Ee263 Homework Problems On Accounting

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EE263

EE364

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CVX101

02/03/2014

CVX101For Credit: NoAttendance: N/ATextbook Used: YesWould Take Again: N/AGrade Received: N/A

11/29/2012

EE263For Credit: N/AAttendance: N/ATextbook Used: NoWould Take Again: N/AGrade Received: N/A

11/11/2012

EE263For Credit: N/AAttendance: N/ATextbook Used: YesWould Take Again: N/AGrade Received: N/A

10/09/2012

EE263For Credit: N/AAttendance: N/ATextbook Used: NoWould Take Again: N/AGrade Received: N/A

03/28/2011

EE364For Credit: N/AAttendance: N/ATextbook Used: YesWould Take Again: N/AGrade Received: N/A

10/04/2010

EE364AFor Credit: N/AAttendance: N/ATextbook Used: NoWould Take Again: N/AGrade Received: N/A

02/23/2008

EE364For Credit: N/AAttendance: N/ATextbook Used: NoWould Take Again: N/AGrade Received: N/A

02/06/2008

EE263For Credit: N/AAttendance: N/ATextbook Used: YesWould Take Again: N/AGrade Received: N/A

10/11/2006

EE263For Credit: N/AAttendance: N/ATextbook Used: YesWould Take Again: N/AGrade Received: N/A

05/29/2006

EE364For Credit: N/AAttendance: N/ATextbook Used: N/AWould Take Again: N/AGrade Received: N/A

07/08/2005

EE364For Credit: N/AAttendance: Not MandatoryTextbook Used: N/AWould Take Again: N/AGrade Received: N/A

05/05/2005

EE263For Credit: N/AAttendance: N/ATextbook Used: N/AWould Take Again: N/AGrade Received: N/A

10/20/2004

EE263For Credit: N/AAttendance: N/ATextbook Used: N/AWould Take Again: N/AGrade Received: N/A

12/03/2003

EE263For Credit: N/AAttendance: N/ATextbook Used: N/AWould Take Again: N/AGrade Received: N/A

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EE263, Fall 2016-17EE263 Homework 8 solution1Minimum energy control.Consider the discrete-time linear dynamical systemx(t+ 1) =Ax(t) +Bu(t),t= 0,1,2, . . .wherex(t)∈Rn, and the inputu(t) is a scalar (hence,A∈Rn×nandB∈Rn×1).The initial state isx(0) = 0.(a) Find the matrixCTsuch thatx(T) =CTu(T−1)...u(1)u(0).(b) For the remainder of this problem, we consider a speci±c system withn= 4. Thedynamics and input matrices areA=0.50.7−0.9−0.50.4−0.70.10.30.70.0−0.60.10.4−0.10.8−0.5,B=1100.Suppose we want the state to bexdesat timeT. Consider the desired statexdes=0.82.3−0.7−0.3.What is the smallestTfor which we can ±nd inputsu(0), . . ., u(T−1), such thatx(T) =xdes? What are the corresponding inputs that achievexdesat this mini-mum time? What is the smallestTfor which we can ±nd inputsu(0), . . ., u(T−1),such thatx(T) =xdesfor anyxdes∈R4? We’ll denote thisTbyTmin.(c) Suppose the energy expended in applying inputsu(0), . . ., u(T−1) isE(T) =T-1st=0(u(t))2.For a givenT(greater thanTmin) andxdes, how can you compute the inputswhich achievex(T) =xdeswith the minimum expense of energy? Consider nowthe desired statexdes=−1101.1

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