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The generalized principal eigenvalue for Hamilton–Jacobi–Bellman equations of ergodic type

2015
*
Annales de l'Institut Henri Poincare. Analyse non linéar
*

This paper is concerned with the

doi:10.1016/j.anihpc.2014.02.003
fatcat:xlyfln5xx5gincbcgmuqywpkam
*generalized*principal eigenvalue for Hamilton-Jacobi-*Bellman*(HJB)*equations*arising in a class of stochastic ergodic control. ... We give a necessary and sufficient condition so that the*generalized*principal eigenvalue of an HJB*equation*coincides with the optimal value of the corresponding ergodic control problem. ... Introduction This paper is concerned with the following Hamilton-Jacobi-*Bellman*(HJB)*equation*of ergodic type: λ − Aφ + H (x, Dφ) + βV = 0 in R N , φ(0) = 0, (EP) where β is a real parameter, Dφ = (∂φ ...##
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Linear Bellman combination for control of character animation

2009
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ACM Transactions on Graphics
*

We demonstrate that

doi:10.1145/1531326.1531388
fatcat:tc7gq55kanaoxfykujegy4inhy
*linear**Bellman*combination outperforms naive combination often succeeding where naive combination fails. ... We demonstrate the applicability of*linear**Bellman*combination to interactive character control of stepping motions and acrobatic maneuvers. ...*Linear**Bellman*combination builds on the observation that the*non*-*linear*HJB*equation*can be*linearized*under a change of variables [Fleming 1978 ]. ...##
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Linear Bellman combination for control of character animation

2009
*
ACM SIGGRAPH 2009 papers on - SIGGRAPH '09
*

We demonstrate that

doi:10.1145/1576246.1531388
fatcat:qvgk6jjdgjb45fk4jjspvnqwg4
*linear**Bellman*combination outperforms naive combination often succeeding where naive combination fails. ... We demonstrate the applicability of*linear**Bellman*combination to interactive character control of stepping motions and acrobatic maneuvers. ...*Linear**Bellman*combination builds on the observation that the*non*-*linear*HJB*equation*can be*linearized*under a change of variables [Fleming 1978 ]. ...##
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Some generalized Gronwall-Bellman type difference inequalities and applications

2021
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Journal of Mathematical Inequalities
*

We establish some

doi:10.7153/jmi-2021-15-15
fatcat:6avfi6s24fc63oj4gboowkqd7u
*generalized*sums-difference inequalities involving a finite sum, which includes three sums and seven sums, respectively. ... We apply our results to boundary value problem of a partial difference*equation*for uniform boundedness, uniqueness and continuous dependence of the solutions. (2010) : 34B15, 26D15, 26D10. ...*BELLMAN*, The stability of solutions of*linear*differential*equations*, Duke Math. J. 10 (1943) 643-647. [8] D. BAINOV, P. ...##
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Page 449 of American Society of Mechanical Engineers. Transactions of the American Society of Mechanical Engineers Vol. 79, Issue 3
[page]

1957
*
American Society of Mechanical Engineers. Transactions of the American Society of Mechanical Engineers
*

J., 1953, 168 pp.
32 “Stability Theory of Differential

*Equations*,"’ by R.*Bellman*, McGraw-Hill Book Company, Inc., New York, N. ... The author emphasizes the possibility of employment of*non*-*linear*theory and techniques to enable design of control systems which yield maximal performance. ...##
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Exploration of Kinematic Optimal Control on the Lie Group SO(3)*

2010
*
IFAC Proceedings Volumes
*

Hamilton-Jacobi-

doi:10.3182/20100901-3-it-2016.00237
fatcat:t27xjzxuazf5tjpkudz733ro3m
*Bellman**equation*on SO(3). ... We investigate a*generalization*of the infinite time horizon*linear*quadratic regulator (LQR) for systems evolving on the special orthogonal group SO(3). ... Hamilton-Jacobi-*Bellman**equation*on SO (3) . ...##
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Page 1793 of Mathematical Reviews Vol. , Issue 83d
[page]

1983
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Mathematical Reviews
*

The

*Bellman**equation*in this case is understood as an*equation*for measures. In the proof he uses a*generalization*of the method of N. V. ... [Pragarauskas, H.] 83d:9308 1b Limit transition in*general*degenerate*Bellman**equations*. II. (Russian. Lithuanian and English summaries) Litovsk. Mat. Sb. 21 (1981), no. 1, 135-154. ...##
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Page 894 of Mathematical Reviews Vol. , Issue 94b
[page]

1994
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Mathematical Reviews
*

and a

*Bellman*differential*equation*. ... From the introduction (translated from the Russian): “We con- sider the example of*linear*differential systems on a finite interval without constraints, with*linear*, in*general*, nonseparate bound- ary ...##
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A Theoretical Connection Between Statistical Physics and Reinforcement Learning
[article]

2021
*
arXiv
*
pre-print

Moreover, when the MDP dynamics are deterministic, the

arXiv:1906.10228v2
fatcat:fkt4i2kjhrarxipjm4up3vriea
*Bellman**equation*for 𝒵 is*linear*, allowing direct solutions that are unavailable for the nonlinear*equations*associated with traditional value functions ... Although value functions and Q-functions can be derived from this partition function and interpreted via average energies, the 𝒵-function provides an object with its own*Bellman**equation*that can form ... We show in Appendix A.2 that the policies learned are related to Boltzmann policies which produce*non**linear**Bellman**equations*at the value function level: ( , ) = (R( , )+ ( + , )) W( , ) [ ( , ) + ( ...##
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Parametric value function approximation: A unified view

2011
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2011 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)
*

The statistically

doi:10.1109/adprl.2011.5967355
dblp:conf/adprl/GeistP11
fatcat:hhntw5pucvafxcmxknr6da57ve
*linearized*LSTD (slLSTD) algorithm [33]*generalizes*LSTD: it does not assume a*linear*parameterization nor the*Bellman*evaluation operator. ... The value function of a given policy satisfies the (*linear*)*Bellman*evaluation*equation*and the optimal value function (which is linked to one of the optimal policies) satisfies the (nonlinear)*Bellman*...##
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Solution of the Hamilton jacobi bellman uncertainties by the interval version of adomian decomposition method

2018
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International Robotics & Automation Journal
*

The proposed interval method is applied to solve the

doi:10.15406/iratj.2018.04.00104
fatcat:w57wutgx2zbvtbkobf3melyfci
*linear*and nonlinear HJB*equations*in association with appropriate numerical solvers. ... In this paper, an interval numerical method is proposed for solving the Hamilton Jacobi*Bellman*(HJB)*Equations*with uncertainties. ... Hamilton Jacobi*Bellman*method can be utilized in different*linear*,*non*-*linear*and even distributed optimal control problems. ...##
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Page 211 of Mathematical Reviews Vol. 18, Issue 3
[page]

1957
*
Mathematical Reviews
*

*Bellman*. Grobman, D. M. Asymptotic behavior of solutions of

*non*-

*linear*s that deviate little from

*linearity*. Dokl. Akad. Nauk SSSR (N.S.) 108 (1956), 571-574. ...

*Bellman*. Beesack, P. R.; and Schwarz, Binyamin. On the zeros of solutions of second-order

*linear*differential

*equations*. Canad. J. Math. 8 (1956), 504-515. ...

##
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Page 619 of Mathematical Reviews Vol. 19, Issue 5
[page]

1958
*
Mathematical Reviews
*

Ex- tensions to more

*general**non*-*linear*problems are suggested. Authors’ summary.*Bellman*, Richard. A variational problem with con- straints in dynamic p i J. Soc. Indust. Appl. ... The minimization of a convex function of variables subject to*linear*inequalities is discussed briefly in*general*terms. ...##
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DYNAMIC PROGRAMMING, SUCCESSIVE APPROXIMATIONS, AND MONOTONE CONVERGENCE

1958
*
Proceedings of the National Academy of Sciences of the United States of America
*

Furthermore, it was shown if the

doi:10.1073/pnas.44.6.578
pmid:16590242
pmcid:PMC528622
fatcat:3sh6uukngjf4pkvgb2vdf6n7na
*equations*of (1.2) are*linear*, H is*linear*, but G is a*non*-*linear*function of only k of the components of x(T), then a computational solution can be effected in terms of ... -The starting point of our investigation is the result contained in an earlier paper, where it was shown that if the*equations*of (1.2) are*linear*, and if the functions F and G are*linear*, then the variational ...##
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Bilinear Classes: A Structural Framework for Provable Generalization in RL
[article]

2021
*
arXiv
*
pre-print

Furthermore, this framework also extends to the infinite dimensional (RKHS) setting: for the the

arXiv:2103.10897v3
fatcat:wlr3tmthtjfnzhfxmefqts5f6e
*Linear*Q^*/V^* model,*linear*MDPs, and*linear*mixture MDPs, we provide sample complexities that have no ... Q-function and the optimal V-function are*linear*in some known feature space. ... Acknowledgements We thank Chi Jin and Qinghua Liu for discussions on Section 6 including the*generalized**linear**bellman*complete model. ...
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