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Keywords
(13)
Approximate Solution
Curse of Dimensionality
hamiltonjacobi...
Infinite Horizon
Numerical Solution
Optimal Control
Ordinary Differential Equation
pontryagin maximum principle
Power Series
Time Optimal Control
Time Use
hamilton jacobi bellman
Higher Order
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Solution of Hamilton Jacobi Bellman equations
Solution of Hamilton Jacobi Bellman equations,10.1109/CDC.2000.912825,C. L. Navasca,A. J. Krener
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Solution of Hamilton Jacobi Bellman equations
(
Citations: 9
)
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C. L. Navasca
,
A. J. Krener
We present a method for the
numerical solution
of the
Hamilton Jacobi Bellman
PDE that arises in an infinite
time optimal control
problem. The method can be of
higher order
to reduce “the curse of dimensionality”. It proceeds in two stages. First the HJB PDE is solved in a neighborhood of the origin using the
power series
method of Al'brecht (1961). From a boundary point of this neighborhood, an extremal trajectory is computed backward in time using the Pontryagin maximum principle. Then ordinary differential equations are developed for the higher partial derivatives of the solution along the extremal. These are solved yielding a
power series
for the
approximate solution
in a neighborhood of the extremal. This is repeated for other extremals and these approximate solutions are fitted together by transferring them to a rectangular grid using splines
Conference:
Conference on Decision and Control  CDC
, vol. 1, pp. 570574 vol.1, 2000
DOI:
10.1109/CDC.2000.912825
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Citation Context
(6)
...Alternately, rather than treating the reachability set as a viscosity solution to the HJB PDE, individual optimal trajectories or expansions about these trajectories may be used to sample and represent the reachability set surface [
11
], [12]...
Marcus J. Holzinger
,
et al.
Optimal reachability sets using Generalized Independent Parameters
...There are a number of approaches that one can take to obtain the solutions of the HJB equations: (1) Assume a linear system with quadratic cost and solve for the optimal controller, (2) find solutions of the HJB equation numerically [1], [
6
], or (3) utilize the state dependent Riccati equation (SDRE) approach [2]...
ChangHee Won
.
Nonlinear nth Cost Cumulant Control and HamiltonJacobiBellman Equat...
...power series. Krener and coworkers [26], [
27
] use Al’brekht’s method to solve for the nonlinear regulator...
...them with randomized planning methods [19], [20] and level set methods [
27
]...
W. Todd Cerven
,
et al.
Constructive controllability algorithms for motion planning and optimi...
...The numerical procedure is described in [
22
]...
Carmeliza Luna Navasca
.
Local Solutions of the Dynamic Programming Equations and the Hamilton ...
...It is similar to that of Navasca and Krener [
15
]...
Carmeliza Navasca
,
et al.
Patchy Solutions of HamiltonJacobiBellman Partial Differential Equat...
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)
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Citations
(9)
Optimal reachability sets using Generalized Independent Parameters
Marcus J. Holzinger
,
Daniel J. Scheeres
,
John Hauser
Published in 2011.
Power Series Solution of the HamiltonJacobiBellman Equation for Timevarying DifferentialAlgebraic Equations
Johan Sjöberg
,
Torkel Glad
Conference:
Conference on Decision and Control  CDC
, 2006
Nonlinear nth Cost Cumulant Control and HamiltonJacobiBellman Equations for Markov Diffusion Process
(
Citations: 9
)
ChangHee Won
Conference:
Conference on Decision and Control  CDC
, 2005
Constructive controllability algorithms for motion planning and optimization
(
Citations: 3
)
W. Todd Cerven
,
Francesco Bullo
Journal:
IEEE Transactions on Automatic Control  IEEE TRANS AUTOMAT CONTR
, vol. 48, no. 4, pp. 575589, 2003
Local Stable Manifold for the Bidirectional DiscreteTime Dynamics
Carmeliza Navasca
Published in 2003.