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Pytlak R. — Numerical Methods for Optimal Control Problems with State Constraints
Pytlak R. — Numerical Methods for Optimal Control Problems with State Constraints



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Название: Numerical Methods for Optimal Control Problems with State Constraints

Автор: Pytlak R.

Аннотация:

While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 240

Добавлена в каталог: 04.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathcal{L}$-stable integration procedure      137
Accessory problem      8 81 167
Active arc      8 92
Active set method      69 170
Adjoint equations      20
Adjoint equations, continuous time      22 67
Adjoint equations, continuous time for implicit systems      132
Adjoint equations, discrete time      25
Adjoint equations, discrete time for implicit systems      138
Adjoint operator      20
Adjoint operator, self-adjoint operator      84
Algebraic state      129
Approximation errors      9
Ascoli’s Theorem      15
Backoff problem      161
Backward differentiation formula (BDF)      133
Barrier function algorithm      29
Barycentric coordinates      42
Basic existence/uniqnuess theorem      14
Bellman’s dynamic programming equation      6
BFGS updating formula      125
BLAS (Basic Linear Algebra Subroutines)      68
Brachistochrone problem      2 9 69
Calculus of variations      1
Chebyshev functional      28
Cholesky factorization      173
Collocation method      8 83
Constraint qualification      36 88
Control function      1 13
Control system      13
Cycling      189
Descent function, nonpositive      34 58 84 87 142
Differential state      129
Differential-algebraic equations, implicit      129
Differential-algebraic equations, index one      130 136
Differential-algebraic equations, semi-explicit      136
Dini derivative      28
Direction finding subproblem      34
Discrete time system      137
Discrete time system, implicit      137
Dominated Convergence Theorem      15
Dual method      171 190
Endpoint constraints      29
Euler — Lagrange equation      2 3
Exact penalty function      29 83 142
Feasible directions algorithm      27
Gauss integration procedure      136
Givens matrix      179
Gradient algorithms      7
Gradient restoration algorithm      76
Gram — Schmidt factorization      176
Gronwall’s lemma      14 60
Hamilton — Jacobi equation      5 6
Hamiltonian      22
Hessenberg matrix      178
hessian      20
Hessian, reduced      21
Implicit function theorem      20
Lagrange multiplier      98 172
Lagrangian      20
Linearized equations      13
Maximum principle, Pontryagin’s      6
Maximum principle, weak      63 39 60
Maximum principle, weak, discrete time      140
Maximum set of linearly independent vectors      98
Mean value theorem      16
Minimax theorem      52
Minimum time problem      2 69
Multiple shooting method      76
Multipoint boundary value problem      76
Newton step      65
Nonlinear programming problem (NLP)      82
Null-space method      170
Optimality conditions, necessary, normal      38
Optimality conditions, sufficiency      98
Pathwise inequality constraint      6 27
Penalty test function      34 58 84 87 142
Piecewise constant approximation      24
Piecewise-linear quadratic programming problem      170
Plane rotation      178
Point of attraction      101
Powell-symmetric-Broyden update (PSB)      121
Primal method      171
Projection      57
Projection, matrix      105
Proximity algorithm      58
Radau IIA integration procedure      136 144
Radon probability measure      32
Range-space method      69 170
Relaxed controls      32
Relaxed dynamics      32
Relaxed necessary optimality conditions      38
Relaxed problem      33
Relaxed state trajectory      32
Reorthogonalization      179
Runge — Kutta integration procedure, explicit      134
Runge — Kutta integration procedure, implicit      129 134
Search directions, set      33
Second order correction      65
Semi-infinite programming (SIP)      67 82
Sensitivity equations      131
Sequential quadratic programming (SQP)      86
Sequential quadratic programming (SQP), reduced gradient      130
simplex      42
Singular subarc      77
State trajectory      1 13
Stepsize selection procedure      146
Stiff equations      147
Strict complementarity condition      99
Strong local minimum      99
Subgradient      65
Superlinear convergence      104 182
Superlinear convergence, two-step      122
Uniform approximation, $(R_{\varepsilon,\mu}, \xi)$      56
Watchdog technique      107 110
Windshear problem      74
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