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

Naoyuki Ichihara
2015 Annales de l'Institut Henri Poincare. Analyse non linéar  
This paper is concerned with the 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  ... 
doi:10.1016/j.anihpc.2014.02.003 fatcat:xlyfln5xx5gincbcgmuqywpkam

Linear Bellman combination for control of character animation

Marco da Silva, Frédo Durand, Jovan Popović
2009 ACM Transactions on Graphics  
We demonstrate that 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 ].  ... 
doi:10.1145/1531326.1531388 fatcat:tc7gq55kanaoxfykujegy4inhy

Linear Bellman combination for control of character animation

Marco da Silva, Frédo Durand, Jovan Popović
2009 ACM SIGGRAPH 2009 papers on - SIGGRAPH '09  
We demonstrate that 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 ].  ... 
doi:10.1145/1576246.1531388 fatcat:qvgk6jjdgjb45fk4jjspvnqwg4

Some generalized Gronwall-Bellman type difference inequalities and applications

Zi un Li
2021 Journal of Mathematical Inequalities  
We establish some 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.  ... 
doi:10.7153/jmi-2021-15-15 fatcat:6avfi6s24fc63oj4gboowkqd7u

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.  ... 

Exploration of Kinematic Optimal Control on the Lie Group SO(3)*

Alessandro Saccon, John Hauser, A. Pedro Aguiar
2010 IFAC Proceedings Volumes  
Hamilton-Jacobi-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) .  ... 
doi:10.3182/20100901-3-it-2016.00237 fatcat:t27xjzxuazf5tjpkudz733ro3m

Page 1793 of Mathematical Reviews Vol. , Issue 83d [page]

1983 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.  ... 

Page 894 of Mathematical Reviews Vol. , Issue 94b [page]

1994 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  ... 

A Theoretical Connection Between Statistical Physics and Reinforcement Learning [article]

Jad Rahme, Ryan P. Adams
2021 arXiv   pre-print
Moreover, when the MDP dynamics are deterministic, the 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( , ) [ ( , ) + (  ... 
arXiv:1906.10228v2 fatcat:fkt4i2kjhrarxipjm4up3vriea

Parametric value function approximation: A unified view

Matthieu Geist, Olivier Pietquin
2011 2011 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)  
The statistically 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  ... 
doi:10.1109/adprl.2011.5967355 dblp:conf/adprl/GeistP11 fatcat:hhntw5pucvafxcmxknr6da57ve

Solution of the Hamilton jacobi bellman uncertainties by the interval version of adomian decomposition method

Navid Razmjooy
2018 International Robotics & Automation Journal  
The proposed interval method is applied to solve the 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.  ... 
doi:10.15406/iratj.2018.04.00104 fatcat:w57wutgx2zbvtbkobf3melyfci

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.  ... 

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.  ... 

DYNAMIC PROGRAMMING, SUCCESSIVE APPROXIMATIONS, AND MONOTONE CONVERGENCE

R. Bellman
1958 Proceedings of the National Academy of Sciences of the United States of America  
Furthermore, it was shown if the 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  ... 
doi:10.1073/pnas.44.6.578 pmid:16590242 pmcid:PMC528622 fatcat:3sh6uukngjf4pkvgb2vdf6n7na

Bilinear Classes: A Structural Framework for Provable Generalization in RL [article]

Simon S. Du, Sham M. Kakade, Jason D. Lee, Shachar Lovett, Gaurav Mahajan, Wen Sun, Ruosong Wang
2021 arXiv   pre-print
Furthermore, this framework also extends to the infinite dimensional (RKHS) setting: for the the 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.  ... 
arXiv:2103.10897v3 fatcat:wlr3tmthtjfnzhfxmefqts5f6e
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