LEADER 08087nam 2202041Ia 450 001 9910807652503321 005 20230120110110.0 010 $a1-282-45796-9 010 $a1-282-93606-9 010 $a9786612936067 010 $a9786612457968 010 $a1-4008-3387-6 024 7 $a10.1515/9781400833870 035 $a(CKB)2520000000006994 035 $a(EBL)485767 035 $a(OCoLC)638859365 035 $a(SSID)ssj0000457488 035 $a(PQKBManifestationID)11924193 035 $a(PQKBTitleCode)TC0000457488 035 $a(PQKBWorkID)10415122 035 $a(PQKB)10475185 035 $a(DE-B1597)446610 035 $a(OCoLC)979779564 035 $a(DE-B1597)9781400833870 035 $a(Au-PeEL)EBL485767 035 $a(CaPaEBR)ebr10364743 035 $a(CaONFJC)MIL293606 035 $a(Au-PeEL)EBL4968557 035 $a(CaONFJC)MIL245796 035 $a(OCoLC)1027190663 035 $a(MiAaPQ)EBC485767 035 $a(MiAaPQ)EBC4968557 035 $a(EXLCZ)992520000000006994 100 $a20090901d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aControl theoretic splines$b[electronic resource] $eoptimal control, statistics, and path planning /$fMagnus Egerstedt and Clyde Martin 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$dc2010 215 $a1 online resource (227 p.) 225 1 $aPrinceton series in applied mathematics 300 $aDescription based upon print version of record. 311 $a0-691-13296-8 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tChapter One. Introduction -- $tChapter Two. Control Systems and Minimum Norm Problems -- $tChapter Three. Eight Fundamental Problems -- $tChapter Four. Smoothing Splines and Generalizations -- $tChapter Five. Approximations and Limiting Concepts -- $tChapter Six. Smoothing Splines with Continuous Data -- $tChapter Seven. Monotone Smoothing Splines -- $tChapter Eight. Smoothing Splines as Integral Filters -- $tChapter Nine. Optimal Transfer between Affine Varieties -- $tChapter Ten. Path Planning and Telemetry -- $tChapter Eleven. Node Selection -- $tBibliography -- $tIndex 330 $aSplines, both interpolatory and smoothing, have a long and rich history that has largely been application driven. This book unifies these constructions in a comprehensive and accessible way, drawing from the latest methods and applications to show how they arise naturally in the theory of linear control systems. Magnus Egerstedt and Clyde Martin are leading innovators in the use of control theoretic splines to bring together many diverse applications within a common framework. In this book, they begin with a series of problems ranging from path planning to statistics to approximation. Using the tools of optimization over vector spaces, Egerstedt and Martin demonstrate how all of these problems are part of the same general mathematical framework, and how they are all, to a certain degree, a consequence of the optimization problem of finding the shortest distance from a point to an affine subspace in a Hilbert space. They cover periodic splines, monotone splines, and splines with inequality constraints, and explain how any finite number of linear constraints can be added. This book reveals how the many natural connections between control theory, numerical analysis, and statistics can be used to generate powerful mathematical and analytical tools. This book is an excellent resource for students and professionals in control theory, robotics, engineering, computer graphics, econometrics, and any area that requires the construction of curves based on sets of raw data. 410 0$aPrinceton series in applied mathematics. 606 $aInterpolation 606 $aSmoothing (Numerical analysis) 606 $aSmoothing (Statistics) 606 $aCurve fitting 606 $aSplines 606 $aSpline theory 610 $aAccuracy and precision. 610 $aAffine space. 610 $aAffine variety. 610 $aAlgorithm. 610 $aApproximation. 610 $aArbitrarily large. 610 $aB-spline. 610 $aBanach space. 610 $aBernstein polynomial. 610 $aBifurcation theory. 610 $aBig O notation. 610 $aBirkhoff interpolation. 610 $aBoundary value problem. 610 $aBézier curve. 610 $aChaos theory. 610 $aComputation. 610 $aComputational problem. 610 $aCondition number. 610 $aConstrained optimization. 610 $aContinuous function (set theory). 610 $aContinuous function. 610 $aControl function (econometrics). 610 $aControl theory. 610 $aControllability. 610 $aConvex optimization. 610 $aConvolution. 610 $aCubic Hermite spline. 610 $aData set. 610 $aDerivative. 610 $aDifferentiable function. 610 $aDifferential equation. 610 $aDimension (vector space). 610 $aDirectional derivative. 610 $aDiscrete mathematics. 610 $aDynamic programming. 610 $aEquation. 610 $aEstimation. 610 $aFiltering problem (stochastic processes). 610 $aGaussian quadrature. 610 $aGradient descent. 610 $aGramian matrix. 610 $aGrowth curve (statistics). 610 $aHermite interpolation. 610 $aHermite polynomials. 610 $aHilbert projection theorem. 610 $aHilbert space. 610 $aInitial condition. 610 $aInitial value problem. 610 $aIntegral equation. 610 $aIterative method. 610 $aKarush?Kuhn?Tucker conditions. 610 $aKernel method. 610 $aLagrange polynomial. 610 $aLaw of large numbers. 610 $aLeast squares. 610 $aLinear algebra. 610 $aLinear combination. 610 $aLinear filter. 610 $aLinear map. 610 $aMathematical optimization. 610 $aMathematics. 610 $aMaxima and minima. 610 $aMonotonic function. 610 $aNonlinear programming. 610 $aNonlinear system. 610 $aNormal distribution. 610 $aNumerical analysis. 610 $aNumerical stability. 610 $aOptimal control. 610 $aOptimization problem. 610 $aOrdinary differential equation. 610 $aOrthogonal polynomials. 610 $aParameter. 610 $aPiecewise. 610 $aPointwise. 610 $aPolynomial interpolation. 610 $aPolynomial. 610 $aProbability distribution. 610 $aQuadratic programming. 610 $aRandom variable. 610 $aRate of convergence. 610 $aRatio test. 610 $aRiccati equation. 610 $aSimpson's rule. 610 $aSimultaneous equations. 610 $aSmoothing spline. 610 $aSmoothing. 610 $aSmoothness. 610 $aSpecial case. 610 $aSpline (mathematics). 610 $aSpline interpolation. 610 $aStatistic. 610 $aStochastic calculus. 610 $aStochastic. 610 $aTelemetry. 610 $aTheorem. 610 $aTrapezoidal rule. 610 $aWaypoint. 610 $aWeight function. 610 $aWithout loss of generality. 615 0$aInterpolation. 615 0$aSmoothing (Numerical analysis) 615 0$aSmoothing (Statistics) 615 0$aCurve fitting. 615 0$aSplines. 615 0$aSpline theory. 676 $a511/.42 686 $aSK 880$2rvk 700 $aEgerstedt$b Magnus$0771533 701 $aMartin$b Clyde$058749 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910807652503321 996 $aControl theoretic splines$94069490 997 $aUNINA