Start Point and Trajectory Analysis for the Minimal Time System Design Algorithm
|
|
- Ann Bryant
- 5 years ago
- Views:
Transcription
1 Start Pont and Trajectory Analy for the Mnmal Tme Sytem Degn Algorthm ALEXANDER ZEMLIAK, PEDRO MIRANDA Department of Phyc and Mathematc Puebla Autonomou Unverty Av San Claudo /n, Puebla, 757 MEXICO Abtract: - The dfferent degn trajectore have been analyzed n the degn pace on the ba of the new ytem degn methodology Optmal poton of the degn algorthm tart pont wa analyzed to mnmze the computer degn tme The ntal pont electon ha been done on the ba of the before dcovered acceleraton effect of the ytem degn proce The geometrcal dvdng urface wa defned and analyzed to obtan the optmal poton of the algorthm tart pont Numercal reult of both pave and actve nonlnear electronc crcut degn prove the poblty of the optmal electon of the degn algorthm tart pont Key-Word: - Tme-optmal degn algorthm, control theory applcaton, optmal tart pont electon Introducton The problem of the computer tme reducton of a large ytem degn one of the eental problem of the total qualty degn mprovement Bede the tradtonally ued dea of pare matr technque and decompoton technque []-[5] ome another way were determne to reduce the total computer degn tme The generalzed theory for the ytem degn on the ba of control theory formulaton wa elaborated n ome prevou work [6]-[8] Th approach erve for the tme-optmal degn algorthm defnton On the other hand th approach gve the poblty to analyze wth a great clearne the degn proce whle movng along the trajectory curve nto the degn pace The man concepton of the theory the ntroducton of the pecal control functon, whch, on the one hand generalze the degn proce and, on the other hand, they gve the poblty to control degn proce to acheve the optmum of the degn objectve functon for the mnmum computer tme Th poblty appear becaue practcally an nfnte number of the dfferent degn tratege that et wthn the bound of the theory, but the dfferent degn tratege have the dfferent operaton number and eecuted computer tme On the bound of th concepton, the tradtonal degn trategy only a one repreentatve of the enormou et of dfferent degn tratege A hown n [8] the potental computer tme gan that can be obtaned by the new degn problem formulaton ncreae when the ze and complety of the ytem ncreae but t realzed only n cae when we have the algorthm for the optmal trajectore real contructon We can defne the formulaton of the ntrnc properte and pecal retrcton of the optmal degn trajectory a one of the frt problem that need to be olved for the optmal algorthm contructon Problem Formulaton The degn proce for any analog ytem degn can be defned [8] a the problem of the generalzed objectve functon F ( X, U ) mnmzaton by mean of the vector equaton: X + = X wth the contrant: where ( u ) g ( X ) + t H () j j =, j =,,, M () N X R, X ( X X ) =,, K X R the vector of M X R N = K + M ), the ndependent varable and the vector the vector of dependent varable ( g j X for all j the ytem model, the ( ) teraton number, t the teraton parameter,
2 t R, H H(X,U) the drecton of the generalzed objectve functon ( X U ) F, decreang, U the vector of the pecal control functon U = ( u, u,, u m ), where u j Ω; Ω = { ; } The generalzed objectve functon F ( X, U) defned a: F ( X, U) = C( X ) + ψ( X, U) where C ( X ) the ordnary degn proce cot functon, and ψ X,U the addtonal penalty functon: ( ) M ψ ( X, U ) = u j g j ( X ) Th problem formulaton ε j= permt to redtrbute the computer tme epene between the problem () olve and the optmzaton procedure () for the functon F ( X, U) The control vector U the man tool for the redtrbuton proce n th cae Practcally an nfnte number of the dfferent degn tratege are produced becaue the vector U depend on the optmzaton current tep The problem of the optmal degn trategy earch formulated now a the typcal problem for the functonal mnmzaton of the control theory The functonal that need to mnmze the total CPU tme T of the degn proce Th functonal depend drectly on the operaton number and more generally on the degn trajectory that ha been realzed The man dffculty of th problem defnton unknown optmal dependence of all control functon u j Th problem the central for uch a type of the degn proce defnton 3 Trajectory Analy The problem of the ntal pont electon for the degn proce one of the eental problem of the tme-optmal algorthm contructon The analy of the degn proce and acceleraton effect for the mplet electronc crcut of the Fg wa provded n [9] Th the two-dmenonal cae Fg Smplet one node crcut The vector of the tate varable X ha two component X = (, ) where = R, = V The nonlnear element ha the followng dependency: R n = r + bv Ung the Law of Krchhoff we can obtan the followng functon g(x): ( X ) ( + r + b ) g (3) = The objectve functon defned by the formula C( X ) = ( k V ), where kv ha the fed value There only one control functon u n th cae becaue there only one dependent parameter The degn trajectory for th eample the curve n two-dmenonal pace, f the numercal degn algorthm appled The optmzaton procedure and the electronc ytem model, n accordance wth the new degn methodology [9], are defned by the net two equaton: ( X U ) + = + t f, ( ) g ( X ) =, =, (4) u (5) where U the vector of control varable, and the component of the movement drecton f ( X, U ) for the =, depend on the optmzaton method Thee functon, for the gradent method for eample, are gven by the formula: δ f ( X, U ) = F ( X, U ) (6) δ δ ( ) ( ) ( u ) f X, U = u F X, U + [ + η( X )] (6 ) δ t where ( X U ) F, the generalzed objectve functon, F ( X, U ) = C( X ) + ug ( X ), η ( X ) ε the mplct functon ( + = η ( X )) and t gve the value of the parameter from the equaton (5), and the operator δ for =, mean: δ δ F F δ F F = +, F = δ δ
3 A hown n [9] we need to elect the ntal pont of the degn proce wth the negatve coordnate In th cae the acceleraton proce can be realzed The famly of the degn curve for the crcut on Fg, whch correpond to the modfed tradtonal degn trategy (u=) and the negatve ntal value of the econd coordnate ( <) of the vector X hown n Fg for the -D phae pace Thee curve have dfferent tart pont but the ame fnal pont F The tart pont were elected on the crcle arc and have the dfferent ntal coordnate The pecal curve S-F, whch marked by thck lne, the eparatng curve Th curve eparate the trajectore that are the canddate for the acceleraton effect achevement (all curve that le under the curve S-F), and the trajectore that can not produce the acceleraton effect (curve that le over the curve S-F) It clear that the projecton of the fnal pont F to all curve of the frt group defne the wtchng pont of the optmal trajectory, whch produce the acceleraton effect All curve of the frt group (-7) approach to the fnal pont F from the left de, and all curve of the econd group (9-6) approach to the fnal pont from the rght de The comparon of the relatve computer tme for all curve of the Fg hown n Fg 3 Fg Trajectore of the modfed tradtonal trategy for the dfferent tart pont wth the negatve coordnate The eparatng curve S-F ha the mnmal computer tme among all of the trajectore At the ame tme th curve can not be ued a the ba for the tmeoptmal trajectory contructon becaue the projecton of the pont F to th curve the ame pont F, but the movement low down near th pont Only the curve that le under the curve S-F erve a the frt part of the tme-optmal trajectory wth the followng jump to the pont F The relatve computer tmeτ of the optmal trajectore wth acceleraton effect (on the ba of the curve -7, Fg ) hown n Fg 4 a the functon of the curve number n The curve 9-6 can be optmzed too but n th cae the tme reducton about -5% only take place Fg 4 how that the total computer tme ncreae when the tart pont approache to the curve S-F, and on the contrary, the more acceleraton can be obtaned f the tart pont le far from the curve S-F (from curve 7 to curve ) So, the tart pont electon wth at leat one negatve ntal coordnate of the vector X and the value of th coordnate that gve the tart pont poton under the eparatng lne are the uffcent condton for the acceleraton effect appearance More detal analy how that the negatve value of the tart pont coordnate below the eparate lne the uffcent condton for the acceleraton effect but not the neceary The phae dagram of Fg 5 nclude two type of the eparate lne The frt lne AFB eparate the trajectore that draw to the fnal pont F from the left and from the rght The econd eparate lne CTFB dvde all the phae pace to the two ubpace All the pont and trajectore that le nde th eparate lne can not produce the acceleraton effect On the other hand, all the pont that le outde the eparate lne and correpondng trajectore produce the acceleraton effect Thee geometrcal condton are the neceary and uffcent to obtan the acceleraton effect Fg 3 Relatve computer tmeτ a the functon of the curve number n Fg 4 Relatve computer tme τ of the optmal trajectore wth acceleraton effect a the functon of the curve number n
4 Fg 5 Phae dagram - for one-node crcut The N-dmenonal cae ha been analyzed below The econd eample correpond to the crcut of Fg 6 Th crcut ha fve ndependent varable a admttance y, y, y3, y4, y5 (K=5) and four dependent varable a nodal voltage V, V, V3, V4 (M=4) Non-lnear crcut element have dependence: y ( ) n = an + bn V V, y ( ) n = an + bn V3 V Non-lnearty parameter bn, bn are equal to The tate parameter vector X nclude nne component: = y, = y, 3 = y3, 4 = y4, 5 = y5, 6 = V, 7 = V, 8 = V3, 9 = V4 The ytem of the optmzaton proce nclude nne equaton and the crcut model nclude four equaton Fg 7 Phae dagram 5-9 for four-node crcut The regon outde the eparate lne nclude the pont and the trajectore that can produce the acceleraton effect In th cae, a for the frt eample, the eparate lne or more general the eparate hyper-urface defne the neceary and uffcent condton for the acceleraton effect etence Actve nonlnear crcut are analyzed below A crcut of the trantor amplfer that cont of three trantor cell hown n Fg 7 The Eber- Moll tatc model of the trantor ha been ued Fg 8 Crcut topology for three-cell trantor amplfer Fg 6 Four-node crcut topology The phae pace of the total tate parameter ha nne dmenon The eparate lne are tranformed to the eparate hyper-urface n th cae The phae projecton of the eparate hyper-urface (eparate lne one and two), whch correpond to the plane 5-9 are hown n Fg 7 The one, two and three trantor cell crcut were analyzed eparately The one trantor cell crcut wa analyzed a the frt eample In th cae we have three ndependent varable y, y, y3 a admttance (K=3) and three dependent varable V, V, V3 a nodal voltage (M=3) The tate parameter vector X nclude component: = y, = y, 3 = y3, 4 = V, 5 = V, 6 = V 3 Fg 9 correpond to the trajectory graph of the modfed tradtonal degn trategy for three above mentoned type of the trantor amplfer
5 (a) =, =,,,K (K=3) (b) =, =,,,K (K=3) (c) =, =,,,K (K=5) (d) =3, =,,,K (K=5) (e) =, =,,,K (K=7) (f) =, =,,,K (K=7) Fg 9 Famly of the curve that correpond to the modfed tradtonal degn trategy and eparate lne for: (a), (b) one-cell; (c), (d) two-cell; and (e), (f) three-cell trantor amplfer
6 Fg 9 (a), (b) how the behavor of the trajectory projecton n the plane 3-6 Fg 9 (a) correpond to the ntal coordnate value =, and Fg 9 (b) to the value = for =,,3 There a great dfference between the actve and the pave crcut The eparate lne and (the projecton of the correpondng eparate hyper urface) have a very trong confguraton for =, that eplan the preence or the abence of the acceleraton effect On the contrary, the eparate hyper urface projecton dappear n the plane 3-6 for the ntal value = It mean that the acceleraton effect oberved alway, for any value of the coordnate 6 becaue all trajectore nclude the poblty to fnh pont jump It very nteretng that the crcut complcaton brng to the further epanon of the acceleraton effect regon We can ee th property from Fg 9 (c), (d) and (e), (f) Fg 9 (c), (d) correpond to the two-cell trantor amplfer and Fg 9 (e), (f) to the three cell amplfer There a gnfcant reducton of the regon of the acceleraton effect abence for two cell amplfer, Fg 9 (c) The projecton of the eparate hyper urface (eparate lne and ) n the plane 5 - have the ame behavor and very narrow regon of the acceleraton effect abence for =, =,,3,4,5 The acceleraton effect alway et for =3 a we can ee n Fg 9 (d) The eparate hyper urface dappear completely for three cell trantor amplfer (Fg 9 (e), (f)) and we can realze acceleraton effect practcally for all tart pont and for all trajectore 4 Concluon The ntal pont electon permt obtan acceleraton effect wth a great probablty The trajectory analy of varou degn tratege how that the concepton of the eparate lne or the eparate hyper urface n general cae very helpful to undertand and defne the neceary and uffcent condton for the degn proce acceleraton effect etence The eparate hyper urface defne the tart pont and the trajectore that can produce the acceleraton effect and can be ued for the optmal degn trajectory contructon The electon of the ntal pont outde of the eparate hyper urface the neceary and uffcent condton for the acceleraton effect etence The eparate hyper urface ha the comple tructure n general cae However, the tuaton mplfed for the actve nonlnear crcut becaue a dappearance of the eparate hyper urface for more complcated crcut It mean that the acceleraton effect can be realzed alway for the comple actve crcut Th effect reduce the total computer tme addtonally and erve a the ba for the optmal or qua-optmal algorthm contructon Acknowledgment Th work wa upported by the Unverdad Autónoma de Puebla, under project VIEPIII5G Reference: [] JR Bunch and DJ Roe, (Ed), Spare Matr Computaton, Acad Pre, NY, 976 [] O Oterby and Z Zlatev, Drect Method for Spare Matrce, Sprnger-Verlag, NY, 983 [3] A George, On Block Elmnaton for Spare Lnear Sytem, SIAM J Numer Anal Vol, No3, 984, pp [4] FF Wu, Soluton of Large-Scale Network by Tearng, IEEE Tran Crcut Syt, Vol CAS- 3, No, 976, pp [5] A Sangovann-Vncentell, LK Chen and LO Chua, An Effcent Cluter Algorthm for Tearng Large-Scale Network, IEEE Tran Crcut Syt, Vol CAS-4, No, 977, pp [6] A Zemlak, One Approach to Analog Sytem Degn Problem Formulaton, Proc IEEE Int Sym on Qualty Electronc Degn ISQED, San Joe, CA, USA, March, pp [7] A Zemlak, Sytem Degn Problem Formulaton by Control Theory, Proc IEEE Int Sym on Crcut and Sytem ISCAS, Sydney, Autrala,,Vol 5, pp 5-8 [8] AM Zemlak, Analog Sytem Degn Problem Formulaton by Optmum Control Theory, IEICE Tran on Fundamental of Electronc, Communcaton and Computer, Vol E84-A, No 8,, pp 9-4 [9] AM Zemlak, Acceleraton Effect of Sytem Degn Proce, IEICE Tran on Fundamental of Electronc, Communcaton and Computer, Vol E85-A, No 7,, pp
Analog System Time-Optimal Design by Generalized Formulation
4th WSEAS Internatonal Conference on ELECTRONICS, CONTROL and SIGNAL PROCESSING, am, Florda, USA, -9 November, 005 (pp.6- Analo System Tme-Optmal Desn by Generalzed Formulaton ALEXANDER ZELIAK Department
More informationAdditional File 1 - Detailed explanation of the expression level CPD
Addtonal Fle - Detaled explanaton of the expreon level CPD A mentoned n the man text, the man CPD for the uterng model cont of two ndvdual factor: P( level gen P( level gen P ( level gen 2 (.).. CPD factor
More informationImprovements on Waring s Problem
Improvement on Warng Problem L An-Png Bejng, PR Chna apl@nacom Abtract By a new recurve algorthm for the auxlary equaton, n th paper, we wll gve ome mprovement for Warng problem Keyword: Warng Problem,
More informationGeneralized Linear Methods
Generalzed Lnear Methods 1 Introducton In the Ensemble Methods the general dea s that usng a combnaton of several weak learner one could make a better learner. More formally, assume that we have a set
More informationNetwork Optimization by Generalized Methodology
Aleander Zemlak Rcardo Pena Network Optmzaton by Generalzed Methodoloy ALEXANDER ZEMLIAK RICARDO PEÑA Department of Physcs and Mathematcs Puebla Autonomous Unversty MEXICO Insttute of Physcs and Technoloy
More informationSmall signal analysis
Small gnal analy. ntroducton Let u conder the crcut hown n Fg., where the nonlnear retor decrbed by the equaton g v havng graphcal repreentaton hown n Fg.. ( G (t G v(t v Fg. Fg. a D current ource wherea
More informationHarmonic oscillator approximation
armonc ocllator approxmaton armonc ocllator approxmaton Euaton to be olved We are fndng a mnmum of the functon under the retrcton where W P, P,..., P, Q, Q,..., Q P, P,..., P, Q, Q,..., Q lnwgner functon
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More informationChapter 11. Supplemental Text Material. The method of steepest ascent can be derived as follows. Suppose that we have fit a firstorder
S-. The Method of Steepet cent Chapter. Supplemental Text Materal The method of teepet acent can be derved a follow. Suppoe that we have ft a frtorder model y = β + β x and we wh to ue th model to determne
More informationTeam. Outline. Statistics and Art: Sampling, Response Error, Mixed Models, Missing Data, and Inference
Team Stattc and Art: Samplng, Repone Error, Mxed Model, Mng Data, and nference Ed Stanek Unverty of Maachuett- Amhert, USA 9/5/8 9/5/8 Outlne. Example: Doe-repone Model n Toxcology. ow to Predct Realzed
More informationImprovements on Waring s Problem
Imrovement on Warng Problem L An-Png Bejng 85, PR Chna al@nacom Abtract By a new recurve algorthm for the auxlary equaton, n th aer, we wll gve ome mrovement for Warng roblem Keyword: Warng Problem, Hardy-Lttlewood
More information4DVAR, according to the name, is a four-dimensional variational method.
4D-Varatonal Data Assmlaton (4D-Var) 4DVAR, accordng to the name, s a four-dmensonal varatonal method. 4D-Var s actually a drect generalzaton of 3D-Var to handle observatons that are dstrbuted n tme. The
More informationVariable Structure Control ~ Basics
Varable Structure Control ~ Bac Harry G. Kwatny Department of Mechancal Engneerng & Mechanc Drexel Unverty Outlne A prelmnary example VS ytem, ldng mode, reachng Bac of dcontnuou ytem Example: underea
More informationArmy Ants Tunneling for Classical Simulations
Electronc Supplementary Materal (ESI) for Chemcal Scence. Ths journal s The Royal Socety of Chemstry 2014 electronc supplementary nformaton (ESI) for Chemcal Scence Army Ants Tunnelng for Classcal Smulatons
More informationSpecification -- Assumptions of the Simple Classical Linear Regression Model (CLRM) 1. Introduction
ECONOMICS 35* -- NOTE ECON 35* -- NOTE Specfcaton -- Aumpton of the Smple Clacal Lnear Regreon Model (CLRM). Introducton CLRM tand for the Clacal Lnear Regreon Model. The CLRM alo known a the tandard lnear
More informationChapter - 2. Distribution System Power Flow Analysis
Chapter - 2 Dstrbuton System Power Flow Analyss CHAPTER - 2 Radal Dstrbuton System Load Flow 2.1 Introducton Load flow s an mportant tool [66] for analyzng electrcal power system network performance. Load
More informationScattering of two identical particles in the center-of. of-mass frame. (b)
Lecture # November 5 Scatterng of two dentcal partcle Relatvtc Quantum Mechanc: The Klen-Gordon equaton Interpretaton of the Klen-Gordon equaton The Drac equaton Drac repreentaton for the matrce α and
More informationModeling of Wave Behavior of Substrate Noise Coupling for Mixed-Signal IC Design
Modelng of Wave Behavor of Subtrate Noe Couplng for Mxed-Sgnal IC Degn Georgo Veron, Y-Chang Lu, and Robert W. Dutton Center for Integrated Sytem, Stanford Unverty, Stanford, CA 9435 yorgo@gloworm.tanford.edu
More informationDistributed Control for the Parallel DC Linked Modular Shunt Active Power Filters under Distorted Utility Voltage Condition
Dtrbted Control for the Parallel DC Lnked Modlar Shnt Actve Power Flter nder Dtorted Utlty Voltage Condton Reearch Stdent: Adl Salman Spervor: Dr. Malabka Ba School of Electrcal and Electronc Engneerng
More informationOn the SO 2 Problem in Thermal Power Plants. 2.Two-steps chemical absorption modeling
Internatonal Journal of Engneerng Reearch ISSN:39-689)(onlne),347-53(prnt) Volume No4, Iue No, pp : 557-56 Oct 5 On the SO Problem n Thermal Power Plant Two-tep chemcal aborpton modelng hr Boyadjev, P
More informationChapter 6 The Effect of the GPS Systematic Errors on Deformation Parameters
Chapter 6 The Effect of the GPS Sytematc Error on Deformaton Parameter 6.. General Beutler et al., (988) dd the frt comprehenve tudy on the GPS ytematc error. Baed on a geometrc approach and aumng a unform
More informationMMA and GCMMA two methods for nonlinear optimization
MMA and GCMMA two methods for nonlnear optmzaton Krster Svanberg Optmzaton and Systems Theory, KTH, Stockholm, Sweden. krlle@math.kth.se Ths note descrbes the algorthms used n the author s 2007 mplementatons
More informationOn the Multicriteria Integer Network Flow Problem
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 5, No 2 Sofa 2005 On the Multcrtera Integer Network Flow Problem Vassl Vasslev, Marana Nkolova, Maryana Vassleva Insttute of
More informationSome modelling aspects for the Matlab implementation of MMA
Some modellng aspects for the Matlab mplementaton of MMA Krster Svanberg krlle@math.kth.se Optmzaton and Systems Theory Department of Mathematcs KTH, SE 10044 Stockholm September 2004 1. Consdered optmzaton
More informationU.C. Berkeley CS294: Beyond Worst-Case Analysis Luca Trevisan September 5, 2017
U.C. Berkeley CS94: Beyond Worst-Case Analyss Handout 4s Luca Trevsan September 5, 07 Summary of Lecture 4 In whch we ntroduce semdefnte programmng and apply t to Max Cut. Semdefnte Programmng Recall that
More informationLecture 21: Numerical methods for pricing American type derivatives
Lecture 21: Numercal methods for prcng Amercan type dervatves Xaoguang Wang STAT 598W Aprl 10th, 2014 (STAT 598W) Lecture 21 1 / 26 Outlne 1 Fnte Dfference Method Explct Method Penalty Method (STAT 598W)
More informationThe Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method
Journal of Electromagnetc Analyss and Applcatons, 04, 6, 0-08 Publshed Onlne September 04 n ScRes. http://www.scrp.org/journal/jemaa http://dx.do.org/0.46/jemaa.04.6000 The Exact Formulaton of the Inverse
More informationA MODIFIED METHOD FOR SOLVING SYSTEM OF NONLINEAR EQUATIONS
Journal of Mathematcs and Statstcs 9 (1): 4-8, 1 ISSN 1549-644 1 Scence Publcatons do:1.844/jmssp.1.4.8 Publshed Onlne 9 (1) 1 (http://www.thescpub.com/jmss.toc) A MODIFIED METHOD FOR SOLVING SYSTEM OF
More informationFUZZY GOAL PROGRAMMING VS ORDINARY FUZZY PROGRAMMING APPROACH FOR MULTI OBJECTIVE PROGRAMMING PROBLEM
Internatonal Conference on Ceramcs, Bkaner, Inda Internatonal Journal of Modern Physcs: Conference Seres Vol. 22 (2013) 757 761 World Scentfc Publshng Company DOI: 10.1142/S2010194513010982 FUZZY GOAL
More informationPhysics 4B. A positive value is obtained, so the current is counterclockwise around the circuit.
Physcs 4B Solutons to Chapter 7 HW Chapter 7: Questons:, 8, 0 Problems:,,, 45, 48,,, 7, 9 Queston 7- (a) no (b) yes (c) all te Queston 7-8 0 μc Queston 7-0, c;, a;, d; 4, b Problem 7- (a) Let be the current
More informationExtended Prigogine Theorem: Method for Universal Characterization of Complex System Evolution
Extended Prgogne Theorem: Method for Unveral Characterzaton of Complex Sytem Evoluton Sergey amenhchkov* Mocow State Unverty of M.V. Lomonoov, Phycal department, Rua, Mocow, Lennke Gory, 1/, 119991 Publhed
More informationMAE140 - Linear Circuits - Winter 16 Final, March 16, 2016
ME140 - Lnear rcuts - Wnter 16 Fnal, March 16, 2016 Instructons () The exam s open book. You may use your class notes and textbook. You may use a hand calculator wth no communcaton capabltes. () You have
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More information728. Mechanical and electrical elements in reduction of vibrations
78. Mechancal and electrcal element n reducton of vbraton Katarzyna BIAŁAS The Slean Unverty of Technology, Faculty of Mechancal Engneerng Inttute of Engneerng Procee Automaton and Integrated Manufacturng
More informationIntroduction to Interfacial Segregation. Xiaozhe Zhang 10/02/2015
Introducton to Interfacal Segregaton Xaozhe Zhang 10/02/2015 Interfacal egregaton Segregaton n materal refer to the enrchment of a materal conttuent at a free urface or an nternal nterface of a materal.
More informationMethod Of Fundamental Solutions For Modeling Electromagnetic Wave Scattering Problems
Internatonal Workhop on MehFree Method 003 1 Method Of Fundamental Soluton For Modelng lectromagnetc Wave Scatterng Problem Der-Lang Young (1) and Jhh-We Ruan (1) Abtract: In th paper we attempt to contruct
More informationLecture Notes on Linear Regression
Lecture Notes on Lnear Regresson Feng L fl@sdueducn Shandong Unversty, Chna Lnear Regresson Problem In regresson problem, we am at predct a contnuous target value gven an nput feature vector We assume
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationCHAPTER 7 CONSTRAINED OPTIMIZATION 2: SQP AND GRG
Chapter 7: Constraned Optmzaton CHAPER 7 CONSRAINED OPIMIZAION : SQP AND GRG Introducton In the prevous chapter we eamned the necessary and suffcent condtons for a constraned optmum. We dd not, however,
More informationAdvanced Mechanical Elements
May 3, 08 Advanced Mechancal Elements (Lecture 7) Knematc analyss and moton control of underactuated mechansms wth elastc elements - Moton control of underactuated mechansms constraned by elastc elements
More informationThe Study of Teaching-learning-based Optimization Algorithm
Advanced Scence and Technology Letters Vol. (AST 06), pp.05- http://dx.do.org/0.57/astl.06. The Study of Teachng-learnng-based Optmzaton Algorthm u Sun, Yan fu, Lele Kong, Haolang Q,, Helongang Insttute
More informationAssortment Optimization under MNL
Assortment Optmzaton under MNL Haotan Song Aprl 30, 2017 1 Introducton The assortment optmzaton problem ams to fnd the revenue-maxmzng assortment of products to offer when the prces of products are fxed.
More informationMean Field / Variational Approximations
Mean Feld / Varatonal Appromatons resented by Jose Nuñez 0/24/05 Outlne Introducton Mean Feld Appromaton Structured Mean Feld Weghted Mean Feld Varatonal Methods Introducton roblem: We have dstrbuton but
More informationMarkov Chain Monte Carlo Lecture 6
where (x 1,..., x N ) X N, N s called the populaton sze, f(x) f (x) for at least one {1, 2,..., N}, and those dfferent from f(x) are called the tral dstrbutons n terms of mportance samplng. Dfferent ways
More informationSolutions to exam in SF1811 Optimization, Jan 14, 2015
Solutons to exam n SF8 Optmzaton, Jan 4, 25 3 3 O------O -4 \ / \ / The network: \/ where all lnks go from left to rght. /\ / \ / \ 6 O------O -5 2 4.(a) Let x = ( x 3, x 4, x 23, x 24 ) T, where the varable
More informationVector Norms. Chapter 7 Iterative Techniques in Matrix Algebra. Cauchy-Bunyakovsky-Schwarz Inequality for Sums. Distances. Convergence.
Vector Norms Chapter 7 Iteratve Technques n Matrx Algebra Per-Olof Persson persson@berkeley.edu Department of Mathematcs Unversty of Calforna, Berkeley Math 128B Numercal Analyss Defnton A vector norm
More informationErrors for Linear Systems
Errors for Lnear Systems When we solve a lnear system Ax b we often do not know A and b exactly, but have only approxmatons  and ˆb avalable. Then the best thng we can do s to solve ˆx ˆb exactly whch
More informationInexact Newton Methods for Inverse Eigenvalue Problems
Inexact Newton Methods for Inverse Egenvalue Problems Zheng-jan Ba Abstract In ths paper, we survey some of the latest development n usng nexact Newton-lke methods for solvng nverse egenvalue problems.
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationComputer-Aided Circuit Simulation and Verification. CSE245 Fall 2004 Professor:Chung-Kuan Cheng
Computer-Aded Crcut Smulaton and Verfcaton CSE245 Fall 24 Professor:Chung-Kuan Cheng Admnstraton Lectures: 5:pm ~ 6:2pm TTH HSS 252 Offce Hours: 4:pm ~ 4:45pm TTH APM 4256 Textbook Electronc Crcut and
More informationOn a direct solver for linear least squares problems
ISSN 2066-6594 Ann. Acad. Rom. Sc. Ser. Math. Appl. Vol. 8, No. 2/2016 On a drect solver for lnear least squares problems Constantn Popa Abstract The Null Space (NS) algorthm s a drect solver for lnear
More informationNatural Language Processing and Information Retrieval
Natural Language Processng and Informaton Retreval Support Vector Machnes Alessandro Moschtt Department of nformaton and communcaton technology Unversty of Trento Emal: moschtt@ds.untn.t Summary Support
More informationInterconnect Modeling
Interconnect Modelng Modelng of Interconnects Interconnect R, C and computaton Interconnect models umped RC model Dstrbuted crcut models Hgher-order waveform n dstrbuted RC trees Accuracy and fdelty Prepared
More informationA Bayes Algorithm for the Multitask Pattern Recognition Problem Direct Approach
A Bayes Algorthm for the Multtask Pattern Recognton Problem Drect Approach Edward Puchala Wroclaw Unversty of Technology, Char of Systems and Computer etworks, Wybrzeze Wyspanskego 7, 50-370 Wroclaw, Poland
More informationChapter 2 - The Simple Linear Regression Model S =0. e i is a random error. S β2 β. This is a minimization problem. Solution is a calculus exercise.
Chapter - The Smple Lnear Regresson Model The lnear regresson equaton s: where y + = β + β e for =,..., y and are observable varables e s a random error How can an estmaton rule be constructed for the
More informationA NUMERICAL MODELING OF MAGNETIC FIELD PERTURBATED BY THE PRESENCE OF SCHIP S HULL
A NUMERCAL MODELNG OF MAGNETC FELD PERTURBATED BY THE PRESENCE OF SCHP S HULL M. Dennah* Z. Abd** * Laboratory Electromagnetc Sytem EMP BP b Ben-Aknoun 606 Alger Algera ** Electronc nttute USTHB Alger
More informationPHYS 705: Classical Mechanics. Calculus of Variations II
1 PHYS 705: Classcal Mechancs Calculus of Varatons II 2 Calculus of Varatons: Generalzaton (no constrant yet) Suppose now that F depends on several dependent varables : We need to fnd such that has a statonary
More informationGrid Generation around a Cylinder by Complex Potential Functions
Research Journal of Appled Scences, Engneerng and Technolog 4(): 53-535, 0 ISSN: 040-7467 Mawell Scentfc Organzaton, 0 Submtted: December 0, 0 Accepted: Januar, 0 Publshed: June 0, 0 Grd Generaton around
More informationMACHINE APPLIED MACHINE LEARNING LEARNING. Gaussian Mixture Regression
11 MACHINE APPLIED MACHINE LEARNING LEARNING MACHINE LEARNING Gaussan Mture Regresson 22 MACHINE APPLIED MACHINE LEARNING LEARNING Bref summary of last week s lecture 33 MACHINE APPLIED MACHINE LEARNING
More informationDO NOT DO HOMEWORK UNTIL IT IS ASSIGNED. THE ASSIGNMENTS MAY CHANGE UNTIL ANNOUNCED.
EE 539 Homeworks Sprng 08 Updated: Tuesday, Aprl 7, 08 DO NOT DO HOMEWORK UNTIL IT IS ASSIGNED. THE ASSIGNMENTS MAY CHANGE UNTIL ANNOUNCED. For full credt, show all work. Some problems requre hand calculatons.
More informationSingular Value Decomposition: Theory and Applications
Sngular Value Decomposton: Theory and Applcatons Danel Khashab Sprng 2015 Last Update: March 2, 2015 1 Introducton A = UDV where columns of U and V are orthonormal and matrx D s dagonal wth postve real
More informationChapter 12. Ordinary Differential Equation Boundary Value (BV) Problems
Chapter. Ordnar Dfferental Equaton Boundar Value (BV) Problems In ths chapter we wll learn how to solve ODE boundar value problem. BV ODE s usuall gven wth x beng the ndependent space varable. p( x) q(
More informationAppendix B. The Finite Difference Scheme
140 APPENDIXES Appendx B. The Fnte Dfference Scheme In ths appendx we present numercal technques whch are used to approxmate solutons of system 3.1 3.3. A comprehensve treatment of theoretcal and mplementaton
More informationOPTIMISATION. Introduction Single Variable Unconstrained Optimisation Multivariable Unconstrained Optimisation Linear Programming
OPTIMIATION Introducton ngle Varable Unconstraned Optmsaton Multvarable Unconstraned Optmsaton Lnear Programmng Chapter Optmsaton /. Introducton In an engneerng analss, sometmes etremtes, ether mnmum or
More informationStructure and Drive Paul A. Jensen Copyright July 20, 2003
Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.
More informationLecture 10 Support Vector Machines II
Lecture 10 Support Vector Machnes II 22 February 2016 Taylor B. Arnold Yale Statstcs STAT 365/665 1/28 Notes: Problem 3 s posted and due ths upcomng Frday There was an early bug n the fake-test data; fxed
More informationChapter Newton s Method
Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve
More informationThe Finite Element Method
The Fnte Element Method GENERAL INTRODUCTION Read: Chapters 1 and 2 CONTENTS Engneerng and analyss Smulaton of a physcal process Examples mathematcal model development Approxmate solutons and methods of
More informationSolution Methods for Time-indexed MIP Models for Chemical Production Scheduling
Ian Davd Lockhart Bogle and Mchael Farweather (Edtor), Proceedng of the 22nd European Sympoum on Computer Aded Proce Engneerng, 17-2 June 212, London. 212 Elever B.V. All rght reerved. Soluton Method for
More informationInductance Calculation for Conductors of Arbitrary Shape
CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors
More informationNON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS
IJRRAS 8 (3 September 011 www.arpapress.com/volumes/vol8issue3/ijrras_8_3_08.pdf NON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS H.O. Bakodah Dept. of Mathematc
More informationELE B7 Power Systems Engineering. Power Flow- Introduction
ELE B7 Power Systems Engneerng Power Flow- Introducton Introducton to Load Flow Analyss The power flow s the backbone of the power system operaton, analyss and desgn. It s necessary for plannng, operaton,
More informationElectrical Circuits II (ECE233b)
Electrcal Crcut II (ECE33b) Applcaton of Laplace Tranform to Crcut Analy Anet Dounav The Unverty of Wetern Ontaro Faculty of Engneerng Scence Crcut Element Retance Tme Doman (t) v(t) R v(t) = R(t) Frequency
More informationcoordinates. Then, the position vectors are described by
Revewng, what we have dscussed so far: Generalzed coordnates Any number of varables (say, n) suffcent to specfy the confguraton of the system at each nstant to tme (need not be the mnmum number). In general,
More informatione i is a random error
Chapter - The Smple Lnear Regresson Model The lnear regresson equaton s: where + β + β e for,..., and are observable varables e s a random error How can an estmaton rule be constructed for the unknown
More informationSuppose that there s a measured wndow of data fff k () ; :::; ff k g of a sze w, measured dscretely wth varable dscretzaton step. It s convenent to pl
RECURSIVE SPLINE INTERPOLATION METHOD FOR REAL TIME ENGINE CONTROL APPLICATIONS A. Stotsky Volvo Car Corporaton Engne Desgn and Development Dept. 97542, HA1N, SE- 405 31 Gothenburg Sweden. Emal: astotsky@volvocars.com
More informationSIMULATION OF WAVE PROPAGATION IN AN HETEROGENEOUS ELASTIC ROD
SIMUATION OF WAVE POPAGATION IN AN HETEOGENEOUS EASTIC OD ogéro M Saldanha da Gama Unversdade do Estado do o de Janero ua Sào Francsco Xaver 54, sala 5 A 559-9, o de Janero, Brasl e-mal: rsgama@domancombr
More informationSeparation Axioms of Fuzzy Bitopological Spaces
IJCSNS Internatonal Journal of Computer Scence and Network Securty VOL3 No October 3 Separaton Axom of Fuzzy Btopologcal Space Hong Wang College of Scence Southwet Unverty of Scence and Technology Manyang
More informationNeural networks. Nuno Vasconcelos ECE Department, UCSD
Neural networs Nuno Vasconcelos ECE Department, UCSD Classfcaton a classfcaton problem has two types of varables e.g. X - vector of observatons (features) n the world Y - state (class) of the world x X
More informationA new Approach for Solving Linear Ordinary Differential Equations
, ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of
More informationA Fast Computer Aided Design Method for Filters
2017 Asa-Pacfc Engneerng and Technology Conference (APETC 2017) ISBN: 978-1-60595-443-1 A Fast Computer Aded Desgn Method for Flters Gang L ABSTRACT *Ths paper presents a fast computer aded desgn method
More informationInner Product. Euclidean Space. Orthonormal Basis. Orthogonal
Inner Product Defnton 1 () A Eucldean space s a fnte-dmensonal vector space over the reals R, wth an nner product,. Defnton 2 (Inner Product) An nner product, on a real vector space X s a symmetrc, blnear,
More informationFeature Selection: Part 1
CSE 546: Machne Learnng Lecture 5 Feature Selecton: Part 1 Instructor: Sham Kakade 1 Regresson n the hgh dmensonal settng How do we learn when the number of features d s greater than the sample sze n?
More informationMATH 5630: Discrete Time-Space Model Hung Phan, UMass Lowell March 1, 2018
MATH 5630: Dscrete Tme-Space Model Hung Phan, UMass Lowell March, 08 Newton s Law of Coolng Consder the coolng of a well strred coffee so that the temperature does not depend on space Newton s law of collng
More informationBOUNDARY ELEMENT METHODS FOR VIBRATION PROBLEMS. Ashok D. Belegundu Professor of Mechanical Engineering Penn State University
BOUNDARY ELEMENT METHODS FOR VIBRATION PROBLEMS by Aho D. Belegundu Profeor of Mechancal Engneerng Penn State Unverty ahobelegundu@yahoo.com ASEE Fello, Summer 3 Colleague at NASA Goddard: Danel S. Kaufman
More informationThe Minimum Universal Cost Flow in an Infeasible Flow Network
Journal of Scences, Islamc Republc of Iran 17(2): 175-180 (2006) Unversty of Tehran, ISSN 1016-1104 http://jscencesutacr The Mnmum Unversal Cost Flow n an Infeasble Flow Network H Saleh Fathabad * M Bagheran
More informationPattern Classification
Pattern Classfcaton All materals n these sldes ere taken from Pattern Classfcaton (nd ed) by R. O. Duda, P. E. Hart and D. G. Stork, John Wley & Sons, 000 th the permsson of the authors and the publsher
More informationELG3336: Op Amp-based Active Filters
ELG6: Op Amp-baed Actve Flter Advantage: educed ze and weght, and thereore paratc. Increaed relablty and mproved perormance. Smpler degn than or pave lter and can realze a wder range o uncton a well a
More informationDEMO #8 - GAUSSIAN ELIMINATION USING MATHEMATICA. 1. Matrices in Mathematica
demo8.nb 1 DEMO #8 - GAUSSIAN ELIMINATION USING MATHEMATICA Obectves: - defne matrces n Mathematca - format the output of matrces - appl lnear algebra to solve a real problem - Use Mathematca to perform
More informationLecture 20: November 7
0-725/36-725: Convex Optmzaton Fall 205 Lecturer: Ryan Tbshran Lecture 20: November 7 Scrbes: Varsha Chnnaobreddy, Joon Sk Km, Lngyao Zhang Note: LaTeX template courtesy of UC Berkeley EECS dept. Dsclamer:
More informationDigital Simulation of Power Systems and Power Electronics using the MATLAB Power System Blockset 筑龙网
Dgtal Smulaton of Power Sytem and Power Electronc ung the MATAB Power Sytem Blocket Power Sytem Blocket Htory Deeloped by IREQ (HydroQuébec) n cooperaton wth Teqm, Unerté aal (Québec), and École de Technologe
More informationParametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010
Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Survey Workng Group Semnar March 29, 2010 1 Outlne Introducton Proposed method Fractonal mputaton Approxmaton Varance estmaton Multple mputaton
More informationProblem #1. Known: All required parameters. Schematic: Find: Depth of freezing as function of time. Strategy:
BEE 3500 013 Prelm Soluton Problem #1 Known: All requred parameter. Schematc: Fnd: Depth of freezng a functon of tme. Strategy: In thee mplfed analy for freezng tme, a wa done n cla for a lab geometry,
More informationInteractive Bi-Level Multi-Objective Integer. Non-linear Programming Problem
Appled Mathematcal Scences Vol 5 0 no 65 3 33 Interactve B-Level Mult-Objectve Integer Non-lnear Programmng Problem O E Emam Department of Informaton Systems aculty of Computer Scence and nformaton Helwan
More informationCurve Fitting with the Least Square Method
WIKI Document Number 5 Interpolaton wth Least Squares Curve Fttng wth the Least Square Method Mattheu Bultelle Department of Bo-Engneerng Imperal College, London Context We wsh to model the postve feedback
More information8 Derivation of Network Rate Equations from Single- Cell Conductance Equations
Physcs 178/278 - Davd Klenfeld - Wnter 2015 8 Dervaton of Network Rate Equatons from Sngle- Cell Conductance Equatons We consder a network of many neurons, each of whch obeys a set of conductancebased,
More informationPART 8. Partial Differential Equations PDEs
he Islamc Unverst of Gaza Facult of Engneerng Cvl Engneerng Department Numercal Analss ECIV 3306 PAR 8 Partal Dfferental Equatons PDEs Chapter 9; Fnte Dfference: Ellptc Equatons Assocate Prof. Mazen Abualtaef
More informationCollege of Computer & Information Science Fall 2009 Northeastern University 20 October 2009
College of Computer & Informaton Scence Fall 2009 Northeastern Unversty 20 October 2009 CS7880: Algorthmc Power Tools Scrbe: Jan Wen and Laura Poplawsk Lecture Outlne: Prmal-dual schema Network Desgn:
More informationOptimal Control of Temperature in Fluid Flow
Kawahara Lab. 5 March. 27 Optmal Control of Temperature n Flud Flow Dasuke YAMAZAKI Department of Cvl Engneerng, Chuo Unversty Kasuga -3-27, Bunkyou-ku, Tokyo 2-855, Japan E-mal : d33422@educ.kc.chuo-u.ac.jp
More information