## Optimal Control Theory for ApplicationsMechanical engineering, an engineering discipline born of the needs of the in dustrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series is a series featuring graduate texts and research monographs intended to address the need for information in con temporary areas of mechanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consulting editors are listed on page ii of this volume. The areas of concentration are applied mathematics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics of materials, processing, thermal science, and tribology. Austin, Texas Frederick F. Ling Preface Optimization is an area of mathematics that is concerned with finding the "best" points, curves, surfaces, and so on. "Best" is determined by minimizing some measure of performance subject to equality and inequality constraints. Points are constrained by algebraic equations; curves are constrained by or dinary differential equations and algebraic equations; surfaces are constrained by partial differential equations, ordinary differential equations, and algebraic equations. |

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### Contents

II | 1 |

III | 2 |

V | 3 |

VI | 4 |

VII | 5 |

VIII | 6 |

IX | 8 |

X | 11 |

CIV | 188 |

CVI | 190 |

CVIII | 192 |

CIX | 194 |

CX | 199 |

CXI | 200 |

CXII | 202 |

CXIII | 204 |

XI | 13 |

XII | 14 |

XIV | 16 |

XV | 18 |

XVI | 22 |

XVII | 26 |

XIX | 27 |

XXI | 29 |

XXII | 30 |

XXIV | 31 |

XXV | 34 |

XXVI | 35 |

XXVII | 36 |

XXVIII | 38 |

XXIX | 42 |

XXX | 43 |

XXXI | 44 |

XXXII | 45 |

XXXIII | 47 |

XXXIV | 50 |

XXXV | 52 |

XXXVI | 53 |

XXXVII | 59 |

XXXVIII | 60 |

XXXIX | 61 |

XL | 63 |

XLI | 66 |

XLII | 67 |

XLIII | 68 |

XLIV | 71 |

XLV | 76 |

XLVI | 77 |

XLVIII | 78 |

LI | 81 |

LII | 82 |

LIV | 85 |

LV | 88 |

LVI | 89 |

LVII | 91 |

LVIII | 95 |

LIX | 97 |

LX | 98 |

LXI | 100 |

LXII | 103 |

LXIII | 105 |

LXIV | 106 |

LXV | 108 |

LXVI | 109 |

LXVII | 110 |

LXVIII | 114 |

LXIX | 115 |

LXX | 116 |

LXXII | 118 |

LXXIII | 119 |

LXXV | 121 |

LXXVI | 122 |

LXXVII | 124 |

LXXVIII | 128 |

LXXIX | 129 |

LXXX | 131 |

LXXXI | 132 |

LXXXII | 133 |

LXXXIII | 134 |

LXXXIV | 136 |

LXXXV | 140 |

LXXXVI | 142 |

LXXXVII | 144 |

LXXXVIII | 145 |

LXXXIX | 147 |

XC | 148 |

XCII | 150 |

XCIII | 151 |

XCIV | 152 |

XCV | 166 |

XCVI | 167 |

XCVII | 169 |

XCVIII | 170 |

XCIX | 173 |

C | 176 |

CI | 177 |

CII | 182 |

CIII | 183 |

CXIV | 205 |

CXVI | 206 |

CXVII | 208 |

CXVIII | 210 |

CXIX | 211 |

CXX | 212 |

CXXI | 213 |

CXXII | 221 |

CXXIII | 224 |

CXXV | 226 |

CXXVI | 230 |

CXXVII | 232 |

CXXVIII | 235 |

CXXIX | 238 |

CXXX | 247 |

CXXXI | 249 |

CXXXII | 250 |

CXXXIII | 251 |

CXXXIV | 255 |

CXXXV | 258 |

CXXXVI | 259 |

CXXXVII | 260 |

CXXXVIII | 261 |

CXXXIX | 264 |

CXL | 267 |

CXLI | 268 |

CXLII | 270 |

CXLIII | 272 |

CXLIV | 275 |

CXLV | 276 |

CXLVI | 277 |

CXLVII | 281 |

CXLVIII | 282 |

CXLIX | 283 |

CL | 285 |

CLI | 287 |

CLII | 288 |

CLIII | 293 |

CLIV | 294 |

CLVI | 296 |

CLVII | 298 |

CLVIII | 302 |

CLIX | 305 |

CLX | 309 |

CLXI | 310 |

CLXII | 312 |

CLXIII | 317 |

CLXIV | 318 |

CLXV | 319 |

CLXVI | 320 |

CLXVII | 321 |

CLXVIII | 322 |

CLXX | 323 |

CLXXI | 324 |

CLXXII | 326 |

CLXXIII | 327 |

CLXXIV | 328 |

CLXXV | 329 |

CLXXVI | 332 |

CLXXVII | 334 |

CLXXVIII | 335 |

CLXXIX | 337 |

CLXXX | 338 |

CLXXXI | 340 |

CLXXXII | 344 |

CLXXXIII | 345 |

CLXXXIV | 347 |

CLXXXV | 349 |

CLXXXVI | 350 |

CLXXXVII | 351 |

CLXXXVIII | 353 |

CLXXXIX | 356 |

CXC | 357 |

CXCI | 358 |

CXCII | 362 |

CXCIII | 364 |

CXCIV | 365 |

CXCV | 366 |

373 | |

377 | |

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### Common terms and phrases

admissible comparison control admissible comparison path augmented performance index calculus of variations Chapter coefficients Const constant control inequality constraint control perturbation corner conditions defined differential constraints differential equations dynamical system equality constraint Euler-Lagrange equations evaluated final point final time problem Find the control finite first-order fixed final free final given Hamiltonian Hence independent differential indicial notation integral constraint Kepler's equation Lagrange multiplier leads Legendre-Clebsch condition minimal control minimal path minimal point minimizes the performance minimizing the distance neighboring optimal path obtained by taking off-boundary optimal control problem optimal point parabola parameter optimization problem perturbation problem prescribed boundary conditions prescribed final conditions prescribed initial conditions quadratic form rewritten satisfied scalar second differential conditions Section Show slack variable solved subarc sufficient conditions taking the differential Taylor series transition matrix vanish vector Weierstrass condition zero

### Popular passages

Page iv - Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, Texas...

Page 374 - Hargraves, CR, and Paris, SW, "Direct Trajectory Optimization Using Nonlinear Programming and Collocation," Journal of Guidance, Control, and Dynamics, Vol. 10, No. 4, 1987, pp.