Gillespie algorithm - Revision history

199.184.22.6: added presentation date

2014-12-16T21:50:13Z

added presentation date

← Older revision		Revision as of 23:50, 16 December 2014
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	~~Marvella~~ is ~~what you can contact her but it~~'~~s not the most feminine title out there~~. ~~Hiring is~~ his ~~occupation~~. ~~The factor she adores most is physique building and~~ now ~~she~~ is ~~attempting to earn money with it. California is our beginning location~~.<br><br>Also visit my ~~web site ::~~ over the counter std test - [http://~~moodle~~.~~kspu~~.~~karelia.ru~~/~~user~~/view~~.php?id=23302&course=1 web link~~] -		They call me Emilia. To do aerobics is a thing that I'm totally addicted to. His family life in South Dakota but his spouse wants them to move. He used to be unemployed but now he is a pc operator but his marketing never arrives.<br><br>Also visit my page over the counter std test, [http://www.adosphere.com/member/28512/blog/view/66112/ check out your url],

194.225.239.94 at 11:18, 17 February 2014

2014-02-17T11:18:44Z

← Older revision		Revision as of 13:18, 17 February 2014
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	~~{{Unreferenced\|date=December 2009}}~~		Marvella is what you can contact her but it's not the most feminine title out there. Hiring is his occupation. The factor she adores most is physique building and now she is attempting to earn money with it. California is our beginning location.<br><br>Also visit my web site :: over the counter std test - [http://moodle.kspu.karelia.ru/user/view.php?id=23302&course=1 web link] -
	~~{{Orphan\|date=December 2009}}~~

	~~In [[control theory]],~~ the ~~'''minimum energy control'''~~ is ~~the control <math>u(t)</math> that will bring a [[linear time invariant]] system~~ to ~~a desired state~~ with ~~a minimum expenditure of energy~~.

	~~Let the linear time invariant (LTI) system be~~
	~~: <math>\dot{\mathbf{x}}(t) = A \mathbf{x}(t) + B \mathbf{u}(t)</math>~~
	~~: <math>\mathbf{y}(t) = C \mathbf{x}(t) + D \mathbf{u}(t)</math>~~
	~~with initial state <math> x(t_0)=x_0 </math>~~. One seeks an input <math> u(t) </math> so that the system will be in the state <math>x_1</math> at time <math>t_1</math>, and for any other input <math>\bar{u}(t)</math>, which also drives the system from <math>x_0</math> to <math>x_1</math> at time <~~math~~>~~t_1~~<~~/math~~> ~~the energy expenditure would be larger~~

	:~~<math> \int_{t_0}^{t_1} \bar{u}^(t) \bar{u}(t) dt \ \geq \ \int_{t_0}^{t_1} u^(t) u(t) dt. </math>~~

	~~To choose this input, first compute the controllability gramian~~

	:~~<math> W_c(t)=\int_{t_0}^t e^{A(t-\tau)}BB^e^{A^(t-\tau)} d\tau.</math>~~

	~~Assuming <math>W_c</math> is nonsingular (if and only if~~ the ~~system is controllable), the minimum energy control is then~~

	~~:<math> u(t) =~~ -~~B^e^{A^(t_1-t)}W_c^{-1}(t_1)~~[~~e^{A(t_1-t_0)}x_0-x_1].<~~/~~math>~~

	~~Substitution into the solution~~

	~~:<math>x(t)=e^{A(t_1-t_0)}x_0+\int_{t_0}^{t_1}e^{A(t_1-\tau)}Bu(\tau)d\tau<~~/~~math>~~

	~~verifies the achievement of state <math>x_1<~~/~~math> at <math>t_1<~~/~~math>~~.

	==~~See also==~~
	* [[LTI system theory]]
	* [[Control engineering]]
	* [[State space (controls)]]

	~~[[Category:Control theory]~~]

129.247.247.240: /* External links */

2014-01-23T14:45:28Z

External links

← Older revision		Revision as of 16:45, 23 January 2014
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	~~Irwin Butts~~ is ~~what my spouse enjoys to call me although I don'~~t ~~truly like being called like~~ that. ~~California is our birth location~~. ~~Playing baseball is~~ the ~~hobby he~~ will ~~by no means quit performing~~. ~~Bookkeeping is my profession~~.<br><br>~~Here~~ is ~~my web page~~: [~~http~~://~~www.escuelavirtual.registraduria.gov.co~~/~~user/view~~.~~php?id~~=~~140944&course~~=~~1 std testing at home~~]		{{Unreferenced\|date=December 2009}}
			{{Orphan\|date=December 2009}}

			In [[control theory]], the '''minimum energy control''' is the control <math>u(t)</math> that will bring a [[linear time invariant]] system to a desired state with a minimum expenditure of energy.

			Let the linear time invariant (LTI) system be
			: <math>\dot{\mathbf{x}}(t) = A \mathbf{x}(t) + B \mathbf{u}(t)</math>
			: <math>\mathbf{y}(t) = C \mathbf{x}(t) + D \mathbf{u}(t)</math>
			with initial state <math> x(t_0)=x_0 </math>. One seeks an input <math> u(t) </math> so that the system will be in the state <math>x_1</math> at time <math>t_1</math>, and for any other input <math>\bar{u}(t)</math>, which also drives the system from <math>x_0</math> to <math>x_1</math> at time <math>t_1</math> the energy expenditure would be larger

			:<math> \int_{t_0}^{t_1} \bar{u}^(t) \bar{u}(t) dt \ \geq \ \int_{t_0}^{t_1} u^(t) u(t) dt. </math>

			To choose this input, first compute the controllability gramian

			:<math> W_c(t)=\int_{t_0}^t e^{A(t-\tau)}BB^e^{A^(t-\tau)} d\tau.</math>

			Assuming <math>W_c</math> is nonsingular (if and only if the system is controllable), the minimum energy control is then

			:<math> u(t) = -B^e^{A^(t_1-t)}W_c^{-1}(t_1)[e^{A(t_1-t_0)}x_0-x_1].</math>

			Substitution into the solution

			:<math>x(t)=e^{A(t_1-t_0)}x_0+\int_{t_0}^{t_1}e^{A(t_1-\tau)}Bu(\tau)d\tau</math>

			verifies the achievement of state <math>x_1</math> at <math>t_1</math>.

			==See also==
			* [[LTI system theory]]
			* [[Control engineering]]
			* [[State space (controls)]]

			[[Category:Control theory]]

en>Gareth Jones: capitalisation of wlink

2012-08-15T15:22:26Z

capitalisation of wlink

New page

Irwin Butts is what my spouse enjoys to call me although I don't truly like being called like that. California is our birth location. Playing baseball is the hobby he will by no means quit performing. Bookkeeping is my profession.<br><br>Here is my web page: [http://www.escuelavirtual.registraduria.gov.co/user/view.php?id=140944&course=1 std testing at home]