problem has sensitivity-seeking or path-constrained arcs, a bang-bang solution may have to switch infinitely often in a finite time interval to approximate the optimal solution. This behavior is referred to as 'chattering' in the optimal control community <~~bibref>~~Zelikin1994</~~bibref~~>. The first example of an optimal control problem exhibiting chattering behavior was given by [[Fuller's problem \| Fuller]].		If an optimal control problem has sensitivity-seeking or path-constrained arcs, a bang-bang solution may have to switch infinitely often in a finite time interval to approximate the optimal solution. This behavior is referred to as 'chattering' in the optimal control community <bib id="Zelikin1994" />. The first example of an optimal control problem exhibiting chattering behavior was given by [[Fuller's problem \| Fuller]].

	In the engineering community chattering behavior is called ''Zeno's phenomenon''. This refers to the great ancient philosopher [http://en.wikipedia.org/wiki/Zeno_of_Elea Zeno of Elea]. Zeno of Elea was a pre-Socratic Greek philosopher of southern Italy and a pupil of [http://en.wikipedia.org/wiki/Parmenides Parmenides]. He is mostly known for his 40 paradoxes, among which the most famous are		In the engineering community chattering behavior is called ''Zeno's phenomenon''. This refers to the great ancient philosopher [http://en.wikipedia.org/wiki/Zeno_of_Elea Zeno of Elea]. Zeno of Elea was a pre-Socratic Greek philosopher of southern Italy and a pupil of [http://en.wikipedia.org/wiki/Parmenides Parmenides]. He is mostly known for his 40 paradoxes, among which the most famous are

SebastianSager at 12:31, 20 November 2010

2010-11-20T12:31:29Z

← Older revision		Revision as of 12:31, 20 November 2010
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	Zeno of Elea was the first to draw attention to the apparent interpretational problems occurring whenever an infinite number of events have to take place in a finite time interval.		Zeno of Elea was the first to draw attention to the apparent interpretational problems occurring whenever an infinite number of events have to take place in a finite time interval.

			== References ==
			<bibreferences/>

	[[Category:Solution characterization]]		[[Category:Solution characterization]]

SebastianSager: added Zeno

2008-11-29T15:18:47Z

added Zeno

← Older revision		Revision as of 15:18, 29 November 2008
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	This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching.		This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching.

			If an optimal control problem has sensitivity-seeking or path-constrained arcs, a bang-bang solution may have to switch infinitely often in a finite time interval to approximate the optimal solution. This behavior is referred to as 'chattering' in the optimal control community <bibref>Zelikin1994</bibref>. The first example of an optimal control problem exhibiting chattering behavior was given by [[Fuller's problem \| Fuller]].

			In the engineering community chattering behavior is called ''Zeno's phenomenon''. This refers to the great ancient philosopher [http://en.wikipedia.org/wiki/Zeno_of_Elea Zeno of Elea]. Zeno of Elea was a pre-Socratic Greek philosopher of southern Italy and a pupil of [http://en.wikipedia.org/wiki/Parmenides Parmenides]. He is mostly known for his 40 paradoxes, among which the most famous are

			* '''The Dichotomy.'''
			Motion is impossible since ''that which is in locomotion must arrive at the half-way stage before it arrives at the goal.''

			* '''The Arrow.'''
			''If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.''

			* '''The Achilles.'''
			''In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.''

			Zeno of Elea was the first to draw attention to the apparent interpretational problems occurring whenever an infinite number of events have to take place in a finite time interval.


	[[Category:Solution characterization]]		[[Category:Solution characterization]]

SebastianSager at 13:01, 9 November 2008

2008-11-09T13:01:52Z

← Older revision		Revision as of 13:01, 9 November 2008
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	This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching.		This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching.

	[[Category:~~Problem~~ characterization]]		[[Category:Solution characterization]]

SebastianSager at 12:54, 9 November 2008

2008-11-09T12:54:55Z

← Older revision		Revision as of 12:54, 9 November 2008
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	This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching.		This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching.

	[[Category:Problem ~~charakterization~~]]		[[Category:Problem characterization]]

SebastianSager at 12:54, 9 November 2008

2008-11-09T12:54:45Z

← Older revision		Revision as of 12:54, 9 November 2008
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	This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching.		This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching.

	[[Category:Problem ~~Category~~]]		[[Category:Problem charakterization]]

SebastianSager: New page: This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching. Category:Problem Category

2008-10-29T17:56:20Z

New page: This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching. Category:Problem Category

New page

This is a category with all control problems that exhibit chattering behavior, i.e., the optimal solution only exists in the limit of infinite switching.

[[Category:Problem Category]]