{"product_id":"control-theoretic-splines-optimal-control-statistics-and-path-planning-9780691132969","title":"Control Theoretic Splines  Optimal Control","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSplines, 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 various methods and applications to show how they arise naturally in the theory of linear control systems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"[T]he book presents an excellent treatment of the topic of control-theoretic splines. It showcases effective and transparent use of optimization technique in function space sellings and of optimal control techniques to problems in the domain of approximation theory.\"--Ilya Kolmanovsky, Mathematical Reviews\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ix      Chapter 1: INTRODUCTION 1  1.1 From Interpolation to Smoothing 1  1.2 Background 2  1.3 The Introduction of Control Theory 4  1.4 Applications 7  1.5 Topical Outline of the Book 8      Chapter 2: CONTROL SYSTEMS AND MINIMUM NORM PROBLEMS 11  2.1 Linear Control Systems 11  2.2 Hilbert Spaces 14  2.3 The Projection Theorem 15  2.4 Optimization and Gateaux Derivatives 18  2.5 The Point-to-Point Transfer Problem 21      Chapter 3: EIGHT FUNDAMENTAL PROBLEMS 25  3.1 The Basic Set-Up 26  3.2 Interpolating Splines 29  3.3 Interpolating Splines with Constraints 31  3.4 Smoothing Splines 35  3.5 Smoothing Splines with Constraints 38  3.6 Dynamic Time Warping 45  3.7 Trajectory Planning 48      Chapter 4: SMOOTHING SPLINES AND GENERALIZATIONS 53  4.1 The Basic Smoothing Problem 56  4.2 The Basic Algorithm 60  4.3 Interpolating Splines with Initial Data 62  4.4 Problems with Additional Constraints 63      Chapter 5: APPROXIMATIONS AND LIMITING CONCEPTS 73  5.1 Basic Assumptions 73  5.2 Convergence of the Smoothing Spline 75  5.3 Quadrature Schemes 80  5.4 Rate of Convergence 82  5.5 Cubic Spline Convergence Bounds 83      Chapter 6: SMOOTHING SPLINES WITH CONTINUOUS DATA 87  6.1 Continuous Data 89  6.2 The Continuous Smoothing Problem 89  6.3 The Basic Two-Point Boundary Value Problem 91  6.4 The General Two-Point Boundary Value Problem 95  6.5 Multipoint Problems 99  6.6 Recursive Splines 101      Chapter 7: MONOTONE SMOOTHING SPLINES 113  7.1 The Monotone Smoothing Problem 113  7.2 Properties of the Solution 115  7.3 Dynamic Programming 118  7.4 Monotone Cubic Splines 120  7.5 Probability Densities 126      Chapter 8: SMOOTHING SPLINES AS INTEGRAL FILTERS 133  8.1 Smoothing Concepts 133  8.2 Splines from Statistical Data 136  8.3 The Optimal Control Problem 141  8.4 The Cubic Smoothing Spline 146      Chapter 9: OPTIMAL TRANSFER BETWEEN AFFINE VARIETIES 155  9.1 Point-to-Point Transfer 155  9.2 Transfer between Affine Varieties 156  9.3 Transfer through Dynamic Programming 158  9.4 A Multi-Agent Problem 164      Chapter 10: PATH PLANNING AND TELEMETRY 169  10.1 The Telemetry Problem 169  10.2 Splines on Spheres 171  10.3 Splines and Bezier Curves 176  10.4 Conflict Resolution for Autonomous Vehicles 185      Chapter 11: NODE SELECTION 193  11.1 Background 193  11.2 Sampling for Interpolation and Smoothing 194  11.3 Optimal Timing Control 195  11.4 Applications to Smoothing Splines 199      Bibliography 205  Index 215","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49917779706199,"sku":"9780691132969","price":59.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691132969.jpg?v=1738449164","url":"https:\/\/bookcurl.com\/products\/control-theoretic-splines-optimal-control-statistics-and-path-planning-9780691132969","provider":"Book Curl","version":"1.0","type":"link"}