{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:01:09Z","timestamp":1760241669204,"version":"build-2065373602"},"reference-count":83,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,7,14]],"date-time":"2018-07-14T00:00:00Z","timestamp":1531526400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["SEP-CONACyT 253677"],"award-info":[{"award-number":["SEP-CONACyT 253677"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The design of a fractional-order closed-loop model reference adaptive control (FOCMRAC) for anesthesia based on a fractional-order model (FOM) is proposed in the paper. This proposed model gets around many difficulties, namely, unknown parameters, lack of state measurement, inter and intra-patient variability, and variable time-delay, encountered in controller designs based on the PK\/PD model commonly used for control of anesthesia, and allows to design a simple adaptive controller based on the Lyapunov analysis. Simulations illustrate the effectiveness and robustness of the proposed control.<\/jats:p>","DOI":"10.3390\/a11070106","type":"journal-article","created":{"date-parts":[[2018,7,16]],"date-time":"2018-07-16T04:05:33Z","timestamp":1531713933000},"page":"106","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Fractional-Order Closed-Loop Model Reference Adaptive Control for Anesthesia"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9615-0112","authenticated-orcid":false,"given":"Gerardo","family":"Navarro-Guerrero","sequence":"first","affiliation":[{"name":"Engineering Graduate Program, Universidad Nacional Autonoma de Mexico (UNAM), 04510 Mexico City, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3305-3179","authenticated-orcid":false,"given":"Yu","family":"Tang","sequence":"additional","affiliation":[{"name":"Engineering Faculty, Universidad Nacional Autonoma de Mexico (UNAM), 04510 Mexico City, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2638","DOI":"10.1056\/NEJMra0808281","article-title":"General anesthesia, sleep, and coma","volume":"27","author":"Brown","year":"2010","journal-title":"N. Engl. J. Med."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1002\/acs.1087","article-title":"Robust control of depth of anesthesia","volume":"23","author":"Dumont","year":"2009","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1007\/s10877-013-9535-5","article-title":"Lessons learned from closed loops in engineering: Towards a multivariable approach regulating depth of anaesthesia","volume":"28","author":"Ionescu","year":"2013","journal-title":"J. Clin. Monit. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1109\/TBME.2014.2365726","article-title":"Advanced Model-Based Control Studies for the Induction and Maintenance of Intravenous Anesthesia","volume":"62","author":"Nascu","year":"2015","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1808","DOI":"10.1213\/ANE.0b013e318203f5ad","article-title":"Closed Loop Anesthesia: Are We Getting Close to Findind the Holy Grail","volume":"112","author":"Absalom","year":"2011","journal-title":"Anest. Analg."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/MCS.2005.1411383","article-title":"Drug Dosing Control in Clinical Pharmacology","volume":"25","author":"Bailey","year":"2005","journal-title":"IEEE Control Syst. Mag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/MDAT.2015.2452904","article-title":"Modeling the Effect of Intravenous Anesthetics: A Path Toward Individualization","volume":"15","author":"Silva","year":"2015","journal-title":"IEEE Des. Test"},{"key":"ref_8","first-page":"24","article-title":"Robust Control of MaintenMain-Phase Anesthesia","volume":"12","author":"Lemos","year":"2014","journal-title":"IEEE Control Syst. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1097\/ALN.0b013e31821a8d80","article-title":"An evaluation of using population pharmacokinetic models to estimate pharmacodynamics parameters for propofol and bispectral index in children","volume":"115","author":"Coppens","year":"2011","journal-title":"Anesthesiology"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"549","DOI":"10.3182\/20060920-3-FR-2912.00097","article-title":"Patient variability and uncertainty quantification in clinical anesthesia: Part I-PKPD modeling and identification","volume":"39","author":"Bibian","year":"2006","journal-title":"IFAC Proc. Vol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1109\/TBME.2011.2177497","article-title":"A direct dynamic dose-response model of propofol for individualized anesthesia care","volume":"59","author":"Hahn","year":"2012","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_12","first-page":"133","article-title":"Reliable nonlinear identification in medical applications","volume":"36","author":"Wang","year":"2003","journal-title":"IFAC Syst. Identif."},{"key":"ref_13","first-page":"571","article-title":"On the use of multivariable piecewise-linear models for predicting human response to anesthesia","volume":"59","author":"Lin","year":"2004","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_14","unstructured":"Silva, M., Medon\u00e7a, T., and Wigren, T. (July, January 30). Online nonlinear identification of the effect of drug in anesthesia using a minimal parameterization and BIS measurements. Proceedings of the 2010 American Control Conference Marriott Waterfront, Baltimore, MD, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s10928-009-9116-x","article-title":"Fractional kinetics in drug absortion and disposition processes","volume":"36","author":"Dokoumetzidis","year":"2009","journal-title":"J. Pharmacokinet. Pharmacodyn."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Copot, D., Chevalier, A., Ionescu, C., and de Keyser, R. (2013, January 28\u201330). A Two-Compartment Fractional Derivative Model for Propofol Diffusion in Anesthesia. Proceedings of the IEEE International Conference on Control Applications, Hyderabad, India.","DOI":"10.1109\/CCA.2013.6662769"},{"key":"ref_17","unstructured":"Copot, D., Ionescu, C., and Kayser, R.D. (2014, January 24\u201329). Relation between fractional order models and diffusion in the body. Proceedings of the 19th IFAC World Congress, Cape Town, South Africa."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s10928-010-9159-z","article-title":"Fractional dynamics pharmacokinetics-pharmacodynamic models","volume":"37","author":"Verotta","year":"2010","journal-title":"J. Pharmacokinet. Pharmacodyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s13318-011-0057-6","article-title":"A nonlinear two compartmental fractional derivative model","volume":"36","year":"2011","journal-title":"Eur. J. Drug Metab. Pharmacokinet."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/0013-4694(50)90014-9","article-title":"Automatic EEG control of general anesthesia","volume":"2","author":"Bickford","year":"1950","journal-title":"Electroencephalogr. Clin. Neurophysiol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1093\/bja\/74.1.66","article-title":"Arterial pressure control with isoflurane using fuzzy logic","volume":"74","author":"Hacisalihzade","year":"1995","journal-title":"Br. J. Anaesth."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1093\/bja\/76.2.245","article-title":"Fuzzy logic control of inspired isoflurane and oxygen concentrations using minimal flow anaesthesia","volume":"76","author":"Curatolo","year":"1996","journal-title":"Br. J. Anaesth."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1097\/00000542-200310000-00010","article-title":"Ability of the bispectral index, autoregressive modelling with exogenous input-derived auditory evoked potentials, and predicted propofol concentrations to measure patient responsiveness during anesthesia with propofol and remifentanil","volume":"99","author":"Struys","year":"2003","journal-title":"Anesthesiology"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF03356572","article-title":"Feedback control in anaesthesia","volume":"14","author":"Asbury","year":"1997","journal-title":"J. Clin. Monit. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1046\/j.1365-2044.2000.01527.x","article-title":"Closed loop control of anaesthesia: An assessment of the bispectral index as the target of control","volume":"55","author":"Morley","year":"2000","journal-title":"Anaesthesia"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.cmpb.2003.11.005","article-title":"Migrating from target-controlled infusion to closed-loop control in general anesthesia","volume":"75","author":"Ting","year":"2004","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_27","unstructured":"Ioannou, P., and Sun, J. (1996). Robust Adaptive Control, Prentice-Hall."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1093\/bja\/83.2.223","article-title":"Closed-loop control of propofol anesthesia","volume":"83","author":"Kenny","year":"1999","journal-title":"Br. J. Anesth."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1034\/j.1399-6576.2000.440819.x","article-title":"Use of an EEG-bispectral closed-loop delivery system for administering propofol","volume":"44","author":"Sakai","year":"2000","journal-title":"Acta Anaesthesiol. Scand."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1097\/00000542-200201000-00017","article-title":"Closed-loop control of anesthesia using Bispectral index: Performance assessment in patients undergoing major orthopedic surgery under combined general and regional anesthesia","volume":"96","author":"Absalom","year":"2002","journal-title":"Anesthesiology"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1097\/00000542-200604000-00012","article-title":"Titration of propofol for anesthetic induction and maintenance guided by the bispectral index: Closed-loop versus manual control: A prospective, ramdomized, multicenter study","volume":"104","author":"Liu","year":"2006","journal-title":"Anesthesiology"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1177\/0310057X0703500306","article-title":"Closed-loop anaesthesia delivery system (CLADS) using bispectral index: A performance assessment study","volume":"35","author":"Puri","year":"2007","journal-title":"Anaesth. Intensive Care"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1046\/j.1365-2044.1998.00467.x","article-title":"Closed-Loop controlled administration of propofol using bispectral analysis","volume":"53","author":"Mortier","year":"1998","journal-title":"Anaesthesia"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1002\/acs.737","article-title":"Adaptive control for non-negative and compartmental dynamical systems with applications to general anesthesia","volume":"17","author":"Haddad","year":"2003","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.sysconle.2005.05.002","article-title":"Adaptive control for nonlinear compartmental dynamical systems with applications to clinical pharmacology","volume":"55","author":"Haddad","year":"2006","journal-title":"Syst. Control Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2161","DOI":"10.1109\/TBME.2008.923142","article-title":"Robust Predictive Control Strategy Applied for Propofol Dosing Using BIS as a ConControl Variable During Anesthesia","volume":"55","author":"Ionescu","year":"2008","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1002\/acs.1073","article-title":"EPSAC-controlled anesthesia with online gain adaptation","volume":"23","author":"Nino","year":"2009","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_38","unstructured":"Furutani, E., Tsurouka, K., Kusudo, S., Shirakami, G., and Fukuda, K. (2010, January 18\u201321). A hypnosis and analgesia control system using a model predictive controller in total intravenous anesthesia during day-case surgery. Proceedings of the SICE Annual Conference, Taipei, Taiwan."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Castro, A., Nunes, C., Amorim, P., and Almeida, F. (2008, January 21\u201324). Hypnotic administration for anesthesia using sliding-mode control. Proceedings of the Conference proceedings Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vancouver, BC, Canada.","DOI":"10.1109\/IEMBS.2008.4650535"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1109\/TNN.2007.899164","article-title":"Neural network adaptive output feedback control for intensive care unit sedation and intraoperative anesthesia","volume":"18","author":"Haddad","year":"2007","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1109\/TCST.2010.2042810","article-title":"Neuroadaptive output feedback control for automated anesthesia with noisy EEG measurements","volume":"19","author":"Haddad","year":"2011","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Navarro-Guerrero, G., and Tang, Y. (2015, January 15\u201318). Adaptive Control for Anesthesia Based on a Simple Fractional-order Model. Proceedings of the IEEE 54th Conference on Decision and Control, Osaka, Japan.","DOI":"10.1109\/CDC.2015.7403101"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1002\/acs.2769","article-title":"Fractional order model reference adaptive control for anesthesia","volume":"31","author":"Tang","year":"2017","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s10877-014-9590-6","article-title":"Automation of anesthesia: A review on multivariable control","volume":"29","author":"Chang","year":"2015","journal-title":"J. Clin. Monit. Comput."},{"key":"ref_45","unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Academic Press."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Kilbas, A., Skivastava, H., and Trujillo, J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier.","DOI":"10.3182\/20060719-3-PT-4902.00008"},{"key":"ref_47","unstructured":"Capelas, E., and Machado, J.T. (2014). Review of Definitions for Fractional Derivatives and Integral. Math. Probl. Eng."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2756","DOI":"10.1016\/j.aop.2008.04.005","article-title":"Fractional vector calculus and fractional Maxwell equations","volume":"323","author":"Tarasov","year":"2008","journal-title":"Ann. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1965","DOI":"10.1016\/j.automatica.2009.04.003","article-title":"Mittag-Leffler stability of fractional order nonlinear dynamic systems","volume":"45","author":"Li","year":"2009","journal-title":"Automatica"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1810","DOI":"10.1016\/j.camwa.2009.08.019","article-title":"Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag Leffler stability","volume":"59","author":"Li","year":"2010","journal-title":"Comput. Math. Appl."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1016\/j.cnsns.2014.10.008","article-title":"Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems","volume":"22","author":"Gallegos","year":"2015","journal-title":"Commun. Nonlinear Sci. Numer Simul."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2951","DOI":"10.1016\/j.cnsns.2014.01.022","article-title":"Lyapunov functions for fractional order systems","volume":"19","author":"Gallegos","year":"2014","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_53","unstructured":"Ladaci, S., Loiseau, J., and Charef, A. (2007, January 9\u201312). Robust adaptive control using a fractional feedforward based on SPR condition. Proceedings of the International Conference on Informatics in Control, Automation and Robotics, Signal Processing, Systems Modeling and Control, Angers, France."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"69","DOI":"10.2478\/v10006-009-0006-6","article-title":"Robust fractional adaptive control based on the strictly positive realness condition","volume":"19","author":"Ladaci","year":"2009","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.amc.2016.04.039","article-title":"On the Lyapunov theory for fractional order systems","volume":"287","author":"Gallegos","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1016\/j.cam.2015.11.008","article-title":"Boundedness and convergence on fractional order systems","volume":"296","author":"Gallegos","year":"2016","journal-title":"J. Comput. Appl. Math."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Evers, A., Maze, M., and Kharasch, E. (2011). Anesthetic Pharmacology, Cambridge University Press.","DOI":"10.1017\/CBO9780511781933"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1097\/00000542-199805000-00006","article-title":"The influence of method of administration and covariates on the pharmacokinetics of propofol in adults volunteers","volume":"88","author":"Schnider","year":"1998","journal-title":"Anesthesiology"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1093\/bja\/67.1.41","article-title":"Pharmacokinetic model driven infusion of propofol in children","volume":"67","author":"Marsh","year":"1991","journal-title":"Br. J. Anaesth."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.ejcon.2015.04.006","article-title":"Modeling and control of pharmacodynamics","volume":"24","author":"Beck","year":"2015","journal-title":"Eur. J. Control"},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Shafer, S., Flood, P., and Schwin, D. (2010). Basic Principles of Pharmacodynamic, Academic Press.","DOI":"10.1016\/B978-0-443-06959-8.00019-4"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Ionescu, C., and Copot, D. (2017, January 20\u201323). Guided closed loop control of analgesia: Are we there yet?. Proceedings of the IEEE 21st International Conference on Intelligent Engineering Systems (INES), Larnaca, Cyprus.","DOI":"10.1109\/INES.2017.8118543"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1097\/00000542-200508000-00018","article-title":"A physiologically based, recirculatory model of the kinetics and dynamics of propofol in man","volume":"103","author":"Upton","year":"2005","journal-title":"Am. Soc. Anesthesiol."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.cmpb.2013.07.020","article-title":"Local identifiability and sensitivity analysis of neuromuscular blockade and depth of hypnosis models","volume":"113","author":"Silva","year":"2014","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_65","first-page":"74","article-title":"On-line identification of propofol pharmacodynamic parameters","volume":"1","author":"Sartori","year":"2005","journal-title":"IEEE Conf. Eng. Med. Biol. Soc."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Alonso, H., Medon\u00e7a, T., Lemos, J., and Wigren, T. (2009, January 26\u201328). A simple model for identification of drug effect. Proceedings of the IEEE International Symposium on Intelligent Signal Processing, Budapest, Hungary.","DOI":"10.1109\/WISP.2009.5286552"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Grizzi, F., and Chiriva-Internati, M. (2005). The complexity of anatomical systems. Theor. Biol. Med. Model.","DOI":"10.1186\/1742-4682-2-26"},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Bassingthwaighte, J., Liebovitch, L., and West, B. (1994). Fractal Physiology, Springer.","DOI":"10.1007\/978-1-4614-7572-9"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/978-0-387-77064-2_4","article-title":"Control from an allometric perspective","volume":"629","author":"West","year":"2009","journal-title":"Adv. Exp. Med. Biol."},{"key":"ref_70","unstructured":"Magin, R. (2006). Fractional Calculus in Bioengineering, Begell House Inc."},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Copot, D., Ionescu, C., and de Keyser, R. (2014, January 23\u201325). Modelling drug interaction using a fractional order pharmacokinetic model. Proceedings of the International Conference on Fractional Differentiation and Its Applications, Catania, Italy.","DOI":"10.1109\/ICFDA.2014.6967361"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/j.chaos.2017.03.054","article-title":"Fractional calculus for respiratory mechanics: Power law impedance, viscoelasticity, and tissue heterogeneity","volume":"102","author":"Ionescu","year":"2017","journal-title":"Chaos Solitons Fractals"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.cnsns.2017.04.001","article-title":"The role of fractional calculus in modeling biological phenomena: A review","volume":"51","author":"Ionescu","year":"2017","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_74","unstructured":"Gonzalez-Olvera, M., Tang, Y., and Navarro-Guerrero, G. (2015, January 14\u201316). Fractional Order System Identification by a Genetic Algorithm. Proceedings of the Congreso Nacional de Control Automatico, AMCA, Mexico."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1016\/S0005-1098(99)00009-6","article-title":"Analytical PID parameter expressions for higher order systems","volume":"35","author":"Isaksson","year":"1999","journal-title":"Automatica"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"680","DOI":"10.3166\/ejc.16.680-694","article-title":"Simple Fractional Order Model Structures and their Applications in Control System Design","volume":"16","author":"Haeri","year":"2010","journal-title":"Eur. J. Control"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.mcm.2009.07.018","article-title":"Approximation of high order integer systems by fractional order reduced-parameter models","volume":"51","author":"Mansouri","year":"2010","journal-title":"Math. Comput. Model."},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Pan, I., and Das, S. (2013). Intelligent Fractional Order Systems and Control, Springer.","DOI":"10.1007\/978-3-642-31549-7"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"2728","DOI":"10.1109\/TAC.2015.2405295","article-title":"Adaptive Output Feedback Based on Closed-Loop Reference Models","volume":"10","author":"Gibson","year":"2015","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_80","doi-asserted-by":"crossref","unstructured":"Navarro-Guerrero, G., and Tang, Y. (2017, January 17\u201319). Closed-Loop Model Reference Fractional Adaptive Control for a Class of Wiener Systems. Proceedings of the IEEE 3rd International Conference on Control Science and Systems Engineering, Beijing, China.","DOI":"10.1109\/CCSSE.2017.8087883"},{"key":"ref_81","unstructured":"Val\u00e9rio, D., and S\u00e1 da Costa, J. (2018, February 10). Ninteger v. 2.3 Fractional Control Toolbox for Matlab (Manual). Available online: http:\/\/web.ist.utl.pt\/~duarte.valerio\/ninteger\/Manual.pdf."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"781","DOI":"10.3182\/20120711-3-BE-2027.00323","article-title":"Comparing different identification approaches for the depth of anesthesia using bis measurements","volume":"45","author":"Alonso","year":"2012","journal-title":"IFAC Proc. Vol."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"2521","DOI":"10.1109\/TBME.2013.2259592","article-title":"Quantification of the Variability in response to propofol Administration in Children","volume":"60","author":"Heusden","year":"2013","journal-title":"IEEE Trans. Biomed. Eng."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/11\/7\/106\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:12:15Z","timestamp":1760195535000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/11\/7\/106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,14]]},"references-count":83,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2018,7]]}},"alternative-id":["a11070106"],"URL":"https:\/\/doi.org\/10.3390\/a11070106","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2018,7,14]]}}}