Kooperativer Bibliotheksverbund

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Format: 1 online resource (803 p.)

Edition: 1st ed.

ISBN: 1-281-17210-3 , 9786611172107 , 0-08-055610-8

Series Statement: Advanced mathematical tools for automatic control engineers ; 1

Content: This book provides a blend of Matrix and Linear Algebra Theory, Analysis, Differential Equations, Optimization, Optimal and Robust Control. It contains an advanced mathematical tool which serves as a fundamental basis for both instructors and students who study or actively work in Modern Automatic Control or in its applications. It is includes proofs of all theorems and contains many examples with solutions. It is written for researchers, engineers, and advanced students who wish to increase their familiarity with different topics of modern and classical mathematics related to System and A

Note: Includes index. , Front Cover; Advanced Mathematical Tools for Automatic Control Engineers; Copyright Page; Table of Contents; Preface; Notations and Symbols; List of Figures; Part I: Matrices and Related Topics; Chapter 1. Determinants; 1.1 Basic Definitions; 1.2 Properties of Numerical Determinants, Minors and Cofactors; 1.3 Linear Algebraic Equations and the Existence of Solutions; Chapter 2. Matrices and Matrix Operations; 2.1 Basic Definitions; 2.2 Some Matrix Properties; 2.3 Kronecker Product; 2.4 Submatrices, Partitioning of Matrices and Schur's Formulas; 2.5 Elementary Transformations on Matrices , 2.6 Rank of a Matrix2.7 Trace of a Quadratic Matrix; Chapter 3. Eigenvalues and Eigenvectors; 3.1 Vectors and Linear Subspaces; 3.2 Eigenvalues and Eigenvectors; 3.3 The Cayley-Hamilton Theorem; 3.4 The Multiplicities and Generalized Eigenvectors; Chapter 4. Matrix Transformations; 4.1 Spectral Theorem for Hermitian Matrices; 4.2 Matrix Transformation to the Jordan Form; 4.3 Polar and Singular-Value Decompositions; 4.4 Congruent Matrices and the Inertia of a Matrix; 4.5 Cholesky Factorization; Chapter 5. Matrix Functions; 5.1 Projectors; 5.2 Functions of a Matrix , 5.3 The Resolvent for a Matrix5.4 Matrix Norms; Chapter 6. Moore-Penrose Pseudoinverse; 6.1 Classical Least Squares Problem; 6.2 Pseudoinverse Characterization; 6.3 Criterion for Pseudoinverse Checking; 6.4 Some Identities for Pseudoinverse Matrices; 6.5 Solution of Least Squares Problem Using Pseudoinverse; 6.6 Cline's Formulas; 6.7 Pseudo-Ellipsoids; Chapter 7. Hermitian and Quadratic Forms; 7.1 Definitions; 7.2 Nonnegative Definite Matrices; 7.3 Sylvester Criterion; 7.4 The Simultaneous Transformation of a Pair of Quadratic Forms; 7.5 Simultaneous Reduction of more than Two Quadratic Forms , 7.6 A Related Maximum-Minimum Problem7.7 The Ratio of Two Quadratic Forms; Chapter 8. Linear Matrix Equations; 8.1 General Type of Linear Matrix Equation; 8.2 Sylvester Matrix Equation; 8.3 Lyapunov Matrix Equation; Chapter 9. Stable Matrices and Polynomials; 9.1 Basic Definitions; 9.2 Lyapunov Stability; 9.3 Necessary Condition of the Matrix Stability; 9.4 The Routh-Hurwitz Criterion; 9.5 The Liénard-Chipart Criterion; 9.6 Geometric Criteria; 9.7 Polynomial Robust Stability; 9.8 Controllable, Stabilizable, Observable and Detectable Pairs; Chapter 10. Algebraic Riccati Equation , 10.1 Hamiltonian Matrix10.2 All Solutions of the Algebraic Riccati Equation; 10.3 Hermitian and Symmetric Solutions; 10.4 Nonnegative Solutions; Chapter 11. Linear Matrix Inequalities; 11.1 Matrices as Variables and LMI Problem; 11.2 Nonlinear Matrix Inequalities Equivalent to LMI; 11.3 Some Characteristics of Linear Stationary Systems (LSS); 11.4 Optimization Problems with LMI Constraints; 11.5 Numerical Methods for LMI Resolution; Chapter 12. Miscellaneous; 12.1 Lambda-Matrix Inequalities; 12.2 Matrix Abel Identities; 12.3 S-Procedure and Finsler Lemma; 12.4 Farkaš Lemma , 12.5 Kantorovich Matrix Inequality , English

Additional Edition: ISBN 0-08-044674-4

Language: English

UID:

Format: 1 online resource (568 p.)

ISBN: 1-282-30936-6 , 9786612309366 , 0-08-091403-9

Content: The second volume of this work continues the approach of the first volume, providing mathematical tools for the control engineer and examining such topics as random variables and sequences, iterative logarithmic and large number laws, differential equations, stochastic measurements and optimization, discrete martingales and probability space. It includes proofs of all theorems and contains many examples with solutions.It is written for researchers, engineers and advanced students who wish to increase their familiarity with different topics of modern and classical mathematics related to

Note: Description based upon print version of record. , Front cover; Half title page; Dedication; Title page; Copyright page; Contents; Preface; Notations and Symbols; List of Figures; List of Tables; PART I: Basics of Probability; Chapter 1. Probability Space; 1.1. Set operations, algebras and sigma-algebras; 1.2. Measurable and probability spaces; 1.3. Borel algebra and probability measures; 1.4. Independence and conditional probability; Chapter 2. Random Variables; 2.1. Measurable functions and random variables; 2.2. Transformation of distributions; 2.3. Continuous random variables; Chapter 3. Mathematical Expectation , 3.1. Definition of mathematical expectation3.2. Calculation of mathematical expectation; 3.3. Covariance, correlation and independence; Chapter 4. Basic Probabilistic Inequalities; 4.1. Moment-type inequalities; 4.2. Probability inequalities for maxima of partial sums; 4.3. Inequalities between moments of sums and summands; Chapter 5. Characteristic Functions; 5.1. Definitions and examples; 5.2. Basic properties of characteristic functions; 5.3. Uniqueness and inversion; PART II: Discrete Time Processes; Chapter 6. Random Sequences; 6.1. Random process in discrete and continuous time , 6.2. Infinitely often events6.3. Properties of Lebesgue integral with probabilistic measure; 6.4. Convergence; Chapter 7. Martingales; 7.1. Conditional expectation relative to a sigma-algebra; 7.2. Martingales and related concepts; 7.3. Main martingale inequalities; 7.4. Convergence; Chapter 8. Limit Theorems as Invariant Laws; 8.1. Characteristics of dependence; 8.2. Law of large numbers; 8.3. Central limit theorem; 8.4. Logarithmic iterative law; PART III: Continuous Time Processes; Chapter 9. Basic Properties of Continuous Time Processes; 9.1. Main definitions; 9.2. Second-order processes , 9.3. Processes with orthogonal and independent incrementsChapter 10. Markov Processes; 10.1. Definition of Markov property; 10.2. Chapman--Kolmogorov equation and transition function; 10.3. Diffusion processes; 10.4. Markov chains; Chapter 11. Stochastic Integrals; 11.1. Time-integral of a sample-path; 11.2. ?-stochastic integrals; 11.3. The Itô stochastic integral; 11.4. The Stratonovich stochastic integral; Chapter 12. Stochastic Differential Equations; 12.1. Solution as a stochastic process; 12.2. Solutions as diffusion processes; 12.3. Reducing by change of variables , 12.4. Linear stochastic differential equationsPART IV: Applications; Chapter 13. Parametric Identification; 13.1. Introduction; 13.2. Some models of dynamic processes; 13.3. LSM estimating; 13.4. Convergence analysis; 13.5. Information bounds for identification methods; 13.6. Efficient estimates; 13.7. Robustification of identification procedures; Chapter 14. Filtering, Prediction and Smoothing; 14.1. Estimation of random vectors; 14.2. State-estimating of linear discrete-time processes; 14.3. State-estimating of linear continuous-time processes; Chapter 15. Stochastic Approximation , 15.1. Outline of chapter , English

Additional Edition: ISBN 0-08-044673-6

Language: English

UID:

Format: 1 Online-Ressource

ISBN: 9783319092096 , 9783319092102

Series Statement: Systems & control: foundations & applications

Language: English

DOI: 10.1007/978-3-319-09210-2

URL: Volltext

URL: Inhaltsverzeichnis

URL: Abstract

Author information: Azhmyakov, Vadim 1965-

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Format: 1 Online-Ressource

ISBN: 9780817681517 , 9780817681524

Series Statement: Systems & control: foundations & applications

Language: English

Keywords: Optimale Kontrolle ; Robuste Optimierung

DOI: 10.1007/978-0-8176-8152-4

URL: Volltext

Author information: Boltjanskij, Vladimir G. 1925-2019

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Format: XXII, 432 S. , Ill.

ISBN: 9780817681517

Series Statement: Systems & Control: Foundations and Applications

Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-0-8176-8152-4

Language: English

Subjects: Mathematics

Keywords: Optimale Kontrolle ; Robuste Optimierung

Author information: Boltjanskij, Vladimir G. 1925-2019

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Format: XII, 204 S. , graph. Darst. , 24 cm

ISBN: 3540761543

Series Statement: Lecture notes in control and information sciences 225

Note: Literaturangaben

Language: English

Subjects: Mathematics

Keywords: Stochastische Optimierung ; Lernender Automat ; Kontrolltheorie ; Automatentheorie ; Lehrbuch

URL: Inhaltsverzeichnis

URL: Inhaltstext

URL: Cover

UID:

Format: XI, 225 S. , Ill., graph. Darst.

Edition: 1. ed.

ISBN: 0080420249

Language: English

Subjects: Computer Science

Keywords: Maschinelles Lernen

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Format: 1 Online ressource (xxviii, 774 Seiten)

ISBN: 9780080446745

In: 1

Language: English

Keywords: Automation ; Kontrolltheorie

URL: Volltext  (URL des Erstveröffentlichers)

UID:

Format: 298 S.

ISBN: 0-247-9429-X

Series Statement: Control engineering series 4

UID:

Format: 1 online resource (526 pages) : , illustrations

ISBN: 0-323-89889-0 , 0-323-89816-5

Note: Front Cover -- Classical and Analytical Mechanics -- Copyright -- Contents -- List of figures -- List of tables -- About the author -- Preface -- Notation -- Introduction -- 1 Kinematics of a point -- 1.1 Products of vectors -- 1.1.1 Internal (scalar) product -- 1.1.2 Vector product -- 1.1.3 Main properties of triple products -- 1.2 Generalized coordinates -- 1.2.1 Different possible coordinates -- 1.2.2 Definition of generalized coordinates -- 1.2.3 Relationship of generalized coordinates with Cartesian -- 1.2.4 Coefficients of Lamé -- 1.3 Kinematics in generalized coordinates -- 1.3.1 Velocity in generalized coordinates -- 1.3.2 Acceleration in generalized coordinates -- 1.4 Movement in the cylindrical and spherical coordinate systems -- 1.4.1 Movement in cylindrical coordinates -- 1.4.2 Movement in spherical coordinates -- 1.5 Normal and tangential accelerations -- 1.6 Some examples -- 1.7 Exercises -- 2 Rigid body kinematics -- 2.1 Angular velocity -- 2.1.1 Definition of a rigid body -- 2.1.2 The Euler theorem -- 2.1.3 Joint rotation with a common pivot -- 2.1.4 Parallel and non-coplanar rotations -- 2.2 Complex movements of the rigid body -- 2.2.1 General relations -- 2.2.2 Plane non-parallel motion and center of velocities -- 2.3 Complex movement of a point -- 2.3.1 Absolute velocity -- 2.3.2 Absolute acceleration -- 2.4 Examples -- 2.5 Kinematics of a rigid body rotation -- 2.5.1 Finite rotations -- 2.5.2 Rotation matrix -- 2.5.3 Composition of rotations -- 2.6 Rotations and quaternions -- 2.6.1 Quaternions -- 2.6.2 Composition or summation of rotations as a quaternion -- 2.7 Differential kinematic equations (DKEs) -- 2.7.1 DKEs in Euler coordinates -- 2.7.2 DKEs in quaternions: Poisson equation -- 2.8 Exercises -- 3 Dynamics -- 3.1 Main dynamics characteristics -- 3.1.1 System of material points. , 3.1.2 Three main dynamics characteristics -- 3.2 Axioms or Newton's laws -- 3.2.1 Newton's axioms -- 3.2.2 Expression for Q̇ -- 3.2.3 Expression for K̇A -- 3.3 Force work and potential forces -- 3.3.1 Elementary and total force work -- 3.3.2 Potential forces -- 3.3.3 Force power and expression for Ṫ -- 3.3.4 Conservative systems -- 3.4 Virial of a system -- 3.4.1 Main definition of virial -- 3.4.2 Virial for homogeneous potential energies -- 3.5 Properties of the center of mass -- 3.5.1 Dynamics of the center of inertia (mass) -- 3.6 ``King/König/Rey'' theorem -- 3.6.1 Principle theorem -- 3.6.2 Moment of inertia and the impulse moment with respect to a pivot -- 3.6.3 A rigid flat body rotating in the same plane -- 3.6.4 Calculation of moments of inertia for different rigid bodies -- 3.6.5 König theorem application -- 3.6.6 Steiner's theorem on the inertia moment -- 3.7 Movements with friction -- 3.8 Exercises -- 4 Non-inertial and variable-mass systems -- 4.1 Non-inertial systems -- 4.1.1 Newton's second law regarding a relative system -- 4.1.2 Rizal's theorem in a relative system -- 4.1.3 Kinetic energy and work in a relative system -- 4.1.4 Some examples dealing with non-inertial systems -- 4.2 Dynamics of systems with variable mass -- 4.2.1 Reactive forces and the Meshchersky equation -- 4.2.2 Tsiolkovsky's rocket formula and other examples -- 4.3 Exercises -- 5 Euler's dynamic equations -- 5.1 Tensor of inertia -- 5.2 Relative kinetic energy and impulse momentum -- 5.2.1 Relative kinetic energy -- 5.2.2 Relative impulse momentum -- 5.3 Some properties of inertial tensors -- 5.3.1 Tensor of inertia as a non-negative symmetric matrix -- 5.3.2 Eigenvalues and eigenvectors of inertial tensors -- 5.3.3 Examples using tensors of inertia -- 5.4 Euler's dynamic equations -- 5.4.1 Special cases of Euler's equations. , 5.5 Dynamic reactions caused by the gyroscopic moment -- 5.6 Exercises -- 6 Dynamic Lagrange equations -- 6.1 Mechanical connections -- 6.2 Generalized forces -- 6.3 Dynamic Lagrange equations -- 6.4 Normal form of Lagrange equations -- 6.5 Electrical and electromechanical models -- 6.5.1 Some physical relations -- 6.5.2 Table of electromechanical analogies -- 6.6 Exercises -- 7 Equilibrium and stability -- 7.1 Definition of equilibrium -- 7.2 Equilibrium in conservative systems -- 7.3 Stability of equilibrium -- 7.3.1 Definition of local stability -- 7.3.2 Stability of equilibrium in conservative systems -- 7.4 Unstable equilibria in conservative systems -- 7.5 Exercises -- 8 Oscillations analysis -- 8.1 Movements in the vicinity of equilibrium points -- 8.1.1 Small oscillations -- 8.1.2 Characteristic polynomial -- 8.1.3 General solution of the characteristic equation -- 8.2 Oscillations in conservative systems -- 8.2.1 Some properties of the characteristic equation -- 8.2.2 Normal coordinates -- 8.3 Several examples of oscillation analysis -- 8.3.1 Three masses joined by springs in circular dynamics -- 8.3.2 Three masses joined by springs with dynamics on a straight line -- 8.3.3 Four spring-bound masses with restricted linear dynamics -- 8.3.4 Three identical pendula held by springs -- 8.3.5 Four-loop LC circuits -- 8.3.6 Finding one polynomial root using other known roots -- 8.3.7 Hint: how to resolve analytically cubic equations -- 8.4 Exercises -- 9 Linear systems of second order -- 9.1 Models governed by second order differential equations -- 9.2 Frequency response -- 9.3 Examples -- 9.3.1 Three-variable systems -- 9.3.2 Electrical circuit -- 9.3.3 Linear system with input delay -- 9.3.4 Mechanical system with friction -- 9.3.5 Electric circuit with variable elements -- 9.4 Asymptotic stability -- 9.4.1 Algebraic criteria. , 9.4.2 Geometric criteria of asymptotic stability -- 9.5 Polynomial robust stability -- 9.5.1 Parametric uncertainty and robust stability -- 9.5.2 The Kharitonov theorem -- 9.6 Exercises -- 10 Hamiltonian formalism -- 10.1 Hamiltonian function -- 10.2 Hamiltonian canonical form -- 10.3 First integrals -- 10.4 Some properties of first integrals -- 10.4.1 Cyclic coordinates -- 10.4.2 Some properties of the Poisson brackets -- 10.4.3 First integrals by inspection -- 10.5 Exercises -- 11 The Hamilton-Jacobi equation -- 11.1 Canonical transformations -- 11.2 The Hamilton-Jacobi method -- 11.3 Hamiltonian action and its variation -- 11.4 Integral invariants -- 11.4.1 Integral invariants of Poincaré and Poincaré-Cartan -- 11.4.2 The Lee Hwa Chung theorem -- 11.5 Canonicity criteria -- 11.5.1 Poincaré theorem: ( c,F) -criterion -- 11.5.2 Analytical expression for the Hamiltonian after a coordinate canonical transformation -- 11.5.3 Brackets of Lagrange -- 11.5.4 Free canonical transformation and the S-canonicity criterion -- 11.6 The Hamilton-Jacobi equation -- 11.7 Complete integral of the Hamilton-Jacobi equation -- 11.7.1 Complete integral -- 11.7.2 Generalized-conservative (stationary) systems with first integrals -- 11.8 On relations with optimal control -- 11.8.1 Problem formulation and value function -- 11.8.2 Hamilton-Jacobi-Bellman equation -- 11.8.3 Verification rule as a sufficient condition of optimality -- 11.8.4 Affine dynamics with a quadratic cost -- 11.8.5 The case when the Hamiltonian admits the existence of first integrals -- 11.8.6 The deterministic Feynman-Kac formula: the general smooth case -- 11.9 Exercises -- 12 Collection of electromechanical models -- 12.1 Cylindrical manipulator (2-PJ and 1-R) -- 12.2 Rectangular (Cartesian) robot manipulator -- 12.3 Scaffolding type robot manipulator -- 12.4 Spherical (polar) robot manipulator. , 12.5 Articulated robot manipulator 1 -- 12.6 Universal programmable manipulator -- 12.7 Cincinnati Milacron T3 manipulator -- 12.8 CD motor, gear, and load train -- 12.9 Stanford/JPL robot manipulator -- 12.10 Unimate 2000 manipulator -- 12.11 Robot manipulator with swivel base -- 12.12 Cylindrical robot with spring -- 12.13 Non-ordinary manipulator with shock absorber -- 12.14 Planar manipulator with two joints -- 12.15 Double ``crank-turn'' swivel manipulator -- 12.16 Robot manipulator of multicylinder type -- 12.17 Arm manipulator with springs -- 12.18 Articulated robot manipulator 2 -- 12.19 Maker 110 -- 12.20 Manipulator on a horizontal platform -- 12.21 Two-arm planar manipulator -- 12.22 Manipulator with three degrees of freedom -- 12.23 CD motor with load -- 12.24 Models of power converters with switching-mode power supply -- 12.24.1 Buck type DC-DC converter -- 12.24.2 Boost type DC-DC converter -- 12.25 Induction motor -- Bibliography -- Index -- Back Cover.

Language: English