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Adaptive Dynamics
Computational Techniques
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Cost Function
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hamiltonjacobi...
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Adaptive dynamic programming
Adaptive dynamic programming,10.1109/TSMCC.2002.801727,IEEE Transactions on Systems, Man, and Cybernetics,John J. Murray,Chadwick J. Cox,George G. Len
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Adaptive dynamic programming
(
Citations: 116
)
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John J. Murray
,
Chadwick J. Cox
,
George G. Lendaris
,
Richard Saeks
Unlike the many
soft computing
applications where it suffices to achieve a "good approximation most of the time," a
control system
must be stable all of the time. As such, if one desires to learn a control law in realtime, a fusion of
soft computing
techniques to learn the appropriate control law with hard computing techniques to maintain the stability constraint and guarantee convergence is required. The objective of the paper is to describe an adaptive
dynamic programming algorithm
(ADPA) which fuses
soft computing
techniques to learn the optimal cost (or return) functional for a stabilizable
nonlinear system
with unknown dynamics and hard computing techniques to verify the stability and convergence of the algorithm. Specifically, the algorithm is initialized with a (stabilizing) cost functional and the system is run with the corresponding control law (defined by the HamiltonJacobiBellman equation), with the resultant state trajectories used to update the cost functional in a
soft computing
mode. Hard computing techniques are then used to show that this process is globally convergent with stepwise stability to the optimal cost functional/control law pair for an (unknown) input affine system with an input quadratic
performance measure
(modulo the appropriate technical conditions). Three specific implementations of the ADPA are developed for 1) the linear case, 2) for the nonlinear case using a locally quadratic approximation to the cost functional, and 3) the nonlinear case using a
radial basis function
approximation of the cost functional; illustrated by applications to flight control.
Journal:
IEEE Transactions on Systems, Man, and Cybernetics  TSMC
, vol. 32, no. 2, pp. 140153, 2002
DOI:
10.1109/TSMCC.2002.801727
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Citation Context
(58)
...In recent years, ADP and related research have gained much attention from researchers [27], [28], [
31
], [33]‐[36], [39]‐[57]...
FeiYue Wang
,
et al.
Adaptive Dynamic Programming for FiniteHorizon Optimal Control of Dis...
...The concept of ADP was introduced by Werbos in 1977 [15]‐[
23
]...
Dongbin Zhao
,
et al.
DHP Method for Ramp Metering of Freeway Traffic
...programming" [
9
], "approximate dynamic programming"...
Derong Liu
,
et al.
Neuralnetworkbased optimal control for a class of nonlinear cdiscret...
...The work in [
8
] introduces an adaptive dynamic programming (ADP) scheme for optimal control of unknown affine systems...
...It will be shown in the next section that the optimal control approach for the affinelike system (7) requires the IGM to be known, while the information of () k F X is not required [1],[4],[
8
]...
H. Zargarzadeh
,
et al.
Online near optimal control of unknown nonaffine systems with applicat...
...Adaptive/approximate dynamic programming (ADP) algorithms have gained much attention from researchers [4]– [
7
], [9], [10], [13], [15]–[17]...
...In [
7
] a convergent ADP algorithm is developed for stabilizing the continuoustime nonlinear systems...
Qinglai Wei
,
et al.
Optimal control for discretetime nonlinear systems with unfixed initi...
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Citations
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Adaptive Dynamic Programming for FiniteHorizon Optimal Control of DiscreteTime Nonlinear Systems With varepsilonError Bound
(
Citations: 11
)
FeiYue Wang
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