Linear Optimal Control

Cover......Page 1
Title Page......Page 3
PREFACE......Page 5
CONTENTS......Page 9
Part I: INTRODUCTION......Page 15
1.1 LINEAR OPTIMAL CONTROL......Page 17
1.2 ABOUT THIS BOOK IN PARTICULAR......Page 19
1.3 PART AND CHAPTER OUTLINE......Page 20
REFERENCES......Page 21
Part II: BASIC THEORY OF THE OPTIMAL REGULATOR......Page 23
2.1 A REVIEW OF THE REGULATOR PROBLEM......Page 25
2.2 THE HAMILTON-JACOBI EQUATION......Page 30
2.3 SOLUTION OF THE FINITE-TIME REGULATOR PROBLEM......Page 37
REFERENCES......Page 44
3.1 THE INFINITE-TIME REGULATOR PROBLEM......Page 45
3.2 STABILITY OF THE TIME-INVARIANT REGULATOR......Page 53
3.3 SUMMARY AND DISCUSSION OF THE REGULATOR PROBLEM RESULTS......Page 57
3.4 EXTENSIONS OF THE REGULATOR PROBLEM......Page 60
REFERENCES......Page 63
4.1 QUALITATIVE STATEMENT OF THE REGULATOR PROBLEM WITH A PRESCRIBED DEGREE OF STABILITY......Page 64
4.2 QUANTITATIVE STATEMENT AND SOLUTION OF THE REGULATOR PROBLEM WITH A PRESCRIBED DEGREE OF STABILITY......Page 67
4.3 EXTENSIONS OF THE PRECEDING RESULTS......Page 73
REFERENCES......Page 75
Part III: PROPERTIES AND APPLICATION OF THEOPTIMAL REGULATOR......Page 77
5.1 THE REGULATOR FROM AN ENGINEERING VIEWPOINT......Page 79
5.2 SOME FUNDAMENTAL FORMULAS......Page 82
5.3 GAIN MARGIN, PHASE MARGIN AND TIME-DELAY TOLERANCE......Page 84
5.4 POSITIONING OF THE CLOSED-LOOP SYSTEM POLES......Page 91
REFERENCES......Page 103
6.1 TOLERANCE OF NONLINEARITIES IN THE FEEDBACK LOOP......Page 105
6.2 RELAY CONTROL SYSTEMS......Page 113
6.3 INTRODUCTION OF RELAYS INTO NOMINALLY OPTIMAL SYSTEMS......Page 125
REFERENCES......Page 130
7.1 THE SENSITIVITY PROBLEM......Page 131
7.2 SENSITIVITY REDUCTION IN OPTIMAL REGULATORS......Page 139
7.3 THE INVERSE REGULATOR PROBLEM......Page 149
7.4 FURTHER DISCUSSION OF THE POLE-POSITIONING PROBLEM......Page 155
REFERENCES......Page 157
8.1 THE NATURE OF THE STATE ESTIMATION PROBLEM......Page 159
8.2 NONSTATISTICAL ESTIMATOR DESIGN WITH FULL ESTIMATOR DIMENSION......Page 163
8.3 NONSTATISTICAL ESTIMATOR DESIGN WITH REDUCED ESTIMATOR DYNAMICS......Page 173
8.4 STATISTICAL ESTIMATOR DESIGN (THE KALMAN-BUCY FILTER)......Page 183
REFERENCES......Page 204
9.1 CONTROLLER DESIGN—BASIC VERSIONS......Page 206
9.2 VARIANTS ON THE BASIC CONTROLLER......Page 217
9.3 SIMPLIFICATIONS OF THE CONTROLLER FOR MULTIPLE-OUTPUT, SINGLE-INPUT SYSTEMS......Page 226
9.4 THE SEPARATION THEOREM......Page 236
REFERENCES......Page 238
Part IV: EXTENSIONS TO MORE COMPLEX PROBLEMS......Page 239
10.1 PROPORTIONAL-PLUS-INTEGRAL FEEDBACK......Page 241
10.2 THE REGULATOR PROBLEM WITH DERIVATIVE CONSTRAINTS......Page 243
10.3 APPLICATION AND PROPERTIES OF OPTIMAL REGULATORS WHICH INCLUDE INTEGRAL FEEDBACK......Page 251
REFERENCES......Page 260
11.1 THE PROBLEM OF ACHIEVING A DESIRED TRAJECTORY......Page 261
11.2 FINITE-TllUE RESULTS......Page 265
11.3 INFINITE-TIME RESULTS......Page 275
REFERENCES......Page 285
12.1 THE BANG-BANG MODE AND LINEAR MODE......Page 286
12.2 LINEAR MODE SOLUTIONS TO THE SINGULAR OPTIMAL CONTROL PROBLEM......Page 296
12.3 PROPERTIES OF THE DUAL-MODE OPTIMAL REGULATOR......Page 305
12.4 OPTIMAL REGULATOR WITH BOUNDS ON THE CONTROL DERIVATIVE......Page 313
REFERENCES......Page 315
13.1 FORMULATION OF SPECIFIC OPTIMAL REGULATOR PROBLEMS......Page 317
13.2 ANALYTICAL RESULTS AND COMPUTATIONAL ASPECTS......Page 322
13.3 PROPERTIES OF OPTIMAL SOLUTIONS......Page 330
13.4 DYNAMIC CONTROLLERS......Page 335
REFERENCES......Page 341
14.1 DISCRETE TIME SYSTEMS......Page 342
14.2 THE INFINITE-TIME REGULATOR PROBLEM FOR TIME-VARYING SYSTEMS......Page 349
REFERENCES......Page 354
Part V: COMPUTATIONAL ASPECTS......Page 355
15.1 PRELIMINARY REMARKS......Page 357
15.2 RICCATI EQUATION SOLUTION WITH THE AID OF A LINEAR DIFFERENTIAL EQUATION......Page 359
15.3 STEADY STATE SOLUTION OF THE RICCATI EQUATION......Page 367
15.4 APPROXIMATE SOLUTIONS OF HIGH-ORDER RICCATI EQUATIONS VIA SINGULAR PERTURBATION......Page 377
REFERENCES......Page 387
Appendix A: BR!EF REV/EW OF SOME RESULTS OF MATRIX THEORY......Page 390
REFERENCES......Page 402
Appendix B: BRIEF REVIEW OF SEVERAL MAJOR RESULTS OF LINEAR SYSrEM THEORY......Page 403
REFERENCES......Page 406
INDEX......Page 407