Modern control theory

목차 (Table of Contents)

• CONTENTS
• PREFACE = xvii
• 1 BACKGROUND AND PREVIEW = 1
• 1.1 Introduction = 1
• 1.2 Systems, Systems Theory and Control Theory = 2
• 1.3 Modeling = 4
• 1.3.1 Analytical Modeling, = 4
• 1.3.2 Experimental Modeling, = 8
• 1.4 Classification of Systems = 12
• 1.5 Mathematical Representation of Systems = 14
• 1.6 Modern Control Theory : The Perspective of This Book = 15
• References = 16
• Illustrative Problems = 17
• Problems = 29
• 2 HIGHLIGHTS OF CLASSICAL CONTROL THEORY = 31
• 2.1 Introduction = 31
• 2.2 System Representation = 31
• 2.3 Feedback = 31
• 2.4 Measures of Performance and Methods of Analysis in Classical Control Theory = 37
• 2.5 Methods of Improving System Performance = 41
• 2.6 Extension of Classical Techniques to More Complex Systems = 48
• References = 49
• Illustrative Problems = 49
• Problems = 68
• 3 STATE VARIABLES AND THE STATE SPACE DESCRIPTION OF DYNAMIC SYSTEMS = 72
• 3.1 Introduction = 72
• 3.2 The Concept of State = 74
• 3.3 State Space Representation of Dynamic Systems = 75
• 3.4 Obtaining the State Equations = 80
• 3.4.1 From Input-Output Differential of Difference Equations = 80
• 3.4.2 Simultaneous Differential Equations = 81
• 3.4.3 Using Simulation Diagrams = 83
• 3.4.4 State Equations From Transfer Functions = 88
• 3.4.5 State Equations Directly From the System's Linear Graph = 98
• 3.5 Interconnection of Subsystems = 101
• 3.6 Comments on the State Space Representation = 102
• References = 103
• Illustrative Problems = 104
• Problems = 118
• 4 FUNDAMENTALS OF MATRIX ALGEBRA = 121
• 4.1 Introduction = 121
• 4.2 Notation = 121
• 4.3 Algebraic Operations with Matrices = 123
• 4.4 The Associative, Commutative and Distributive Law of Matrix Algebra = 125
• 4.5 Matrix Transpose, Conjugate and the Associative Matrix = 126
• 4.6 Determinants, Minors and Cofactors = 126
• 4.7 Rank and Trace of a Matrix = 128
• 4.8 Matrix Inversion = 129
• 4.9 Partitioned Matrices = 131
• 4.10 Elementary Operations and Elementary Matrices = 132
• 4.11 Differentiation and Integration of Matrices = 133
• 4.12 Additional Matrix Calculus = 134
• 4.12.1 The Gradient Vector and Differentiation with Respect to a Vector = 134
• 4.12.2 Generalized Taylor Series = 137
• 4.12.3 Vectorizing a Matrix = 138
• References = 140
• Illustrative Problems = 140
• Problems = 155
• 5 VECTORS AND LINEAR VECTOR SPACES = 157
• 5.1 Introduction = 157
• 5.2 Planar and Three-Dimensional Real Vector Spaces = 158
• 5.3 Axiomatic Definition of a Linear Vector Space = 159
• 5.4 Linear Dependence and Independence = 161
• 5.5 Vectors Which Span a Space ; Basis Vectors and Dimensionality = 164
• 5.6 Special Operations and Definitions in Vector Spaces = 166
• 5.7 Orthogonal Vectors and Their Construction = 168
• 5.8 Vector Expansions and the Reciprocal Basis Vectors = 172
• 5.9 Linear Manifolds, Subspaces and Projections = 177
• 5.10 Product Spaces = 178
• 5.11 Transformations or Mappings = 179
• 5.13 Some Finite Dimensional Transformations = 184
• 5.14 Some Transformations on Infinite Dimensional Spaces = 189
• References = 190
• Illustrative Problems = 191
• Problems = 204
• 6 SIMULATANEOUS LINEAR EQUATIONS = 207
• 6.1 Introduction = 207
• 6.2 Statement of the Problem and Conditions for Solutions = 207
• 6.3 The Row-Reduced Echelon Form of a Matrix = 209
• 6.3.1 Applications to Polynomial Matrices = 212
• 6.3.2 Application to Matrix Fraction Description of Systems = 214
• 6.4 Solution by Partitioning = 214
• 6.5 A Gram-Schmidt Expansion Method of Solution = 215
• 6.6 Homogeneous Linear Equations = 218
• 6.7 The Underdetermined Case = 219
• 6.8 The Overdetermined Case = 221
• 6.9 Two Basic Problems in Control Theory = 226
• 6.9.1 A Control Problem = 226
• 6.9.2 A State Estimation Problem = 228
• 6.10 Lyapunov Equations = 229
• References = 231
• Illustrative Problems = 231
• Problems = 242
• 7 EIGENVALUES AND EIGENVECTORS = 245
• 7.1 Introduction = 245
• 7.2 Definition of the Eigenvalue-Eigenvector Problem = 245
• 7.3 Eigenvalues = 246
• 7.4 Determination of Eigenvectors = 247
• 7.5 Determination of Generalized Eigenvectors = 256
• 7.6 Iterative Computer Methods for Determining Eigenvalues and Eigenvectors = 260
• 7.7 Spectral Decomposition and Invariance Properties = 263
• 7.8 Bilinear and Quadratic Forms = 264
• 7.9 Miscellaneous Uses of Eigenvalues and Eigenvectors = 265
• References = 266
• Illustrative Problems = 267
• Problems = 280
• 8 FUNCTIONS OF SQUARE MATRICES AND THE CAYLEY-HAMILTON THEOREM = 282
• 8.1 Introduction = 282
• 8.2 Powers of a Matrix and Matrix Polynomials = 282
• 8.3 Infinite Series and Analytic Functions of a Matrix = 283
• 8.4 The Characteristic Polynomial and Cayley-Hamilton Theorem = 286
• 8.5 Some Uses of the Cayley-Hamilton Theorem = 287
• 8.6 Solution of the Unforced State Equations = 291
• References = 292
• Illustrative Problems = 292
• Problems = 306
• 9 ANALYSIS OF CONTINUOUS- AND DISCRETE-TIME LINEAR STATE EQUATIONS = 308
• 9.1 Introduction = 308
• 9.2 First-Order Scalar Differential Equations = 309
• 9.3 The Constant Coefficient Matrix Case = 310
• 9.4. System Modes and Modal Decomposition = 312
• 9.5 The Time-Varying Matrix Case = 314
• 9.6 The Transition Matrix = 316
• 9.7 Summary of Continuous-Time Linear System Solutions = 318
• 9.8 Discrete-Time Models of Continuous-Time Systems = 319
• 9.9 Analysis of Constant Coefficient Discrete-Time State Equations = 322
• 9.10 Modal Decomposition = 323
• 9.11 Time-Variable Coefficients = 324
• 9.13 Summary of Discrete-Time Linear System Solutions = 325
• References = 325
• Illustrative Problems = 325
• Problems = 340
• 10 STABILITY = 342
• 10.1 Introduction = 342
• 10.2 Equilibrium Points and Stability Concepts = 343
• 10.3 Stability Definitions = 344
• 10.4 Linear System Stability = 346
• 10.5 Linear Constant Systems = 348
• 10.6 The Direct Method of Lyapunov = 349
• 10.7 A Cautionary Note on Time-Varying Systems = 358
• 10.8 Use of Lyapunov's Method in Feedback Design = 361
• References = 364
• Illustrative Problems = 365
• Problems = 370
• 11 CONTROLLABILITY AND OBSERVABILITY FOR LINEAR SYSTEMS = 373
• 11.1 Introduction = 373
• 11.2 Definitions = 373
• 11.2.1 Controllability = 374
• 11.2.2 Observability = 375
• 11.2.3 Dependence on the Model = 375
• 11.3 Time-Invariant Systems with Distinct Eigenvalues = 376
• 11.4 Time-Invariant Systems with Arbitrary Eigenvalues = 377
• 11.5 Yet Another Controllability／Obervability Condition = 379
• 11.6 Time-Varying Linear Systems = 380
• 11.6.1 Controllability of Continuous-Time Systems = 380
• 11.6.2 Obervability of Continuous-Time Systems = 382
• 11.6.3 Discrete-Time Systems = 383
• 11.7 Kalman Canonical Forms = 383
• 11.8 Stabilizability and Detectability = 386
• References = 387
• Illustrative Problems = 387
• Problems = 401
• 12 THE RELATIONSHIP BETWEEN STATE VARIABLE AND TRANSFER FUNCTION DESCRIPTIONS OF SYSTEMS = 404
• 12.1 Introduction = 404
• 12.2 Transfer Function Matrices From State Equations = 404
• 12.3 State Equations From Transfer Matrices : Realizations = 406
• 12.4 Definition and Implication of Irreducible Realizations = 408
• 12.5 The Determination of Irreducible Realizations = 411
• 12.5.1 Jordan Canonical Form Approach = 411
• 12.5.2 Kalman Canonical Form Approach to Minimal Realizations = 419
• 12.6 Minimal Realizations From Matrix Fraction Description = 422
• 12.7 Concluding Comments = 425
• References = 425
• Illustrative Problems = 426
• Problems = 440
• 13 DESIGN OF LINEAR FEEDBACK CONTROL SYSTEMS = 443
• 13.1 Introduction = 443
• 13.2 State Feeback and Output Feedback = 443
• 13.3 The Effect of Feedback on System Properties = 446
• 13.4 Pole Assignment Using State Feedback = 448
• 13.5 Partial Pole Placement Using Static Output Feedback = 457
• 13.6 Obervers-Reconstructing the State From Available Outputs = 461
• 13.6.1 Continuous-Time Full-State Observers = 461
• 13.6.2 Discrete-Time Full-State Obserbers = 464
• 13.6.3 Continuous-Time Reduced Order Observers = 470
• 13.6.4 Discrete-Time Reduced-Order Observers = 471
• 13.7 A Separation Principle For Feedback Controllers = 474
• 13.8 Transfer Function Version of Pole-Placement／Observer Design = 475
• 13.8.1 The Full-State Observer = 478
• 13.8.2 The Reduced-Order Observer = 482
• 13.8.3 The Discrete-Time Pole Placement／Observer Problem = 484
• 13.9 The Design of Decoupled or Noninteracting Systems = 486
• References = 488
• Illustrative Problems = 489
• Problems = 498
• 14 AN INTRODUCTION TO OPTIMAL CONTROL THEORY = 501
• 14.1 Introduction = 501
• 14.2 Statement of the Optimal Control Problem = 501
• 14.3 Dynamic Programming = 503
• 14.3.1 General Introduction to the Principle of Optimality = 503
• 14.3.2 Application to Discrete-Time Optimal Control = 505
• 14.3.3 The Discrete-Time Linear Quadratic Problem = 507
• 14.3.4 The Infinite Horizon, Constant Gain Solution = 512
• 14.4 Dynamic Programming Approach to Continuous-Time Optimal Control = 515
• 14.4.1 Linear-Quadratic (LQ) Problem : The Continuous Riccati Equation = 517
• 14.4.2 Infinite Time-To-Go Problem : The Algebraic Riccati Equation = 522
• 14.5 Pontryagin's Minimum Principle = 523
• 14.6 Separation Theorem = 525
• 14.7 Robustness Issues = 527
• 14.8 Extensions = 533
• 14.9 Concluding Comments = 539
• References = 540
• Illustrative Problems = 541
• Problems = 559
• 15 AN INTRODUCTION TO NONLINEAR CONTROL SYSTEMS = 563
• 15.1 Introduction = 563
• 15.2 Linearzation : Analysis of Small Deviations from Nominal = 565
• 15.3 Dynamic Linearization Using State Feedback = 570
• 15.4 Harmonic Linearization : Describing Functions = 573
• 15.5 Applications of Describing Functions = 578
• 15.6 Lyapunov Stability Theory and Related Frequency Domain Results = 582
• References = 588
• Illustrative Problems = 589
• Problems = 614
• ANSWERS TO PROBLEMS = 618
• INDEX = 639