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McEneaney W.M. — Max-Plus Methods for Nonlinear Control and Estimation
McEneaney W.M. — Max-Plus Methods for Nonlinear Control and Estimation



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Название: Max-Plus Methods for Nonlinear Control and Estimation

Автор: McEneaney W.M.

Аннотация:

The central focus of this work is the control of nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems, nonlinear robust H-infinity control problems, and nonlinear risk-sensitive stochastic control problems.

Well-known dynamic programming arguments show there is a direct relationship between the solution of a control problem, and the solution of a corresponding Hamilton — Jacobi — Bellman (HJB) partial differential equation (PDE). The max-plus-based methods examined in this monograph belong to an entirely new class of methods for the solution of nonlinear control problems and their associated HJB PDEs; they are not equivalent to either of the more commonly used finite element or characteristic approaches. The potential advantages of max-plus-based approaches lie in the fact that solution operators for nonlinear HJB problems are linear over the max-plus algebra, and this linearity is exploited in the construction of algorithms.

The book will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods. Researchers and practitioners tangentially interested in this area will also find a readable, concise discussion of the subject through a careful selection of specific chapters and sections. Basic knowledge of control theory for systems with dynamics governed by differential equations is required; the material on risk-sensitive stochastic control requires knowledge of systems governed by stochastic differential equations.


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 241

Добавлена в каталог: 12.05.2008

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Предметный указатель
$B_R$      14
$C_r^L$      15
$C_R^{-+}$      22
$H_{\infty}$      4 5
$H_{\infty}$ attenuation bound      59
$L_{\infty}/L_2$-gain      198
$R^-$      11
$R^{-+}$      15
$S_{\tau}$      8 57 61
$\bar{B}_R$      14
$\mathcal{S}$      14
$\mathcal{S}_R$      14
$\mathcal{S}_R^{c-+}$      23
$\mathcal{S}_R^{cL-+}$      23
$\mathcal{S}_R^{cL}$      14
$\mathcal{S}_R^{c}$      14
$\mathcal{S}_{\bar{R}}$      14
$\mathcal{S}_{\bar{R}}^{cL}$      14
$\mathcal{S}_{\bar{R}}^{c}$      14
$\varepsilon$-optimal      42 51
a-complete      15
active control      5
Additive identity      11
Additive inverse      11
Affine equation      210
Affine power method      212
Algebraic Riccati equation      147
Algorithm      84 164 194
Allowable error in B      98
Ascoli — Arzela theorem      55
Available storage      40
B-complete      15
Bases      15
Basis expansion      9 15
Basis function pairs      126
Bicharacteristics      7
Boundary condition      7
Calculus of variations      187
Cauchy problem      50
Cauchy — Schwarz      37
Characteristic equations      2
Characteristics      7
Classical solution      42
Commutative semifield      11
complete      15
Completion      22 23
Computing B      122
Concave      19
continuous      22
Continuous linear functional      29
Control space      3 32
Convergence      97 104 107
Convex      13
Convex analysis      16
Convex conjugate      16
Convex dual      16
Convex function      13
Convexification      26
Cost criterion      4
Curse-of-complexity      169
Curse-of-dimensionality      7 10 143 158
Curse-of-dimensionality-free      143
Differential games      3
Differential Riccati equation      147
Directed graph      81
Disturbance attenuation parameter      5
Disturbance space      3
DP      1
DPE      2 31
dpp      1 31 87 200
Duality      16
Dynamic programming      1 31
Dynamic programming equation      2 31
Dynamic programming principle      1 31
Dynamics      3 32 35
Eigenfunction      2
Eigenvector equation      70 72
Elliott — Kalton      5 94
Error analysis      97
Error bound for eigenvector      124
Error bound, total      125
Error summary      124
Errors in approximation of B      119
Fenchel transform      15
Finite element method      2 7
Finite time-horizon problem      43
Fourier/Laplace series      15
Fourier/Laplace transform      15
Fundamental solution      187
Game problem      93
Gronwall’s inequality      38
Hamilton — Jacobi — Bellman      1 42
Hamilton — Jacobi — Isaacs      94
HJB PDE      1 7 42 48
inf*      27
Infinite time-horizon problem      34 39 48 58 199
Information state      185
Initial condition      3 32
Input process      3
Kernel      156
Legendre transform      15
Legendre/Fenchel transform      9 144
Lipschitz      15
Locally bounded      5
Locally Lipschitz      53
Lower semicontinuous      22
Max-plus additive      197
Max-plus affine      9 205
Max-plus algebra      1 8 11
Max-plus analysis      11
Max-plus basis      20 58
Max-plus basis expansion      111
Max-plus eigenvalue      81
Max-plus eigenvector      9 57 97
Max-plus expectation      3
Max-plus functional analysis      22
Max-plus linear      2 9
Max-plus linearity      57 60 66
Max-plus multiplicative      197
Max-plus probability      185 200
Max-plus propagation      192
Max-plus stochastic control      3
Max-plus vector space      8 12 14
min*      26
Min-plus algebra      4 93
Minimal semiconvexity constant      14
Minimizing control      84
Mixed $L_{\infty}/L_1$      197
Mixed $L_{\infty}/L_2$      5
Moduloid      12
Moore — Penrose inverse      59 184
Multiplicative identity      11
Multiplicative inverse      11
Nonanticipative      5
Nonlinear $H_{\infty}$ control      93
Observation process      6
Opposite space      24 26
Partial differential equation      1 31
Payoff      4 33–35 39
PDE      31
Power method      72 104
Power method convergence      124
Precedence graph      81
Reflexivity      22 30
Riesz representation theorem      29
Robust/$H_{\infty}$ filter      6 183
Runge — Kutta method      122
Running cost      4
Semiconcave      19
Semiconcavity      88
Semiconvex      67
Semiconvex dual      163
Semiconvex duality      151
Semiconvexity      66 187 206
Semiconvexity constant      14
Semigroup      2 7 61
Semigroup properties      8
Semigroup, monotonicity of      103
Space of semiconvex functions      8 13
Stopping-time problem      199
Terminal cost      4
Truncation error      97 107 110 125
Two-parameter families      21
Uniformly semiconcave      151
Uniformly semiconvex      150
Unique continuous solution      48
Value      4 33 40 44 50
Variational inequality      204
Viscosity solution      7 31 42 44 49 50 53 60 87 149
Viscosity subsolution      44 49
Viscosity supersolution      44 49
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