{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T07:21:38Z","timestamp":1768288898510,"version":"3.49.0"},"reference-count":42,"publisher":"Institute of Electronics, Information and Communications Engineers (IEICE)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEICE Trans. Fundamentals"],"published-print":{"date-parts":[[2022,1,1]]},"DOI":"10.1587\/transfun.2021eai0002","type":"journal-article","created":{"date-parts":[[2021,7,11]],"date-time":"2021-07-11T22:06:45Z","timestamp":1626041205000},"page":"1-10","source":"Crossref","is-referenced-by-count":2,"title":["Kernel-Based Hamilton-Jacobi Equations for Data-Driven Optimal Control: The General Case"],"prefix":"10.1587","volume":"E105.A","author":[{"given":"Yuji","family":"ITO","sequence":"first","affiliation":[{"name":"TOYOTA CENTRAL R&D LABS., INC."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenji","family":"FUJIMOTO","sequence":"additional","affiliation":[{"name":"Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"532","reference":[{"key":"1","doi-asserted-by":"publisher","unstructured":"[1] T. Nishi, P. Doshi, and D. Prokhorov, \u201cMerging in congested freeway traffic using multipolicy decision making and passive actor-critic learning,\u201d IEEE Trans. Intell. Veh., vol.4, no.2, pp.287-297, 2019. 10.1109\/tiv.2019.2904417","DOI":"10.1109\/TIV.2019.2904417"},{"key":"2","doi-asserted-by":"crossref","unstructured":"[2] M. Torchio, N.A. Wolff, D.M. Raimondo, L. Magni, U. Krewer, R.B. Gopaluni, J.A. Paulson, and R.D. Braatz, \u201cReal-time model predictive control for the optimal charging of a lithium-ion battery,\u201d Proc. 2015 Annual American Control Conf., pp.4536-4541, 2015. 10.1109\/acc.2015.7172043","DOI":"10.1109\/ACC.2015.7172043"},{"key":"3","doi-asserted-by":"publisher","unstructured":"[4] B. Hu, G. Su, J. Jiang, J. Sheng, and J. Li, \u201cUncertain prediction for slope displacement time-series using Gaussian process machine learning,\u201d IEEE Access, vol.7, pp.27535-27546, 2019. 10.1109\/access.2019.2894807","DOI":"10.1109\/ACCESS.2019.2894807"},{"key":"4","doi-asserted-by":"publisher","unstructured":"[5] W. Guo, T. Pan, Z. Li, and S. Chen, \u201cModel calibration method for soft sensors using adaptive Gaussian process regression,\u201d IEEE Access, vol.7, pp.168436-168443, 2019. 10.1109\/access.2019.2954158","DOI":"10.1109\/ACCESS.2019.2954158"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[6] Y. Ito, K. Fujimoto, Y. Tadokoro, and T. Yoshimura, \u201cOn stabilizing control of Gaussian processes for unknown nonlinear systems,\u201d Preprints of the 20th IFAC World Congress, pp.15955-15960, 2017. 10.1016\/j.ifacol.2017.08.1861","DOI":"10.1016\/j.ifacol.2017.08.1861"},{"key":"6","doi-asserted-by":"crossref","unstructured":"[7] V. Vovk, \u201cKernel ridge regression,\u201d Empirical Inference: Festschrift in Honor of Vladimir N. Vapnik, pp.105-116, Springer-Verlag Berlin Heidelberg, Berlin, Heidelberg, 2013. 10.1007\/978-3-642-41136-6_11","DOI":"10.1007\/978-3-642-41136-6_11"},{"key":"7","doi-asserted-by":"publisher","unstructured":"[8] M.P. Deisenroth, C.E. Rasmussen, and J. Peters, \u201cGaussian process dynamic programming,\u201d Neurocomputing, vol.72, no.7-9, pp.1508-1524, 2009. 10.1016\/j.neucom.2008.12.019","DOI":"10.1016\/j.neucom.2008.12.019"},{"key":"8","doi-asserted-by":"publisher","unstructured":"[9] P. Hemakumara and S. Sukkarieh, \u201cLearning UAV stability and control derivatives using Gaussian processes,\u201d IEEE Trans. Robot., vol.29, no.4, pp.813-824, 2013. 10.1109\/tro.2013.2258732","DOI":"10.1109\/TRO.2013.2258732"},{"key":"9","doi-asserted-by":"publisher","unstructured":"[10] M.P. Deisenroth, D. Fox, and C.E. Rasmussen, \u201cGaussian processes for data-efficient learning in robotics and control,\u201d IEEE Trans. Pattern Anal. Mach. Intell., vol.37, no.2, pp.408-423, 2015. 10.1109\/tpami.2013.218","DOI":"10.1109\/TPAMI.2013.218"},{"key":"10","doi-asserted-by":"publisher","unstructured":"[11] F. Xie, W. Hong, W. Wu, K. Liang, and C. Qiu, \u201cCurrent distribution method of induction motor for electric vehicle in whole speed range based on Gaussian process,\u201d IEEE Access, vol.7, pp.165974-165984, 2019. 10.1109\/access.2019.2953293","DOI":"10.1109\/ACCESS.2019.2953293"},{"key":"11","doi-asserted-by":"crossref","unstructured":"[12] K. Chen, J. Yi, and D. Song, \u201cGaussian processes model-based control of underactuated balance robots,\u201d Proc. 2019 International Conf. on Robotics and Automation, pp.4458-4464, 2019. 10.1109\/icra.2019.8794097","DOI":"10.1109\/ICRA.2019.8794097"},{"key":"12","unstructured":"[13] J. Kocijan, R. Murray-Smith, C.E. Rasmussen, and B. Likar, \u201cPredictive control with Gaussian process models,\u201d Proc. IEEE Region 8 EUROCON 2003. Computer as a Tool., 2003. 10.1109\/eurcon.2003.1248042"},{"key":"13","doi-asserted-by":"crossref","unstructured":"[14] A. Grancharova, J. Kocijan, and T.A. Johansen, \u201cExplicit stochastic nonlinear predictive control based on Gaussian process models,\u201d Proc. 2007 European Control Conf., 2007. 10.23919\/ecc.2007.7068422","DOI":"10.23919\/ECC.2007.7068422"},{"key":"14","doi-asserted-by":"crossref","unstructured":"[15] G. Cao, Gaussian Process based Model Predictive Control, Ph.D. thesis, Massey University, 2017.","DOI":"10.1109\/AMC.2016.7496359"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[16] L. Hewing, J. Kabzan, and M.N. Zeilinger, \u201cCautious model predictive control using Gaussian process regression,\u201d IEEE Trans. Control Syst. Technol., vol.28, no.6, pp.2736-2743, 2020. 10.1109\/tcst.2019.2949757","DOI":"10.1109\/TCST.2019.2949757"},{"key":"16","doi-asserted-by":"crossref","unstructured":"[17] T.X. Nghiem, \u201cLinearized Gaussian processes for fast data-driven model predictive control,\u201d Proc. 2019 American Control Conference, pp.1629-1634, 2019. 10.23919\/acc.2019.8814476","DOI":"10.23919\/ACC.2019.8814476"},{"key":"17","doi-asserted-by":"crossref","unstructured":"[18] E. Bradford, L. Imsland, and E.A. del Rio-Chanona, \u201cNonlinear model predictive control with explicit back-offs for Gaussian process state space models,\u201d Proc. IEEE 58th Conf. on Decision and Control, pp.4747-4754, 2019. 10.1109\/cdc40024.2019.9029443","DOI":"10.1109\/CDC40024.2019.9029443"},{"key":"18","doi-asserted-by":"crossref","unstructured":"[19] Y. Pan and E.A. Theodorou, \u201cData-driven differential dynamic programming using Gaussian processes,\u201d Proc. 2015 Annual American Control Conf., pp.4467-4472, 2015. 10.1109\/acc.2015.7172032","DOI":"10.1109\/ACC.2015.7172032"},{"key":"19","doi-asserted-by":"crossref","unstructured":"[20] J. Boedecker, J.T. Springenberg, J. Wulfing, and M. Riedmiller, \u201cApproximate real-time optimal control based on sparse Gaussian process models,\u201d Proc. 2014 IEEE Symp. on Adaptive Dynamic Programming and Reinforcement Learning, 2014. 10.1109\/adprl.2014.7010608","DOI":"10.1109\/ADPRL.2014.7010608"},{"key":"20","doi-asserted-by":"crossref","unstructured":"[21] Y. Ito, K. Fujimoto, and Y. Tadokoro, \u201cSecond-order bounds of Gaussian kernel-based functions and its application to nonlinear optimal control with stability,\u201d arXiv:1707.06240v1, 2017.","DOI":"10.23919\/ACC.2018.8431159"},{"key":"21","unstructured":"[22] F. Berkenkamp, M. Turchetta, A.P. Schoellig, and A. Krause, \u201cSafe model-based reinforcement learning with stability guarantees,\u201d Proc. Advances in Neural Information Processing Systems 30, pp.908-918, 2017."},{"key":"22","doi-asserted-by":"publisher","unstructured":"[23] Y. Ito, K. Fujimoto, and Y. Tadokoro, \u201cKernel-based Hamilton-Jacobi equations for data-driven optimal and H-infinity control,\u201d IEEE Access, vol.8, pp.131047-131062, 2020. 10.1109\/access.2020.3009357","DOI":"10.1109\/ACCESS.2020.3009357"},{"key":"23","doi-asserted-by":"crossref","unstructured":"[24] F.L. Lewis, D.L. Vrabie, and V.L. Syrmos, Optimal Control, 3rd ed., John Wiley &amp; Sons, Hoboken, New Jersey, 2012. 10.1002\/9781118122631","DOI":"10.1002\/9781118122631"},{"key":"24","unstructured":"[25] C.M. Bishop, Pattern Recognition and Machine Learning (Information Science and Statistics), Springer-Verlag New York, Secaucus, NJ, USA, 2006."},{"key":"25","doi-asserted-by":"publisher","unstructured":"[26] J.J. Murray, C.J. Cox, G.G. Lendaris, and R. Saeks, \u201cAdaptive dynamic programming,\u201d IEEE Trans. Systems, Man, and Cybern. C, vol.32, no.2, pp.140-153, 2002. 10.1109\/tsmcc.2002.801727","DOI":"10.1109\/TSMCC.2002.801727"},{"key":"26","doi-asserted-by":"crossref","unstructured":"[27] Y. Huang and W.M. Lu, \u201cNonlinear optimal control: Alternatives to Hamilton-Jacobi equation,\u201d Proc. IEEE 35th Conf. on Decision and Control, pp.3942-3947, 1996. 10.1109\/cdc.1996.577297","DOI":"10.1109\/CDC.1996.577297"},{"key":"27","doi-asserted-by":"publisher","unstructured":"[28] D. McCaffrey and S.P. Banks, \u201cGeometric existence theory for the control-affine nonlinear optimal regulator,\u201d J. Math. Anal. Appl., vol.305, no.1, pp.380-390, 2005. 10.1016\/j.jmaa.2004.12.017","DOI":"10.1016\/j.jmaa.2004.12.017"},{"key":"28","doi-asserted-by":"publisher","unstructured":"[29] C.H. Won and S. Biswas, \u201cOptimal control using an algebraic method for control-affine non-linear systems,\u201d Int. J. Control, vol.80, no.9, pp.1491-1502, 2007. 10.1080\/00207170701411375","DOI":"10.1080\/00207170701411375"},{"key":"29","doi-asserted-by":"crossref","unstructured":"[30] E. Todorov, \u201cEigenfunction approximation methods for linearly-solvable optimal control problems,\u201d Proc. 2009 IEEE Symp. on Adaptive Dynamic Programming and Reinforcement Learning, 2009. 10.1109\/adprl.2009.4927540","DOI":"10.1109\/ADPRL.2009.4927540"},{"key":"30","doi-asserted-by":"publisher","unstructured":"[31] R. Kamalapurkar, J.A. Rosenfeld, and W.E. Dixon, \u201cEfficient model-based reinforcement learning for approximate online optimal control,\u201d Automatica, vol.74, pp.247-258, 2016. 10.1016\/j.automatica.2016.08.004","DOI":"10.1016\/j.automatica.2016.08.004"},{"key":"31","doi-asserted-by":"publisher","unstructured":"[32] P. Giesl, \u201cConstruction of a local and global Lyapunov function for discrete dynamical systems using radial basis functions,\u201d J. Approx. Theory, vol.153, no.2, pp.184-211, 2008. 10.1016\/j.jat.2008.01.007","DOI":"10.1016\/j.jat.2008.01.007"},{"key":"32","doi-asserted-by":"publisher","unstructured":"[33] P. Giesl and S. Hafstein, \u201cReview on computational methods for Lyapunov functions,\u201d Discrete and Continuous Dynamical Systems-Series B, vol.20, no.8, pp.2291-2331, 2015. 10.3934\/dcdsb.2015.20.2291","DOI":"10.3934\/dcdsb.2015.20.2291"},{"key":"33","doi-asserted-by":"publisher","unstructured":"[34] J. Bouvrie and B. Hamzi, \u201cKernel methods for the approximation of some key quantities of nonlinear systems,\u201d J. Computational Dynamics, vol.4, no.1, pp.1-19, 2017. 10.3934\/jcd.2017001","DOI":"10.3934\/jcd.2017001"},{"key":"34","doi-asserted-by":"crossref","unstructured":"[35] R.W. Beard, G. Saridis, and J. Wen, \u201cApproximate solutions to the time-invariant Hamilton-Jacobi-Bellman equation,\u201d J. Optimiz. Theory Appl., vol.96, pp.589-626, 1998. 10.1023\/a:1022664528457","DOI":"10.1023\/A:1022664528457"},{"key":"35","doi-asserted-by":"publisher","unstructured":"[36] Y. Zhu, D. Zhao, X. Yang, and Q. Zhang, \u201cPolicy iteration for <i>H<\/i><sub>\u221e<\/sub> optimal control of polynomial nonlinear systems via sum of squares programming,\u201d IEEE Trans. Cybern., vol.48, no.2, pp.500-509, 2018. 10.1109\/tcyb.2016.2643687","DOI":"10.1109\/TCYB.2016.2643687"},{"key":"36","unstructured":"[37] C. Dugas, Y. Bengio, F. B\u00e9lisle, C. Nadeau, and R. Garcia, \u201cIncorporating second-order functional knowledge for better option pricing,\u201d Advances in Neural Information Processing Systems, pp.451-457, 2000."},{"key":"37","doi-asserted-by":"publisher","unstructured":"[38] A.J. van der Schaft, \u201c<i>L<\/i><sub>2<\/sub>-gain analysis of nonlinear systems and nonlinear state feedback <i>H<\/i><sub>\u221e<\/sub> control,\u201d IEEE Trans. Autom. Control, vol.37, no.6, pp.770-784, 1992. 10.1109\/9.256331","DOI":"10.1109\/9.256331"},{"key":"38","doi-asserted-by":"publisher","unstructured":"[39] D. McCaffrey, \u201cGeometric existence theory for the control-affine <i>H<\/i><sub>\u221e<\/sub> problem,\u201d J. Math. Anal. Appl., vol.324, no.1, pp.682-695, 2006. 10.1016\/j.jmaa.2005.12.034","DOI":"10.1016\/j.jmaa.2005.12.034"},{"key":"39","unstructured":"[40] J. Morimoto and K. Doya, \u201cRobust reinforcement learning,\u201d Advances in Neural Information Processing Systems, pp.1061-1067, 2001."},{"key":"40","unstructured":"[41] C.E. Rasmussen and H. Nickisch, Gaussian Process Regression and Classification Toolbox version 4.2, 2018."},{"key":"41","unstructured":"[42] J. Nocedal and S.J. Wright, Numerical Optimization, 2nd ed., Springer Science+Business Media, LLC, New York, 2006."},{"key":"42","doi-asserted-by":"crossref","unstructured":"[43] J.R. Dormand and P.J. Prince, \u201cA family of embedded Runge-Kutta formulae,\u201d J. Comput. Appl. Math., vol.6, pp.19-26, 1980. 10.1016\/0771-050x(80)90013-3","DOI":"10.1016\/0771-050X(80)90013-3"}],"container-title":["IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/transfun\/E105.A\/1\/E105.A_2021EAI0002\/_pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T22:06:19Z","timestamp":1725401179000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/transfun\/E105.A\/1\/E105.A_2021EAI0002\/_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,1]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022]]}},"URL":"https:\/\/doi.org\/10.1587\/transfun.2021eai0002","relation":{},"ISSN":["0916-8508","1745-1337"],"issn-type":[{"value":"0916-8508","type":"print"},{"value":"1745-1337","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,1]]},"article-number":"2021EAI0002"}}