{"product_id":"interval-analysis-application-in-the-optimal-control-problems-hardback-9781394190973","title":"Interval Analysis; Application in the Optimal Control Problems (Hardback) 9781394190973","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eInterval Analysis\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eApplication in the Optimal Control Problems\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eNavid Razmjooy (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781394190973, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 28 November 2023\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e208 pages\u003cbr\u003e22.9 x 15.2 x 1.5 cm, 0.558 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cb\u003eInterval Analysis\u003c\/b\u003e \u003cp\u003e\u003cb\u003eAn innovative and unique application of interval analysis to optimal control problems\u003c\/b\u003e \u003c\/p\u003e\n\u003cp\u003eIn \u003ci\u003eInterval Analysis: Application in the Optimal Control Problems\u003c\/i\u003e, celebrated researcher and engineer Dr. Navid Razmjooy delivers an expert discussion of the uncertainties in the analysis of optimal control problems. In the book, Dr. Razmjooy uses an open-ended approach to solving optimal control problems with indefinite intervals. Utilizing an extended, Runge-Kutta method, the author demonstrates how to accelerate its speed with the piecewise function. \u003c\/p\u003e\n\u003cp\u003eYou’ll find recursive methods used to achieve more compact answers, as well as how to solve optimal control problems using the interval Chebyshev’s function. The book also contains: \u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003e A thorough introduction to common errors and mistakes, generating uncertainties in physical models\u003c\/li\u003e \u003cli\u003e Comprehensive explorations of the literature on the subject, including Hukurara’s derivatives\u003c\/li\u003e \u003cli\u003e Practical discussions of the interval analysis and its variants, including the classical (Minkowski) methods\u003c\/li\u003e \u003cli\u003e Complete treatments of existing control methods, including classic, conventional advanced, and robust control.\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003ePerfect for master’s and PhD students working on system uncertainties, \u003ci\u003eInterval Analysis: Application in the Optimal Control Problems\u003c\/i\u003e will also benefit researchers working in laboratories, universities, and research centers.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eAbout the Author viii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Preface and Overview 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 1: Preface and Overview 1\u003c\/p\u003e \u003cp\u003eChapter 2: Introduction 2\u003c\/p\u003e \u003cp\u003eChapter 3: Literature Review 2\u003c\/p\u003e \u003cp\u003eChapter 4: Introduction to Interval Analysis and Solving the Problems with Interval Uncertainties 2\u003c\/p\u003e \u003cp\u003eChapter 5: Stability and Controllability Based on Interval Analysis 3\u003c\/p\u003e \u003cp\u003eChapter 6: Optimal Control of the Systems with Interval Uncertainties 3\u003c\/p\u003e \u003cp\u003eChapter 7: Conclusions 3\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Introduction 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Background 5\u003c\/p\u003e \u003cp\u003e2.2 Relationship Between Error and Uncertainty 7\u003c\/p\u003e \u003cp\u003e2.3 Expert Perspectives on Interval Analysis 8\u003c\/p\u003e \u003cp\u003e2.4 Precision Analysis of Interval-Based Models (Self-Validated Numeric) 10\u003c\/p\u003e \u003cp\u003e2.5 Concepts of the Ordinary and Interval-based Optimal Control 11\u003c\/p\u003e \u003cp\u003e2.6 Orthogonal Spectral Methods 13\u003c\/p\u003e \u003cp\u003e2.7 Desired Confidence Interval 13\u003c\/p\u003e \u003cp\u003e2.8 Conclusions 14\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Literature Review 17\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Introduction to Interval Analysis and Solving the Problems with Interval Uncertainties 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 29\u003c\/p\u003e \u003cp\u003e4.2 Introduction to IA 30\u003c\/p\u003e \u003cp\u003e4.3 The Algebra of Interval Sets 31\u003c\/p\u003e \u003cp\u003e4.3.1 Classic Interval Algebra (Minkowski Method) 31\u003c\/p\u003e \u003cp\u003e4.3.2 Mathematical Norm and Distance in the IA 33\u003c\/p\u003e \u003cp\u003e4.3.3 Kaucher Extended Interval Analysis 33\u003c\/p\u003e \u003cp\u003e4.3.4 Modal Interval Analysis 34\u003c\/p\u003e \u003cp\u003e4.3.5 Hukuhara Difference Method 35\u003c\/p\u003e \u003cp\u003e4.4 Interval Representations 36\u003c\/p\u003e \u003cp\u003e4.5 Interval Complex Integers 39\u003c\/p\u003e \u003cp\u003e4.6 Interval Vector and Matrix 41\u003c\/p\u003e \u003cp\u003e4.6.1 Vector and Matrix IA 41\u003c\/p\u003e \u003cp\u003e4.6.2 Interval Vector Norm 42\u003c\/p\u003e \u003cp\u003e4.6.3 Interval Matrix Analysis 42\u003c\/p\u003e \u003cp\u003e4.6.3.1 Conceptional Example: Wrapping Effect 43\u003c\/p\u003e \u003cp\u003e4.6.4 Interval Matrices Norm 44\u003c\/p\u003e \u003cp\u003e4.6.5 Interval Determination of a Matrix 45\u003c\/p\u003e \u003cp\u003e4.6.6 The Inverse of a Regular Interval Matrix 45\u003c\/p\u003e \u003cp\u003e4.6.7 Eigenvalues and Eigenvectors of an Interval Matrix 45\u003c\/p\u003e \u003cp\u003e4.7 Solving Linear Systems with Interval Parameters 46\u003c\/p\u003e \u003cp\u003e4.8 Interval Functions 46\u003c\/p\u003e \u003cp\u003e4.8.1 Overestimated Interval Function 46\u003c\/p\u003e \u003cp\u003e4.8.2 Minimal Interval Function 48\u003c\/p\u003e \u003cp\u003e4.9 Determining the Minimal Interval 49\u003c\/p\u003e \u003cp\u003e4.9.1 Uniform Interval Functions 49\u003c\/p\u003e \u003cp\u003e4.9.2 Nonuniform Interval Functions 49\u003c\/p\u003e \u003cp\u003e4.9.3 Interval Power Series 50\u003c\/p\u003e \u003cp\u003e4.10 Interval Derivative and Integral Functions 52\u003c\/p\u003e \u003cp\u003e4.10.1 Interval Derivative 52\u003c\/p\u003e \u003cp\u003e4.10.2 Interval Integration 53\u003c\/p\u003e \u003cp\u003e4.11 Centered Inclusion Method 54\u003c\/p\u003e \u003cp\u003e4.11.1 Linearized Interval Functions Around the Center 54\u003c\/p\u003e \u003cp\u003e4.11.2 Taylor Inclusion Functions 54\u003c\/p\u003e \u003cp\u003e4.12 Interval Nonlinear Systems 56\u003c\/p\u003e \u003cp\u003e4.13 Analysis of the Interval Dynamic Systems in the Presence of Interval Uncertainties 57\u003c\/p\u003e \u003cp\u003e4.13.1 Solving the Interval Initial Value Problems 58\u003c\/p\u003e \u003cp\u003e4.14 The Interval Runge–Kutta Method (IRKM) for Interval Differential Equations 60\u003c\/p\u003e \u003cp\u003e4.14.1 Introduction 60\u003c\/p\u003e \u003cp\u003e4.14.2 Generalized IRKM (GIRKM) Based on Switching Points 63\u003c\/p\u003e \u003cp\u003e4.14.3 Numerical Examples 66\u003c\/p\u003e \u003cp\u003e4.15 Interval Uncertainty Analyses based on Orthogonal Functions 78\u003c\/p\u003e \u003cp\u003e4.15.1 Interval Ε-orthogonal 79\u003c\/p\u003e \u003cp\u003e4.15.2 Interval Weierstrass's Theorem 79\u003c\/p\u003e \u003cp\u003e4.16 Interval Orthogonal Polynomials 79\u003c\/p\u003e \u003cp\u003e4.16.1 Legendre Polynomials 80\u003c\/p\u003e \u003cp\u003e4.16.2 Chebyshev Polynomials 80\u003c\/p\u003e \u003cp\u003e4.16.3 Interval Orthogonal Functions 82\u003c\/p\u003e \u003cp\u003e4.17 Piecewise Extension of the Interval Orthogonal Functions 83\u003c\/p\u003e \u003cp\u003e4.18 Conclusion 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Stability and Controllability Based on Interval Analysis 91\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 91\u003c\/p\u003e \u003cp\u003e5.1.1 Classical Control Theory 91\u003c\/p\u003e \u003cp\u003e5.1.2 Advanced Modern Control Systems Theory 92\u003c\/p\u003e \u003cp\u003e5.1.3 Optimal Control 93\u003c\/p\u003e \u003cp\u003e5.1.4 Robust Control 94\u003c\/p\u003e \u003cp\u003e5.1.5 Adaptive Control Theory 95\u003c\/p\u003e \u003cp\u003e5.2 Interval Stability and Controllability 95\u003c\/p\u003e \u003cp\u003e5.3 Interval Stability 96\u003c\/p\u003e \u003cp\u003e5.4 Characteristic Polynomial 97\u003c\/p\u003e \u003cp\u003e5.5 Routh–Hurwitz Stability Test 98\u003c\/p\u003e \u003cp\u003e5.6 Kharitonov's Theorem (Interval Routh–Hurwitz Stability Test) 99\u003c\/p\u003e \u003cp\u003e5.6.1 Kharitonov Polynomial Theory 99\u003c\/p\u003e \u003cp\u003e5.6.2 A Centered Representation of the Interval Routh–Hurwitz Stability Criterion 102\u003c\/p\u003e \u003cp\u003e5.7 Interval Stability Based on Linear Matrix Inequalities 102\u003c\/p\u003e \u003cp\u003e5.7.1 The Positive Matrix of the Interval Matrix 102\u003c\/p\u003e \u003cp\u003e5.7.2 Stability Analysis of the Interval Systems 103\u003c\/p\u003e \u003cp\u003e5.7.3 Linear Matrix Inequalities 104\u003c\/p\u003e \u003cp\u003e5.8 Controllability and Observability 107\u003c\/p\u003e \u003cp\u003e5.9 Controllability and Observability Based on Interval Criteria 107\u003c\/p\u003e \u003cp\u003e5.9.1 Singular Values for Analyzing the Controllability 111\u003c\/p\u003e \u003cp\u003e5.10 Conclusions 117\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Optimal Control of the Systems with Interval Uncertainties 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 121\u003c\/p\u003e \u003cp\u003e6.2 Indirect Methods 123\u003c\/p\u003e \u003cp\u003e6.3 Direct Methods 123\u003c\/p\u003e \u003cp\u003e6.4 Optimal Control Problem in the Presence of Interval Uncertainties 127\u003c\/p\u003e \u003cp\u003e6.5 Interval Optimal Control Based on the Indirect Method 128\u003c\/p\u003e \u003cp\u003e6.5.1 Analysis of the Standard Interval Calculus of Variations 129\u003c\/p\u003e \u003cp\u003e6.6 Analysis of the Problem of the Interval Optimal Control Based on Euler–Lagrange Equations 131\u003c\/p\u003e \u003cp\u003e6.7 Solving Optimal Control Problems with Interval Uncertainties: Interval Runge–Kutta Method 132\u003c\/p\u003e \u003cp\u003e6.8 Optimal Control of Problems with Interval Uncertainties Using the Chebyshev Inclusion Method 146\u003c\/p\u003e \u003cp\u003e6.9 Piecewise Interval Chebyshev Method for OCPs 152\u003c\/p\u003e \u003cp\u003e6.10 Solving Quadratic Optimal Control Problems with Interval Uncertainties Based on Indirect Method: Interval Quadratic Regulator 159\u003c\/p\u003e \u003cp\u003e6.11 Problem Statement (Interval Quadratic Regulator) 173\u003c\/p\u003e \u003cp\u003e6.12 Interval Optimal Control Based on Direct Method 179\u003c\/p\u003e \u003cp\u003e6.13 Applied Simulations 183\u003c\/p\u003e \u003cp\u003e6.14 Conclusion 192\u003c\/p\u003e \u003cp\u003eReferences 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Conclusions 197\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIndex 199\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Electronics \u0026amp; communications engineering [\u003ca title=\"See our other books on Electronics \u0026amp; communications engineering\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Electronics%20\u0026amp;%20communications%20engineering%20%5BTJ%5D%22\"\u003eTJ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-IEEE Press","offers":[{"title":"Brand 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