Modern Control Engineering

Preface

Chapter 1 State Representation of Dynamical Systems


1.1 State Equations


1.2 Linear State Equations


1.3 Fundamental Matrices


1.4 The Transition Matrix


1.5 Inclusion of the Forcing or Control Variables


1.6 Eigenvalues and Eigenvectors


1.7 Discrete-Time State Equations


1.8 Stability of Discrete-Time Linear Systems


1.9 Controllability


1.10 Observability

Problems

Chapter 2 Finite Dimensional Optimization


2.1 Motivation


2.2 Unconstrained Maxima and Minima


2.3 Equality Constraints


2.4 Inequality Constraints


2.5 Convexity and Sufficiency


2.6 Linear Programming


2.7 Direct Methods of Minimization


2.8 An Illustrative Minimization Example


2.9 Minimization by Steepest Descent


2.10 Second Order Gradients


2.11 Conjugate Direction Methods


2.12 One Dimensional Searches


2.13 Davidon-Fletcher-Powell


2.14 Fletcher-Reeves


2.15 Powell's Method


2.16 Direct Methods for Constrained Minimization


2.17 Penalty Functions


2.18 Use of Transformations


2.19 Parameterization of Dynamical Control Problems


2.20 Optimal Control of Dynamical Discrete-Time Systems

Problems

Chapter 3 Infinite Dimensional Optimization


3.1 A Classic Problem and a Classical Solution


3.2 Dynamical Optimization with no Terminal Constraints


3.3 A Simple Control Problem


3.4 Terminal Constraints and Variable Terminal Time


3.5 An Elementary Thrust-Programming Problem


3.6 A Foretaste of Computational Difficulties


3.7 The Linear-Quadratic Control Problem


3.8 Design of a Lateral Autostabilizer for an Aircraft


3.9 Stability of the Linear-Quadratic Regulator


3.10 Inequality Constraints


3.11 Pontryagin's Maximum or Minimum Principle


3.12 Additional Necessary Conditions and Sufficiency


3.13 Singular Control


3.14 Computation of Optimal Control — Direct and Indirect Methods


3.15 Boundary Iterations


3.16 Quasilinearization


3.17 Gradient Method in Function Space


3.18 Second Variations


3.19 Conjugate Gradients


3.20 Computations with Inequality Constraints

Problems

Chapter 4 Dynamic Programming


4.1 Historical Background


4.2 A Multi-Stage Decision Problem


4.3 The Principle of Optimality


4.4 A Simple Control Problem in Discrete Time


4.5 The General Calculation of Optimal Control by Dynamic Programming


4.6 Results for Linear Multivariable Digital Control Systems


4.7 An Example of Discrete-Time Control


4.8 Computation of Nonlinear Discrete-Time Control


4.9 The Continuous Form of Dynamic Programming


4.10 A Special Solution of the Hamilton-Jacobi Equation


4.11 Differential Dynamic Programming

Problems

Chapter 5 Introductory Stochastic Estimation and Control


5.1 Deterministic Multivariable Observers


5.2 The Kaiman Filter


5.3 Extensions of the Kaiman Filter


5.4 An Example of the Extended Kaiman Filter


5.5 Stochastic Feedback Control


5.6 The Stochastic Linear-Quadratic Control Problem

Problems

Chapter 6 Actual and Potential Applications


6.1 Resume — Practical Significance of the Results


6.2 Linear Control with Quadratic Criteria


6.3 Static and Dynamic Optimization


6.4 Applications of the Kaiman Filter

Chapter 7 Appendices


7.1 Stability of Discrete-Time Linear Systems


7.2 Differentiation of Matrix Expressions


7.3 Canonical Form for a Single-Output Linear System


7.4 Markov Sequences

Chapter 8 Supplement — Introduction to Matrices and State Variables


8.1 Matrices and Vectors


8.2 Numerical Solution of Ordinary Differential Equations


8.3 The Generalized Newton-Raphson Process


8.4 State Variable Characterization of Dynamical Systems

Chapter 9 Bibliography and References

Index