UID:
edoccha_9958072089902883
Format:
1 online resource (xv, 341 pages) :
,
illustrations
ISBN:
1-283-52535-6
,
9786613837806
,
0-08-095521-5
Series Statement:
Mathematics in science and engineering
Content:
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank
Note:
Front Cover; Random Processes in Nonlinear Control Systems; Copyright Page; Contents; Editor's Foreword; Preface; INTRODUCTION; Chapter 1. NONLINEAR TRANSFORMATIONS WITHOUT FEEDBACK; 1.1 Nonlinear Lagless Transformations; 1.2 Nonlinear Transformations with Lag; 1.3 The Problem of Synthesis. Optimal Conditions for Various Classes of Transformations; 1.4 The Application of Methods of Synthesis. Nonlinear Filters; 1.5 Statistical Linearization; Chapter 2. NONLINEAR TRANSFORMATION WITH FEEDBACK. STATIONARY STATES; 2.1 A Short Description of the Basic Methods of Investigation
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2.2 The Application of Statistical Linearization to the Analysis of Nonlinear Transformations with Normally Distributed Stationary Signals; 2.3 Computation of Frequency Distortions Introduced by Nonlinear Elements; 2.4 Restrictions Imposed by the Requirement That the Input Signal of the Nonlinear System Be Normal; 2.5 The Synthesis of Linear Compensation Networks in Closed-Loop Systems with Nonlinearities; 2.6 Application of the Theory of Markov Processes in the Study of Some Nonlinear Systems; Chapter 3. NONLINEAR TRANSFORMATIONS WITH FEEDBACK. NONSTATIO NARY STATES
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3.1 The Transformation of a Slowly Changing Signal in the Presence of a High-Frequency Random Interference; 3.2 Passage of a Slowly Varying Random Signal through a System in a State with Periodic Oscillations; 3.3 Transformation of the Sum of Wide-Band, Normal, Random Signals, and Harmonic Signals in a Nonlinear System with Feedback (Method of Statistical Linearization); 3.4 Random Disturbances of Periodic States in Relay Systems (Exact Solution by the Method of Alignment); Chapter 4. EXTREMAL SYSTEMS; 4.1 Basic Principles of the Operation of Extremal Systems
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4.2 Extremal Systems with a Time Separation between Testing and Operation Systems with Proportional Action; 4.3 Discrete Extremal Systems with Constant Steps; 4.4 Extremal Systems in Which Testing and Operation Are Separated by a Frequency Band; 4.5 An Automatic Extremal System with Simultaneous Testing and Operation; Appendix I: FUNCTIONS my(mx, sx), h1(mx, sx), a2 (mx, sx), AND a3 (mx, sx) FOR SEVERAL TYPICAL NONLINEARITIES; 1. The Ideal Relay Y = l sgn X; 2. A Relay with a Dead Zone; 3. An Element with a Bounded Zone of Linearity; 4. An Element with a Dead Zone
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5. An Element with a Bounded Zone of Linearity and a Dead Zone; 6. An Element with a Characteristic of the Form Y = Nx2 sgn x; 7. An Element with the Characteristic Y = Nx3; 8. A Relay with a Hysteresis Loop; 9. An Element with a Bounded Zone of Linearity with Nonsymmetrical Bounds; Appendix II: REPRESENTATION OF A LAGLESS NONLINEAR TRANSFORMATION IN THE FORM OF AN INTEGRAL TRANSFORMATION IN A COMPLEX REGION. THE THEOREM OF R. PRICE; Appendix III: COMPUTATION OF THE INTEGRALS In; Appendix IV: THE COEFFICIENTS OF STATISTICAL LINEARIZATION h1(a, s) AND h2(a, s) FOR TYPICAL NONLlNEARITIES; 1. The Ideal Relay
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English
Additional Edition:
ISBN 0-12-551650-9
Language:
English
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