{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:52:49Z","timestamp":1760147569924,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,11]],"date-time":"2023-02-11T00:00:00Z","timestamp":1676073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We focus on the dual interval control problem of multidimensional objects with delay. We propose a new nonparametric algorithm. In such a case, it is not necessary to determine a parametric structure of the investigated object. Another difficulty lies in the complex nature of the decision-making field as it might not be flexible or convenient for decision-makers to exactly quantify their opinions with crisp numbers. Due to this fact, we introduce the interval-valued observations into the algorithm by means of the single-level constraint interval arithmetic. The results of computational experiments illustrate the effectiveness of the algorithm in the case of using intervals instead of crisp values.<\/jats:p>","DOI":"10.3390\/axioms12020193","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T02:14:11Z","timestamp":1676254451000},"page":"193","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Nonparametric Dual Control Algorithm of Multidimensional Objects with Interval-Valued Observations"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0290-6477","authenticated-orcid":false,"given":"Manuel","family":"Arana-Jim\u00e9nez","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, INDESS, University of C\u00e1diz, 11405 Jerez, Spain"}]},{"given":"Alexander V.","family":"Medvedev","sequence":"additional","affiliation":[{"name":"Department of Information Systems, School of Space and Information Technology, Siberian Federal University, 660041 Krasnoyarsk, Russia"}]},{"given":"Ekaterina","family":"Chzhan","sequence":"additional","affiliation":[{"name":"Department of Intelligent Control Systems, School of Space and Information Technology, Siberian Federal University, 660041 Krasnoyarsk, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,11]]},"reference":[{"key":"ref_1","unstructured":"Feldbaum, A.A. (1963). Fundamentals of the Theory of Optimal Automatic Systems, Fizmatgiz Publishing."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/S1474-6670(17)45327-4","article-title":"Adaptive dual control methods: An overview","volume":"28","author":"Wittenmark","year":"1995","journal-title":"IFAC Proc. Vol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/0022-247X(71)90161-2","article-title":"Problems of identification and control","volume":"34","author":"Astrom","year":"1971","journal-title":"J. Math. Anal. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1109\/TAC.1980.1102417","article-title":"A multiple model adaptive dual control algorithm for stochastic systems with unknown parameters","volume":"25","author":"Wenk","year":"1980","journal-title":"Autom. Control."},{"key":"ref_5","unstructured":"Filatov, N.M., and Unbehauen, H. (2000, January 4). Survey of adaptive dual control methods. Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium, Lake Louise, AB, Canada."},{"key":"ref_6","unstructured":"Umenberger, J., and Sch\u00f6n, T.B. (2020, January 11\u201312). Optimistic robust linear quadratic dual control. Proceedings of the 2nd Conference on Learning for Dynamics and Control, Berkeley, CA, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.arcontrol.2017.11.001","article-title":"Stochastic model predictive control with active uncertainty learning: A Survey on dual control","volume":"45","author":"Mesbah","year":"2018","journal-title":"Annu. Rev. Control."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.jprocont.2015.04.012","article-title":"MPC-based dual control with online experiment design","volume":"32","author":"Heirung","year":"2015","journal-title":"J. Process. Control"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.automatica.2017.01.030","article-title":"Dual adaptive model predictive control","volume":"80","author":"Heirung","year":"2017","journal-title":"Automatica"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3071","DOI":"10.1002\/aic.16180","article-title":"Model predictive control with active learning under model uncertainty: Why, when, and how","volume":"64","author":"Heirung","year":"2018","journal-title":"AIChE J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.jprocont.2016.02.003","article-title":"Data driven nonparametric identification and model based control of glucose-insulin process in type 1 diabetics","volume":"41","author":"Bhattacharjee","year":"2016","journal-title":"J. Process. Control"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.jprocont.2018.10.003","article-title":"Dual robust nonlinear model predictive control: A multi-stage approach","volume":"72","author":"Thangavel","year":"2018","journal-title":"J. Process. Control"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5930","DOI":"10.1109\/TSG.2019.2893285","article-title":"The Dual Control With Consideration of Security Operation and Economic Efficiency for Energy Hub","volume":"10","author":"Sun","year":"2019","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_14","unstructured":"Byun, H.E., Kim, B., and Lee, B. (2019, January 6\u20139). Dual Adaptive Control of a Fed-Batch Bioreactor Based on Approximate Dynamic Programming. Proceedings of the Foundations of Process Analytics and Machine Learning (FOPAM 2019), Raleigh, NC, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1002\/acs.2862","article-title":"Model-based vs data-driven adaptive control: An overview","volume":"32","author":"Benosman","year":"2018","journal-title":"Int. J. Adapt. Control. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.ins.2012.07.014","article-title":"From model-based control to data-driven control: Survey, classification and perspective","volume":"235","author":"Hou","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_17","first-page":"909","article-title":"Formulas for data-driven control: Stabilization, optimality, and robustness","volume":"65","author":"Tesi","year":"2019","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/S0005-1098(97)00181-7","article-title":"Dual Adaptive Control of Nonlinear Stochastic Systems using Neural Networks","volume":"34","author":"Fabrit","year":"1998","journal-title":"Automatica"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1177\/0142331214553503","article-title":"Functional adaptive dual control of a class of nonlinear MIMO systems","volume":"37","author":"Fabri","year":"2015","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Cao, S., Xu, W., and Hu, X. (2015, January 23\u201325). Dual adaptive control of nonlinear stochastic systems based on echo state network. Proceedings of the 27th Chinese Control and Decision Conference (CCDC 2015), Qingdao, China.","DOI":"10.1109\/CCDC.2015.7162732"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"96","DOI":"10.17516\/1997-1397-2017-10-1-96-107","article-title":"On the Nonparametric Identification and Dual Adaptive Control of Dynamic Processes","volume":"10","author":"Medvedev","year":"2017","journal-title":"J. Sib. Fed. Univ. Math. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.fss.2014.06.017","article-title":"Single level constraint interval arithmetic","volume":"257","author":"Lodwick","year":"2014","journal-title":"Fuzzy Sets Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1778","DOI":"10.1080\/00207179.2017.1410575","article-title":"Discrete-time interval optimal control problem","volume":"92","author":"Campos","year":"2019","journal-title":"Int. J. Control."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.fss.2019.10.002","article-title":"Interval optimal control for uncertain problems","volume":"402","author":"Leal","year":"2021","journal-title":"Fuzzy Sets Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Trean\u0163\u0103, S. (2021). On a Dual Pair of Multiobjective Interval-Valued Variational Control Problems. Mathematics, 9.","DOI":"10.3390\/math9080893"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/MCI.2018.2881644","article-title":"Fuzzy control systems: Past, present and future","volume":"14","author":"Nguyen","year":"2019","journal-title":"IEEE Comput. Intell. Mag."},{"key":"ref_27","unstructured":"Xuehui, M., Qian, F., and Zhang, S. (2020, January 27\u201329). Dual control for stochastic systems with multiple uncertainties. Proceedings of the Shenyang, China IEEE 2020 39th Chinese Control Conference (CCC), Shenyang, China."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"9258","DOI":"10.1002\/rnc.6331","article-title":"Estimation of dual-mode nonlinear stochastic systems with unknown parameters","volume":"32","author":"Ji","year":"2022","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.fss.2019.05.003","article-title":"Fuzzy interval optimal control problem","volume":"385","author":"Campos","year":"2020","journal-title":"Fuzzy Sets Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"376","DOI":"10.3103\/S8756699019040083","article-title":"Fuzzy Optimization in Discrete-Continuous Control Systems for Multiple-Operation Technological Processes","volume":"55","author":"Mitroshin","year":"2019","journal-title":"Optoelectron. Instrum. Data Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1016\/j.na.2008.12.005","article-title":"Generalized Hukuhara differentiability of interval-valued functions and interval differential equations","volume":"71","author":"Stefanini","year":"2009","journal-title":"Nonlinear Anal."},{"key":"ref_32","unstructured":"Moore, R.E. (1966). Interval Analysis, Prentice Hall."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Moore, R.E. (1979). Method and Applications of Interval Analysis, SIAM.","DOI":"10.1137\/1.9781611970906"},{"key":"ref_34","unstructured":"Alefeld, G., and Herzberger, J. (1983). Introduction to Interval Computations, Academic Press."},{"key":"ref_35","unstructured":"Tikhonov, A.N., and Arsenin, V.I. (1977). Solution of Ill-Posed Problems, John Wiley & Sons."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Turetsky, V. (2021). Two Inverse Problems Solution by Feedback Tracking Control. Axioms, 10.","DOI":"10.3390\/axioms10030137"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"108830","DOI":"10.1016\/j.automatica.2020.108830","article-title":"Kernel-based identification of non-causal systems with application to inverse model control","volume":"114","author":"Blanken","year":"2020","journal-title":"Automatica"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.conengprac.2014.12.015","article-title":"Iterative motion feedforward tuning: A data-driven approach based on instrumental variable identification","volume":"37","author":"Boeren","year":"2015","journal-title":"Control. Eng. Pract."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1137\/1110024","article-title":"On non-parametric estimates of density functions and regression curves","volume":"10","author":"Nadaraya","year":"1965","journal-title":"Theory Probab. Its Appl."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1214\/aos\/1032526955","article-title":"Asymptotics for kernel estimate of sliced inverse regression","volume":"24","author":"Zhu","year":"1996","journal-title":"Ann. Stat."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"H\u00e4rdle, W. (1990). Applied Nonparametric Regression, Cambridge University Press.","DOI":"10.1017\/CCOL0521382483"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1080\/03610918.2019.1652319","article-title":"Modification of the adaptive Nadaraya-Watson kernel method for nonparametric regression (simulation study)","volume":"51","author":"Ali","year":"2022","journal-title":"Commun.-Stat.-Simul. Comput."},{"key":"ref_43","unstructured":"Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis, Chapman and Hall."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/2\/193\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:31:57Z","timestamp":1760121117000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/2\/193"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,11]]},"references-count":43,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["axioms12020193"],"URL":"https:\/\/doi.org\/10.3390\/axioms12020193","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2023,2,11]]}}}