LEADER 06558nam 2200469 450 001 9910830218203321 005 20231213075739.0 010 $a1-394-19098-0 010 $a1-394-19100-6 035 $a(MiAaPQ)EBC30980066 035 $a(Au-PeEL)EBL30980066 035 $a(OCoLC)1412621154 035 $a(EXLCZ)9929128125100041 100 $a20231213d2024 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInterval Analysis $eApplication in the Optimal Control Problems /$fNavid Razmjooy 205 $aFirst edition. 210 1$aHoboken, New Jersey :$cJohn Wiley & Sons, Inc.,$d[2024] 210 4$dİ2024 215 $a1 online resource (211 pages) 225 1 $aIEEE Press Series on Control Systems Theory and Applications Series 311 08$aPrint version: Razmjooy, Navid Interval Analysis Newark : John Wiley & Sons, Incorporated,c2023 9781394190973 320 $aIncludes bibliographical references and index. 327 $aCover -- Title Page -- Copyright Page -- Contents -- About the Author -- Chapter 1 Preface and Overview -- .Chapter 1: Preface and Overview -- .Chapter 2: Introduction -- .Chapter 3: Literature Review -- .Chapter 4: Introduction to Interval Analysis and Solving the Problems with Interval Uncertainties -- .Chapter 5: Stability and Controllability Based on Interval Analysis -- .Chapter 6: Optimal Control of the Systems with Interval Uncertainties -- .Chapter 7: Conclusions -- Chapter 2 Introduction -- 2.1 Background -- 2.2 Relationship Between Error and Uncertainty -- 2.3 Expert Perspectives on Interval Analysis -- 2.4 Precision Analysis of Interval-Based Models (Self-Validated Numeric) -- 2.5 Concepts of the Ordinary and Interval-based Optimal Control -- 2.6 Orthogonal Spectral Methods -- 2.7 Desired Confidence Interval -- 2.8 Conclusions -- References -- Chapter 3 Literature Review -- References -- Chapter 4 Introduction to Interval Analysis and Solving the Problems with Interval Uncertainties -- 4.1 Introduction -- 4.2 Introduction to IA -- 4.3 The Algebra of Interval Sets -- 4.3.1 Classic Interval Algebra (Minkowski Method) -- 4.3.2 Mathematical Norm and Distance in the IA -- 4.3.3 Kaucher Extended Interval Analysis -- 4.3.4 Modal Interval Analysis -- 4.3.5 Hukuhara Difference Method -- 4.4 Interval Representations -- 4.5 Interval Complex Integers -- 4.6 Interval Vector and Matrix -- 4.6.1 Vector and Matrix IA -- 4.6.2 Interval Vector Norm -- 4.6.3 Interval Matrix Analysis -- 4.6.3.1 Conceptional Example: Wrapping Effect -- 4.6.4 Interval Matrices Norm -- 4.6.5 Interval Determination of a Matrix -- 4.6.6 The Inverse of a Regular Interval Matrix -- 4.6.7 Eigenvalues and Eigenvectors of an Interval Matrix -- 4.7 Solving Linear Systems with Interval Parameters -- 4.8 Interval Functions -- 4.8.1 Overestimated Interval Function. 327 $a4.8.2 Minimal Interval Function -- 4.9 Determining the Minimal Interval -- 4.9.1 Uniform Interval Functions -- 4.9.2 Nonuniform Interval Functions -- 4.9.3 Interval Power Series -- 4.10 Interval Derivative and Integral Functions -- 4.10.1 Interval Derivative -- 4.10.2 Interval Integration -- 4.11 Centered Inclusion Method -- 4.11.1 Linearized Interval Functions Around the Center -- 4.11.2 Taylor Inclusion Functions -- 4.12 Interval Nonlinear Systems -- 4.13 Analysis of the Interval Dynamic Systems in the Presence of Interval Uncertainties -- 4.13.1 Solving the Interval Initial Value Problems -- 4.14 The Interval Runge-Kutta Method (IRKM) for Interval Differential Equations -- 4.14.1 Introduction -- 4.14.2 Generalized IRKM (GIRKM) Based on Switching Points -- 4.14.3 Numerical Examples -- 4.15 Interval Uncertainty Analyses based on Orthogonal Functions -- 4.15.1 Interval ?-orthogonal -- 4.15.2 Interval Weierstrass's Theorem -- 4.16 Interval Orthogonal Polynomials -- 4.16.1 Legendre Polynomials -- 4.16.2 Chebyshev Polynomials -- 4.16.3 Interval Orthogonal Functions -- 4.17 Piecewise Extension of the Interval Orthogonal Functions -- 4.18 Conclusion -- References -- Chapter 5 Stability and Controllability Based on Interval Analysis -- 5.1 Introduction -- 5.1.1 Classical Control Theory -- 5.1.2 Advanced Modern Control Systems Theory -- 5.1.3 Optimal Control -- 5.1.4 Robust Control -- 5.1.5 Adaptive Control Theory -- 5.2 Interval Stability and Controllability -- 5.3 Interval Stability -- 5.4 Characteristic Polynomial -- 5.5 Routh-Hurwitz Stability Test -- 5.6 Kharitonov's Theorem (Interval Routh-Hurwitz Stability Test) -- 5.6.1 Kharitonov Polynomial Theory -- 5.6.2 A Centered Representation of the Interval Routh-Hurwitz Stability Criterion -- 5.7 Interval Stability Based on Linear Matrix Inequalities -- 5.7.1 The Positive Matrix of the Interval Matrix. 327 $a5.7.2 Stability Analysis of the Interval Systems -- 5.7.3 Linear Matrix Inequalities -- 5.8 Controllability and Observability -- 5.9 Controllability and Observability Based on Interval Criteria -- 5.9.1 Singular Values for Analyzing the Controllability -- 5.10 Conclusions -- References -- Chapter 6 Optimal Control of the Systems with Interval Uncertainties -- 6.1 Introduction -- 6.2 Indirect Methods -- 6.3 Direct Methods -- 6.4 Optimal Control Problem in the Presence of Interval Uncertainties -- 6.5 Interval Optimal Control Based on the Indirect Method -- 6.5.1 Analysis of the Standard Interval Calculus of Variations -- 6.6 Analysis of the Problem of the Interval Optimal Control Based on Euler-Lagrange Equations -- 6.7 Solving Optimal Control Problems with Interval Uncertainties: Interval Runge-Kutta Method -- 6.8 Optimal Control of Problems with Interval Uncertainties Using the Chebyshev Inclusion Method -- 6.9 Piecewise Interval Chebyshev Method for OCPs -- 6.10 Solving Quadratic Optimal Control Problems with Interval Uncertainties Based on Indirect Method: Interval Quadratic Regulator -- 6.11 Problem Statement (Interval Quadratic Regulator) -- 6.12 Interval Optimal Control Based on Direct Method -- 6.13 Applied Simulations -- 6.14 Conclusion -- References -- Chapter 7 Conclusions -- Index -- EULA. 410 0$aIEEE Press series on electronics technology. 606 $aInterval analysis (Mathematics) 615 0$aInterval analysis (Mathematics) 676 $a354.81150006 700 $aRazmjooy$b Navid$f1987-$01670764 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830218203321 996 $aInterval Analysis$94032821 997 $aUNINA