Category:Solution characterization - Revision history

FelixMueller at 12:58, 28 January 2016

2016-01-28T12:58:03Z

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	~~[[Category:Main]]~~
	[[Category:Problem characterization]]		[[Category:Problem characterization]]

FelixMueller at 12:57, 28 January 2016

2016-01-28T12:57:20Z

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			[[Category:Main]]
	[[Category:Problem characterization]]		[[Category:Problem characterization]]

JonasSchulze: Text replacement - "" to ""

2016-01-23T10:10:58Z

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

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

	[[Category:Problem characterization]]		[[Category:Problem characterization]]

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

2016-01-20T17:54:24Z

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

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	The classification that we propose for switching decisions is based on insight from Pontryagin's maximum principle <~~bibref>~~Pontryagin1962</~~bibref~~> applied here only to the relaxation of the binary control functions <math>\omega(\cdot)</math>, denoted by <math>\alpha(\cdot) \in [0,1]^{n_\omega}</math>. In the analysis of linear control problems one distinguishes three cases: bang-bang arcs, sensitivity-seeking arcs, and path-constrained arcs, <~~bibref>~~Srinivasan2003</~~bibref~~>, where an arc is defined to be a nonzero time-interval. Of course a problem's solution can show two or even all three behaviors at once on different time arcs.		The classification that we propose for switching decisions is based on insight from Pontryagin's maximum principle <bib id="Pontryagin1962" /> applied here only to the relaxation of the binary control functions <math>\omega(\cdot)</math>, denoted by <math>\alpha(\cdot) \in [0,1]^{n_\omega}</math>. In the analysis of linear control problems one distinguishes three cases: bang-bang arcs, sensitivity-seeking arcs, and path-constrained arcs, <bib id="Srinivasan2003" />, where an arc is defined to be a nonzero time-interval. Of course a problem's solution can show two or even all three behaviors at once on different time arcs.

	Additionally we characterize solutions, whenever chattering or sliding mode behavior occurs.		Additionally we characterize solutions, whenever chattering or sliding mode behavior occurs.

SebastianSager: Initial setup of IMA paper text

2010-11-20T12:19:03Z

Initial setup of IMA paper text

← Older revision		Revision as of 12:19, 20 November 2010
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	~~In this category all sub-categories are listed~~ that ~~describe specific behavior~~ of ~~an optimal solution~~. ~~Hence~~, ~~all problems can be identified that share common characteristics~~, ~~such as~~ an ~~optimal relaxed~~ solution ~~of bang bang type~~.		The classification that we propose for switching decisions is based on insight from Pontryagin's maximum principle <bibref>Pontryagin1962</bibref> applied here only to the relaxation of the binary control functions <math>\omega(\cdot)</math>, denoted by <math>\alpha(\cdot) \in [0,1]^{n_\omega}</math>. In the analysis of linear control problems one distinguishes three cases: bang-bang arcs, sensitivity-seeking arcs, and path-constrained arcs, <bibref>Srinivasan2003</bibref>, where an arc is defined to be a nonzero time-interval. Of course a problem's solution can show two or even all three behaviors at once on different time arcs.

			Additionally we characterize solutions, whenever chattering or sliding mode behavior occurs.

			== References ==
			<bibreferences/>

	[[Category:Problem characterization]]		[[Category:Problem characterization]]

SebastianSager: New page: In this category all sub-categories are listed that describe specific behavior of an optimal solution. Hence, all problems can be identified that share common characteristics, such as an o...

2008-11-09T13:01:24Z

New page: In this category all sub-categories are listed that describe specific behavior of an optimal solution. Hence, all problems can be identified that share common characteristics, such as an o...

New page

In this category all sub-categories are listed that describe specific behavior of an optimal solution. Hence, all problems can be identified that share common characteristics, such as an optimal relaxed solution of bang bang type.

[[Category:Problem characterization]]