Linear Optimal Control

Cover
Title Page
PREFACE
CONTENTS
Part I: INTRODUCTION
Chapter 1: INTRODUCTION
1.1 LINEAR OPTIMAL CONTROL
1.2 ABOUT THIS BOOK IN PARTICULAR
1.3 PART AND CHAPTER OUTLINE
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Part II: BASIC THEORY OF THE OPTIMAL REGULATOR
Chapter 2: THE STANDARD REGULATOR PROBLEM\342\200\224I
2.1 A REVIEW OF THE REGULATOR PROBLEM
2.2 THE HAMILTON-JACOBI EQUATION
2.3 SOLUTION OF THE FINITE-TIME REGULATOR PROBLEM
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Chapter 3: THE STANDARD REGULATOR PROBLEM\342\200\224II
3.1 THE INFINITE-TIME REGULATOR PROBLEM
3.2 STABILITY OF THE TIME-INVARIANT REGULATOR
3.3 SUMMARY AND DISCUSSION OF THE REGULATOR PROBLEM RESULTS
3.4 EXTENSIONS OF THE REGULATOR PROBLEM
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Chapter 4: THE REGULATOR WlTH A PRESCRIBED DEGREE OF STABILITY
4.1 QUALITATIVE STATEMENT OF THE REGULATOR PROBLEM WITH A PRESCRIBED DEGREE OF STABILITY
4.2 QUANTITATIVE STATEMENT AND SOLUTION OF THE REGULATOR PROBLEM WITH A PRESCRIBED DEGREE OF STABILITY
4.3 EXTENSIONS OF THE PRECEDING RESULTS
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Part III: PROPERTIES AND APPLICATION OF THEOPTIMAL REGULATOR
Chapter 5: PROPERTIES OF REGUfATOR SYSrEMS WITH A CIASSICAL CONTROL INTERPRETATION
5.1 THE REGULATOR FROM AN ENGINEERING VIEWPOINT
5.2 SOME FUNDAMENTAL FORMULAS
5.3 GAIN MARGIN, PHASE MARGIN AND TIME-DELAY TOLERANCE
5.4 POSITIONING OF THE CLOSED-LOOP SYSTEM POLES
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Chapter 6: INSERTION OF NONLINEARITIES IN OPTIMAL REGULATORS
6.1 TOLERANCE OF NONLINEARITIES IN THE FEEDBACK LOOP
6.2 RELAY CONTROL SYSTEMS
6.3 INTRODUCTION OF RELAYS INTO NOMINALLY OPTIMAL SYSTEMS
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Chapter 7: SENSITIVITY ASPECTS OF OPTIMAL REGULATORS
7.1 THE SENSITIVITY PROBLEM
7.2 SENSITIVITY REDUCTION IN OPTIMAL REGULATORS
7.3 THE INVERSE REGULATOR PROBLEM
7.4 FURTHER DISCUSSION OF THE POLE-POSITIONING PROBLEM
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Chapter 8: STATE ESTIMATOR DESIGN
8.1 THE NATURE OF THE STATE ESTIMATION PROBLEM
8.2 NONSTATISTICAL ESTIMATOR DESIGN WITH FULL ESTIMATOR DIMENSION
8.3 NONSTATISTICAL ESTIMATOR DESIGN WITH REDUCED ESTIMATOR DYNAMICS
8.4 STATISTICAL ESTIMATOR DESIGN (THE KALMAN-BUCY FILTER)
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Chapter 9: SYSTEM DESIGN USING STATE ESTIMATORS
9.1 CONTROLLER DESIGN\342\200\224BASIC VERSIONS
9.2 VARIANTS ON THE BASIC CONTROLLER
9.3 SIMPLIFICATIONS OF THE CONTROLLER FOR MULTIPLE-OUTPUT, SINGLE-INPUT SYSTEMS
9.4 THE SEPARATION THEOREM
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Part IV: EXTENSIONS TO MORE COMPLEX PROBLEMS
Chapter 10: OPTIMAL LINEAR REGULATORS WITH INPUT DISTURBANCES
10.1 PROPORTIONAL-PLUS-INTEGRAL FEEDBACK
10.2 THE REGULATOR PROBLEM WITH DERIVATIVE CONSTRAINTS
10.3 APPLICATION AND PROPERTIES OF OPTIMAL REGULATORS WHICH INCLUDE INTEGRAL FEEDBACK
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Chapter 11: TRACKING SYSTEMS
11.1 THE PROBLEM OF ACHIEVING A DESIRED TRAJECTORY
11.2 FINITE-TllUE RESULTS
11.3 INFINITE-TIME RESULTS
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Chapter 12: OPTIMAL REGULATORS WITH DUAL-MODE CONTROL
12.1 THE BANG-BANG MODE AND LINEAR MODE
12.2 LINEAR MODE SOLUTIONS TO THE SINGULAR OPTIMAL CONTROL PROBLEM
12.3 PROPERTIES OF THE DUAL-MODE OPTIMAL REGULATOR
12.4 OPTIMAL REGULATOR WITH BOUNDS ON THE CONTROL DERIVATIVE
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Chapter 13: OPTIMAL LINEAR REGULATORS WITH CONTROLLER CONSTRAINTS
13.1 FORMULATION OF SPECIFIC OPTIMAL REGULATOR PROBLEMS
13.2 ANALYTICAL RESULTS AND COMPUTATIONAL ASPECTS
13.3 PROPERTIES OF OPTIMAL SOLUTIONS
13.4 DYNAMIC CONTROLLERS
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Chapter 14: TWO FURTHER TOPICS
14.1 DISCRETE TIME SYSTEMS
14.2 THE INFINITE-TIME REGULATOR PROBLEM FOR TIME-VARYING SYSTEMS
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Part V: COMPUTATIONAL ASPECTS
Chapter 15: SOLUTION OF THE RICCATI EQUATION
15.1 PRELIMINARY REMARKS
15.2 RICCATI EQUATION SOLUTION WITH THE AID OF A LINEAR DIFFERENTIAL EQUATION
15.3 STEADY STATE SOLUTION OF THE RICCATI EQUATION
15.4 APPROXIMATE SOLUTIONS OF HIGH-ORDER RICCATI EQUATIONS VIA SINGULAR PERTURBATION
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Appendix A: BR!EF REV/EW OF SOME RESULTS OF MATRIX THEORY
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Appendix B: BRIEF REVIEW OF SEVERAL MAJOR RESULTS OF LINEAR SYSrEM THEORY
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INDEX