For control engineers, optimal control is a tool to design a primal controller which secures system stability and fulfils a certain set of specifications via the optimisation of a specific performance index. In this way, troublesome trial-and-error controller tuning procedures are avoided. The next step is to assess the possibility of practical implementation, and this usually leads to a need to implement some controller trade-offs. To this end, this book aims to construct bridges between conventional parameter optimisation and the methods of optimal control theory. Optimal Control Engineering with Matlab teaches students efficiently how to apply the well-known standard optimal control theory as well as recently developed methods for the practical implementation of optimal controllers for dynamic systems. In this book, the author uses his experience gained over twenty-five years of teaching and supervising graduate and postgraduate students in many engineering specialisations to communicate the essentials of a very important branch of control system theory to a new generation of engineering students.
Preface xi
Acknowledgments xiii
Chapter 1 Mathematical Background and 1 (34)
Optimal Problem Modeling
1.1 Introduction 1 (1)
1.2 Optimal Control in Engineering 2 (1)
1.3 Controller Design Concepts 3 (1)
1.4 Finite Dimensional Optimization---A 4 (5)
Mathematical Review
1.5 Optimal Problem Modeling 9 (26)
Problems 30 (2)
References 32 (3)
Chapter 2 Controller Design Based on 35 (60)
Parameter Optimization
2.1 Introduction 35 (1)
2.2 Performance Indices 35 (6)
2.3 Preliminary Design Concept - The 41 (3)
Inward Approach
2.4 Parameter Optimization Design - 44 (11)
Outward Approach
2.5 Limitations of Parameter Optimization 55 (9)
2.6 Parameter Optimization with 64 (6)
Constraints
2.7 Control Vector Parameterization 70 (5)
2.8 Parameters Optimization via Genetic 75 (20)
Algorithms
Problems 79 (5)
List of MATLAB Programs 84 (10)
References 94 (1)
Chapter 3 Calculus of Variations 95 (30)
3.1 Introduction 95 (1)
3.2 Motivation 95 (2)
3.3 Standard Problem Statement 97 (10)
3.4 Transverzality Conditions 107 (6)
3.5 Extreme Functional with Dynamic 113 (12)
Constraints
Problems 118 (6)
References 124 (1)
Chapter 4 Optimal Control Based on Calculus 125 (66)
of Variations
4.1 Introduction 125 (1)
4.2 Optimal Criteria 125 (2)
4.3 Statement of Optimal Control Problem 127 (5)
4.4 Necessary Conditions of Optimality 132 (13)
4.5 Terminal Controllers and Regulators 145 (10)
4.6 Terminal Constraints and Variable 155 (9)
Terminal Time
4.7 Approximate Optimal State-Feedback 164 (3)
Control
4.8 Numerical Solution Using MATLAB TBVP 167 (24)
Solver
Problems 176 (7)
List of MATLAB Programs 183 (6)
References 189 (2)
Chapter 5 Optimal Control with Input and 191 (68)
State Variable Constraints
5.1 Introduction 191 (1)
5.2 Input Constraints Optimization 191 (2)
5.3 Pontryagin's Principle 193 (4)
5.4 Optimal Time Problem 197 (14)
5.5 Minimum Control-Effort Problems 211 (19)
5.6 Singular Problem 230 (12)
5.7 Inequality Constraint of Pure State 242 (17)
Variable
Problems 250 (5)
List of MATLAB Programs 255 (3)
References 258 (1)
Chapter 6 Dynamic Programming 259 (56)
6.1 Introduction 259 (1)
6.2 Multi-Stage Decision Problem and 259 (2)
Principle of Optimality
6.3 A Simple Control Problem in 261 (8)
Discrete-Time
6.4 Continuous Form of Dynamic Programming 269 (11)
6.5 Parametric Expansion 280 (9)
6.6 Cross-Product Terms 289 (1)
6.7 Differential Dynamic Programming DDP 290 (25)
Problems 300 (6)
List of MATLAB Programs 306 (7)
References 313 (2)
Chapter 7 Linear-Quadratic (LQ) Optimal 315 (72)
Control
7.1 Introduction 315 (1)
7.2 Types of Optimal Control Problems 315 (1)
7.3 Optimal Solution of the State 316 (7)
Regulating Problem
7.4 Selection of the Q and R Matrices 323 (5)
7.5 Optimal Solution of the Output 328 (7)
Regulating Problem
7.6 Optimal Solution of the Tracking 335 (13)
Problem
7.7 Equivalent Quadratic Cost Functional 348 (5)
7.8 Solution Based on Hamiltonian Matrix 353 (7)
for Invariant Systems
7.9 Discrete-Time LQ Optimal Control 360 (7)
7.10 Iterative LQ for Nonlinear Systems 367 (20)
Problems 372 (7)
List of MATLAB Programs 379 (6)
References 385 (2)
Chapter 8 Optimal Solution Based on Genetic 387 (32)
Programming
8.1 Introduction 387 (1)
8.2 Genetic Programming Review 387 (4)
8.3 Enhanced Genetic Programming 391 (13)
8.4 Synthesizing Input Constraints 404 (15)
Optimal Control Problem
Problems 416 (1)
References 417 (2)
Index 419
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