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Noname manuscript No. (will be inserted by the editor) Adaptive identifier for uncertain complex-valued discrete-time nonlinear systems based on recurrent neural networks M. Alfaro-Ponce · I. Salgado · A. Arguelles · I. Chairez Received: date / Accepted: date Abstract Recently, the study of dynamic systems and signals in the frequency domain motivates the emergence of new tools. In particular, electrophysiological and communications signals in the complex domain can be analyzed but hardly, they can be modeled. This problem promotes an attractive field of researching in system theory. As a consequence, adaptive algorithms like neural networks are interesting tools to deal with the identification problem of this kind of systems. In this study, a new learning process for recurrent neural network applied on complex-valued discrete-time nonlinear systems is proposed. The Lyapunov stability framework is applied to obtain the corresponding learning laws by means of the so-called Lyapunov control functions. The region where the identification error converges is defined by the power of uncertainties and perturbations that affects the nonlinear discrete-time complex system. This zone is obtained as an alterna- tive result of the same Lyapunov analysis. An off-line training algorithm is derived in order to reduce the size of the convergence zone. The training is executed using a set of some off-line measurements coming from the uncertain system. Numerical results are developed to prove the efficiency of the methodology proposed in this study. A first example is oriented to identify the dynamics of a nonlinear discrete time complex-valued system and the second one to model the dynamics of an electrophysiological signal separated in magnitude and phase. Keywords Complex-valued systems · Non-parametric modeling · Recurrent neural networks · Lyapunov control functions. M. Alfaro-Ponce, I. Salgado and A. Arguelles Neural networks and non-conventional computing laboratory, Centro de Investigacion en Computacion, Instituto Politecnico Nacional I. Chairez Bioprocess Department Unidad Profesional Interdisciplinaria de Biotecnologia Instituto Politecnico Nacional. E-mail: [email protected] The corresponding author. Bioresource Technology 212 (2016) 207–216 Contents lists available at ScienceDirect Bioresource Technology journal homepage: www.elsevier.com/locate/biortech A novel culture medium designed for the simultaneous enhancement of biomass and lipid production by Chlorella vulgaris UTEX 26 ⇑ Citlally Ramírez-López, Isaac Chairez, Luis Fernández-Linares Unidad Profesional Interdisciplinaria de Biotecnología, Instituto Politécnico Nacional, Mexico h i g h l i g h t s graphical abstract A new culture medium for Chlorella vulgaris UTEX 26 was designed. Biomass and lipid concentrations were increased. The new culture medium can be used to perform recycling cultures. Main fatty acids from Chlorella vulgaris UTEX 26 were C16 and C18. article info a b s t r a c t Article history: A novel culture medium to enhance the biomass and lipid production simultaneously by Chlorella vulgaris Received 20 January 2016 UTEX 26 was designed in three stages of optimization. Initially, a culture medium was inferred applying Received in revised form 16 March 2016 the response surface method to adjust six factors [NaNO3, NH4HCO3, MgSO4Á7H2O, KH2PO4,K2HPO4 and Accepted 11 April 2016 (NH ) HPO ], which were selected on the basement of BBM (Bold’s Basal Medium) and HAMGM (Highly Available online 13 April 2016 4 2 4 Assimilable Minimal Growth Medium) culture media. Afterwards, the nitrogen source compound was optimized to reduce both, ammonium and nitrate concentrations. As result of the optimization process, Keywords: À the proposed culture medium improved 40% the biomass (0.73 g L 1) compared with the BBM medium Chlorella vulgaris and 85% the lipid concentration (281 mg LÀ1), with respect to HAMGM medium. Some culture media Response surface method Culture medium components concentrations were reduced up to 50%. Gas chromatography analysis revealed that Ammonium bicarbonate C16:0, C18:0, C18:1, C18:2 and C18:3 were the major fatty acids produced by C. vulgaris UTEX 26. Fatty acids Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction bioelectricity, methane produced by anaerobic digestion of the algal biomass, biohydrogen produced under anaerobic conditions, Microalgae production offers the potential to produce bioen- bioethanol (sugar fermentation) and biodiesel derived from ergy as well as high value compounds, wastewater treatment, microalgal oil (Hadj-Romdhane et al., 2012; Aguirre et al., 2013; nitrogen fixing and CO2 mitigation (Hadj-Romdhane et al., 2012; Fon Sing et al., 2013; Ramanna et al., 2014). Mendoza et al., 2013). Microalgae have been taken into considera- For large-scale microalgae culture, open ponds or raceways tion as a feedstock for renewable biofuels production, such as are used by their low cost (Fon Sing et al., 2013). However, to improve the microalgae production in this kind of culture system, it is necessary to use an adequate culture medium selected ⇑ Corresponding author at: Departamento de Bioprocesos, Unidad Profesional for every microalgae species, different culture strategies (contin- Interdisciplinaria de Biotecnología, Instituto Politécnico Nacional, C.P. 07340 Ciudad uous or sequenced batch) and to recycle the wasted culture de México, Mexico. E-mail address: [email protected] (L. Fernández-Linares). medium. http://dx.doi.org/10.1016/j.biortech.2016.04.051 0960-8524/Ó 2016 Elsevier Ltd. All rights reserved. Colaboración Aspectos ambientales a considerar en vertederos: Emplazamiento y emisiones de biogás Autores: Francisco J. Colomer-Mendoza1,3, Características del vertedero: 1 1 Superfi cie ocupada Ferrán García-Darás , Vicente Vives-Peris , Nº Declaración de Impacto Publicado en: Capacidad Lidón Herrera-Prats1, Fabián Robles-Martinez2,3 Ambiental Tipo de residuo 1 Universidad Jaume I, 2 Unidad Profesional Interdisciplinaria de Tiempo explotación Biotecnología, 3 REDISA 1 Campo de En Medio, BOC nº 39 (26/02/10) y nº -- Cantabria 54 (19/03/2010) -- RCDs -- 2 San Bartolomé de BOC nº 128, (02/07/08) y -- I Meruelo, Cantabria BOC nº 201 (17/10/08) 2.500.000 t NTRODUCCIÓN RNP El depósito de residuos -- en vertedero es la última opción en 3 Toledo DOCM nº28 (10/02/2010) -- -- la jerarquía de gestión de residuos RNP que marca la Unión Europea en sus -- programas de acción. Sin embargo, más 4 Castañeda, Cantabria BOC (07/07/09) 50 ha 7.500.000 m3 del 50% de los residuos que se generan RNP en España acaban en vertedero. En este 20-25 años trabajo se han analizando en primer 5 Reocín, Cantabria BOC nº244 (22/12/2006) -- -- lugar, 14 declaraciones de impacto RSI ambiental de proyectos de vertederos -- españoles y se han dilucidado los 6 Cubilos del Sil y BOCYL nº114 (16/06/10) -- 3 factores ambientales que se consideran Ponferrada, León 6.000.000 m RNP para permitir su ejecución. Entre 16 años ellos se destaca entre otros el uso del 7 La Tahá, Granada BOJA nº5 (08/01/07) -- suelo, la hidrología, las emisiones de 51.000 m3 RSI gases y la proximidad a poblaciones. -- En segundo lugar, se ha realizado 8 Mallabia, Vizcaya BOPV (22/12/2006) -- un inventario de los vertederos 1.318.000 m3 RNP controlados españoles y se ha estudiado -- el efecto en cada uno de los citados 9 Zaldívar, Vizcaya BOPV nº2007051 -- factores ambientales. Así mismo, se (13/03/07) 418.499 m3 RNP han buscado correlaciones entre las -- emisiones de los vertederos de cada 10 Guadalajara DOCM nº99 (24/05/11) -- una de las comunidades autónomas y -- factores como la geografía, el clima y RSI y RNP -- la densidad de población. Por último, 11 La Robla, León BOCYL nº124 (30/06/08) -- se ha contrastado esta información 2.199.800 m3 con las directrices sobre vertederos RNP 12 años que marca la normativa de la Unión 12 Tineo, Asturias BOPA nº51 (03/03/09) -- Europea, la española, la de la EPA -- (Environmental Protection Agency) RNP de EE.UU., analizando el grado de -- 13 Igorre, Vizcaya BOPV nº91 (14/05/07) -- cumplimiento. 3.328.100 m3 En la ubicación de un vertedero RSI y RNP entran en juego múltiples factores 20 años 14 Zaragoza, Aragón BOA nº76 (30/06/04) -- ambientales. Según el Real Decreto -- Legislativo 1/2008, cualquier RSU vertedero controlado que reciba más -- de 10 t/día de residuos o tenga una Tabla 1: resumen de las características de los vertederos analizados en función de su DIA correspondiente 726 Dyna Marzo - Abril 2013 • Vol. 88 nº2 INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING Int. J. Adapt. Control Signal Process. 2017; 31:83–96 Published online 25 April 2016 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/acs.2685 Adaptive control of discrete-time nonlinear systems by recurrent neural networks in quasi-sliding mode like regime Ivan Salgado1, Cornelio Yañez1, Oscar Camacho2 and Isaac Chairez3,*,† 1CIC-Instituto Politecnico Nacional, Mexico City, Mexico 2CIDETEC-Instituto Politecnico Nacional, Mexico City, Mexico 3Bioprocesses Department UPIBI-Instituto Politecnico Nacional, Mexico City, Mexico SUMMARY The aim of this study was to design an adaptive control strategy based on recurrent neural networks (RNNs). This neural network was designed to obtain a non-parametric approximation (identification) of discrete- time uncertain nonlinear systems. A discrete-time Lyapunov candidate function was proposed to prove the convergence of the identification error. The adaptation laws to adjust the free parameters in the RNN were obtained in the same stability analysis. The control scheme used the states of the identifier, and it was developed fulfilling the necessary conditions to establish a behavior comparable with a quasi-sliding mode regime. This controller does not use the regular form of the switching function that commonly appears in the sliding mode control designs. The Lyapunov candidate function to design the controller and the identifier simultaneously requires the existence of positive definite solutions of two different matrix inequalities. As consequence, a class of separation principle was proven when the RNN-based identifier and the controller were designed by the same analysis.

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