Computing Optimal Distances to Pareto Sets of Multi-Objective Optimization Problems in Asymmetric Normed Lattices

[EN] Given a finite dimensional asymmetric normed lattice, we provide explicit formulae for the optimization of the associated (non-Hausdorff) asymmetric distance among a subset and a point. Our analysis has its roots and finds its applications in the current development of effective algorithms for multi-objective optimization programs. We are interested in providing the fundamental theoretical results for the associated convex analysis, fixing in this way the framework for this new optimization tool. The fact that the associated topology is not Hausdorff forces us to define a new setting and to use a new point of view for this analysis. Existence and uniqueness theorems for this optimization are shown. Our main result is the translation of the original abstract optimal distance problem to a clear optimization scheme. Actually, this justifies the algorithms and shows new aspects of the numerical and computational methods that have been already used in visualization of multi-objective optimization problems.This work was supported by the Ministerio de Economia y Competitividad (Spain) under grants DPI2015-71443-R and MTM2016-77054-C2-1-P.Blasco, X.; Reynoso-Meza, G.; Sánchez Pérez, EA.; Sánchez Pérez, JV. (2019). Computing Optimal Distances to Pareto Sets of Multi-Objective Optimization Problems in Asymmetric Normed Lattices. Acta Applicandae Mathematicae. 159(1):75-93. https://doi.org/10.1007/s10440-018-0184-z7593159

Tuning and comparison of design concepts applying Pareto optimality. A case study of Cholette bioreactor

[EN] The linear control PI (D) and its variants are control structures (design concepts) that are still used in industrial processes. The control engineer will prefer one over another according to a desired tradeoff among complexity and performance indices. Given that this exchange might be in conflict, an analisis using multiobjective optimisation tools could be interesting. With this perspective, different Pareto fronts from different design concetps are compared, enabling a global, and not punctual, performance comparison. In this work a global methodology for comparing design concepts in dfferent stages was developed. The first step was to establish a region of stability. In the second stage, the stability region was considered as a search space for the multiobjective optimization process, approximating a Pareto set and front. In the third stage, a multicriteria analysis of the Pareto fronts was carried out, together with the simulation in the time domain for the output and control signals. As case study to validate this proposal the Cholette’s biorreactor was selected. The proposed methodology allows a better understanding of a conceptual solution, justifies and determines the use of a design concept thus meeting the needs of the designer.[ES] El control lineal PI(D) y sus variantes, son estructuras de control (conceptos de diseño) que actualmente se siguen utilizando en procesos industriales. La elección de una estructura de control sobre otra reside en el intercambio de prestaciones entre complejidad y rendimiento. Dado que este intercambio de prestaciones normalmente estará en conflicto, un análisis desde el punto de vista multiobjetivo puede ser de interés. Desde tal perspectiva, se analizan frentes de Pareto de diferentes conceptos de diseño, con lo que se realiza una comparación global y no puntual de tales conceptos. En este trabajo se plantea una propuesta metodológica para dicha comparación en diferentes etapas. La primera, fue establecer una región de estabilidad. En la segunda etapa se consideró la región de estabilidad como espacio de búsqueda para el proceso de optimización multiobjetivo calculando un conjunto y frente de Pareto. En la tercera etapa se realizó un análisis multicriterio de los frentes de Pareto, junto con la simulación en el dominio del tiempo para las señales de salida y de control. Como caso de estudio para validar la propuesta se ha elegido el biorreactor de Cholette que presenta diferentes condiciones de operación. 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Multi-objective optimization framework to obtain model-based guidelines for tuning biological synthetic devices: an adaptive network case

Background: Model based design plays a fundamental role in synthetic biology. Exploiting modularity, i.e. using biological parts and interconnecting them to build new and more complex biological circuits is one of the key issues. In this context, mathematical models have been used to generate predictions of the behavior of the designed device. Designers not only want the ability to predict the circuit behavior once all its components have been determined, but also to help on the design and selection of its biological parts, i.e. to provide guidelines for the experimental implementation. This is tantamount to obtaining proper values of the model parameters, for the circuit behavior results from the interplay between model structure and parameters tuning. However, determining crisp values for parameters of the involved parts is not a realistic approach. Uncertainty is ubiquitous to biology, and the characterization of biological parts is not exempt from it. Moreover, the desired dynamical behavior for the designed circuit usually results from a trade-off among several goals to be optimized. Results: We propose the use of a multi-objective optimization tuning framework to get a model-based set of guidelines for the selection of the kinetic parameters required to build a biological device with desired behavior. The design criteria are encoded in the formulation of the objectives and optimization problem itself. As a result, on the one hand the designer obtains qualitative regions/intervals of values of the circuit parameters giving rise to the predefined circuit behavior; on the other hand, he obtains useful information for its guidance in the implementation process. These parameters are chosen so that they can effectively be tuned at the wet-lab, i.e. they are effective biological tuning knobs. To show the proposed approach, the methodology is applied to the design of a well known biological circuit: a genetic incoherent feed-forward circuit showing adaptive behavior. Conclusion: The proposed multi-objective optimization design framework is able to provide effective guidelines to tune biological parameters so as to achieve a desired circuit behavior. Moreover, it is easy to analyze the impact of the context on the synthetic device to be designed. That is, one can analyze how the presence of a downstream load influences the performance of the designed circuit, and take it into account.Research in this area is partially supported by Spanish government and European Union (FEDER-CICYT DPI2011-28112-C04-01, and DPI2014-55276-C5-1-R). Yadira Boada thanks grant FPI/2013-3242 of Universitat Politecnica de Valencia; Gilberto Reynoso-Meza gratefully acknowledges the partial support provided by the postdoctoral fellowship BJT-304804/2014-2 from the National Council of Scientific and Technologic Development of Brazil (CNPq) for the development of this work. We are grateful to Alejandra Gonzalez-Bosca for her collaboration on this topic while doing her Bachelor thesis, and to Dr. Jose Luis Pitarch from Universidad de Valladolid for his advise in algorithmic implementations and for proof reading the manuscript.Boada Acosta, YF.; Reynoso Meza, G.; Picó Marco, JA.; Vignoni, A. (2016). Multi-objective optimization framework to obtain model-based guidelines for tuning biological synthetic devices: an adaptive network case. BMC Systems Biology. 10:1-19. https://doi.org/10.1186/s12918-016-0269-0S11910ERASynBio. Next steps for european synthetic biology: a strategic vision from erasynbio. 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Tuning of Pareto-optimal robust controllers for multivariable systems. Application on helicopter of two-degress-of-freedom

[ES] La sintonización de controladores Pareto-óptimo robustos ha sido empleada para mejorar el rendimiento de un helicóptero de dos grados de libertad con un algoritmo de control lineal. El procedimiento de sintonización del controlador está basado en la minimización simultánea de las integrales de la suma del cuadrado del error y de la acción de control. Como resultado de dicha minimización y dado que los objetivos entran en conflicto, se obtiene un conjunto de soluciones que describen un frente de Pareto. Posteriormente, un proceso de análisis en los mismos es llevado a cabo para seleccionar los controladores a implementar en el sistema físico. Los resultados experimentales con los controladores seleccionados muestran que el procedimiento de ajuste es eficaz y práctico.[EN] The tuning of Pareto-optimal robust controllers was applied to improve the performance of a helicopter with two-degrees-of-freedom with a linear control algorithm. The tuning procedure is based on the simultaneous minimization of the integral of square sum of errors and the integral of square sum of control action. A 2D Pareto front is built with these integrals. Afterwards, a decision-making process is carried out to select the most preferable controller. Experimental results on the physical platform validate the tuning procedure as practical and reliable.Dirección General de Educación Tecnológica Superior (DGEST), Consejo Nacional de Ciencia y Tecnología (CONACyT), l Ministerio de Economía y Competitividad de España y Consejo Nacional de Desarrollo Científico y Tecnológico de BrasilCarrillo Ahumada, J.; Reynoso Meza, G.; Sanchís Saez, J.; García Nieto, S.; García Alvarado, M. (2015). Sintonización de controladores Pareto-óptimo robustos para sistemas multivariables. Aplicación en un helicóptero de 2 grados de libertad. Revista Iberoamericana de Automática e Informática industrial. 12(2):177-188. https://doi.org/10.1016/j.riai.2015.03.002OJS177188122Carrillo-Ahumada, J., Rodríguez-Jimenes, G. C., & García-Alvarado, M. A. (2011). Tuning optimal-robust linear MIMO controllers of chemical reactors by using Pareto optimality. Chemical Engineering Journal, 174(1), 357-367. doi:10.1016/j.cej.2011.09.007Coello Coello, C. A. (2006). Evolutionary multi-objective optimization: a historical view of the field. IEEE Computational Intelligence Magazine, 1(1), 28-36. doi:10.1109/mci.2006.1597059Corne, D.W., Knowles, J.D., 2007. Techniques for highly multiobjective optimisation: some nondominated points are better than others. En: Proceedings of the 9th annual conference on Genetic and evolutionary computation. GECCO ‘07. ACM, New York, NY, USA, pp. 773-780.CSS, 2012. Unmanned aerial vehicle. special issue. IEEE Control Systems magazine 32 (5).Unmanned Aerial Vehicles and Control: Lockheed Martin Advanced Technology Laboratories. (2012). IEEE Control Systems, 32(5), 32-34. doi:10.1109/mcs.2012.2205474Gabriel, C., 2008. Modelling, simulation and control of a twin rotor mimo-system. Master thesis, Polytechnic University of Valencia, Spain.García-Sanz, M., & Elso, J. (2007). Ampliación del benchmark de diseño de controladores para el cabeceo de un helicóptero. Revista Iberoamericana de Automática e Informática Industrial RIAI, 4(1), 107-110. doi:10.1016/s1697-7912(07)70196-6García-Sanz, M., & Elso, J. (2007). Resultados Del Benchmark de Diseño De Controladores Para el Cabeceo de un Helicóptero. Revista Iberoamericana de Automática e Informática Industrial RIAI, 4(4), 117-120. doi:10.1016/s1697-7912(07)70251-0Garcia-Alvarado, M. A., & Ruiz-López, I. I. (2010). A design method for robust and quadratic optimal MIMO linear controllers. Chemical Engineering Science, 65(11), 3431-3438. doi:10.1016/j.ces.2010.02.033Hernández, L. H., Pestana, J., Palomeque, D. C., Campoy, P., & Sanchez-Lopez, J. L. (2013). Identificación y control en cascada mediante inversión de no linealidades del cuatrirrotor para el Concurso de Ingeniería de Control CEA IFAC 2012. Revista Iberoamericana de Automática e Informática Industrial RIAI, 10(3), 356-367. doi:10.1016/j.riai.2013.05.008Huba, M. (2013). Performance measures, performance limits and optimal PI control for the IPDT plant. Journal of Process Control, 23(4), 500-515. doi:10.1016/j.jprocont.2013.01.002Ishibuchi, H., Tsukamoto, N., Nojima, Y., 2008. Evolutionary many-objective optimization: A short review. En: Evolutionary Computation, 2008. CEC 2008. (IEEE World Congress on Computational Intelligence). IEEE Congress on.Juang, J.-G., Lin, R.-W., & Liu, W.-K. (2008). Comparison of classical control and intelligent control for a MIMO system. Applied Mathematics and Computation, 205(2), 778-791. doi:10.1016/j.amc.2008.05.061Juang, J.-G., Liu, W.-K., & Lin, R.-W. (2011). A hybrid intelligent controller for a twin rotor MIMO system and its hardware implementation. ISA Transactions, 50(4), 609-619. doi:10.1016/j.isatra.2011.06.006Lotov, A., Miettinen, K., 2008. Visualizing the Pareto frontier. In: Branke, J., Deb, K., Miettinen, K., Slowinski, R. (Eds.), Multiobjective Optimization. Vol. 5252 of Lecture Notes in Computer Science. Springer Berlin /Heidel-berg, pp. 213-243.Marler, R. T., & Arora, J. S. (2004). Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization, 26(6), 369-395. doi:10.1007/s00158-003-0368-6Rahideh, A., Shaheed, M., april 2009. Robust model predictive control of a twin rotor mimo system. En: Mechatronics, 2009. ICM 2009. IEEE International Conference on. pp. 1-6.Rahideh, A., & Shaheed, M. H. (2012). Constrained output feedback model predictive control for nonlinear systems. Control Engineering Practice, 20(4), 431-443. doi:10.1016/j.conengprac.2011.12.003Reynoso-Meza, G., Sanchis, J., Blasco, X., Herrero, J.M., August 2014a. A stabilizing PID controller sampling procedure for stochastic optimizers. En: Memories of the 19th World Congress IFAC 2014. pp. 8158-8163.Reynoso-Meza, G., Blasco, X., Sanchis, J., & Martínez, M. (2014). Controller tuning using evolutionary multi-objective optimisation: Current trends and applications. Control Engineering Practice, 28, 58-73. doi:10.1016/j.conengprac.2014.03.003Reynoso-Meza, G., Sánchez, H.S., Blasco, X., Vilanova, R., August 2014c. Reliability based multiobjective optimization design procedure for PI controller tuning. En: Memories of the 19th World Congress IFAC 2014. pp. 10263-10268.Ruiz-López, I. I., Rodríguez-Jimenes, G. C., & García-Alvarado, M. A. (2006). Robust MIMO PID controllers tuning based on complex/real ratio of the characteristic matrix eigenvalues. Chemical Engineering Science, 61(13), 4332-4340. doi:10.1016/j.ces.2006.02.015Skogestad, S. (2003). Simple analytic rules for model reduction and PID controller tuning. Journal of Process Control, 13(4), 291-309. doi:10.1016/s0959-1524(02)00062-8Sánchez, H.S., Vilanova, R., 2013a. Multiobjective tuning of PI controller using the NNC method: Simplified problem definition and guidelines for decision making. En: Proceedings of the 18th. IEEE Conference on emerging technologies & factory automation (ETFA).Sánchez, H.S., Vilanova, R., 2013b. Nash-based criteria for selection of pareto optimal controller. En: Proceedings of the 17th. International Conference on System Theory, Control anmd Computing.Tao, C. W., Taur, J. S., & Chen, Y. C. (2010). Design of a parallel distributed fuzzy LQR controller for the twin rotor multi-input multi-output system. Fuzzy Sets and Systems, 161(15), 2081-2103. doi:10.1016/j.fss.2009.12.007Tao, C.-W., Taur, J.-S., Chang, Y.-H., & Chang, C.-W. (2010). A Novel Fuzzy-Sliding and Fuzzy-Integral-Sliding Controller for the Twin-Rotor Multi-Input–Multi-Output System. IEEE Transactions on Fuzzy Systems, 18(5), 893-905. doi:10.1109/tfuzz.2010.2051447Toha, S., Tokhi, M., nov. 2009. Dynamic nonlinear inverse-model based control of a twin rotor system using adaptive neuro-fuzzy inference system. En: Computer Modeling and Simulation, 2009. EMS ‘09. Third UKSim European Symposium on. pp. 107-111.Vargas, F. J., Salgado, M. E., & Silva, E. I. (2011). Optimal ripple-free deadbeat control using an integral of time squared error (ITSE) index. Automatica, 47(9), 2134-2137. doi:10.1016/j.automatica.2011.06.006Velasco, J., García-Nieto, S., Reynoso-Meza, G., Sanchis, J., 2013. Implementación de un sistema hardware-in-the-loop para la simulación en tiempo real de pilotos automáticos para uavs. En: de Automática, C.E. (Ed.), Memorias de las XXXIV Jornadas de Automática.Vilanova, R., Alfaro, V. M., & Arrieta, O. (2012). Simple robust autotuning rules for 2-DoF PI controllers. ISA Transactions, 51(1), 30-41. doi:10.1016/j.isatra.2011.09.001Wen, P., & Lu, T.-W. (2008). Decoupling control of a twin rotor MIMO system using robust deadbeat control technique. IET Control Theory & Applications, 2(11), 999-1007. doi:10.1049/iet-cta:20070335Witczak, M., Puig, V., de Oca, S., oct. 2010. A fault-tolerant control scheme for non-linear discrete-time systems: Application to the twin-rotor system. En: Control and Fault-Tolerant Systems (SysTol), 2010 Conference on. pp. 861-866

Comparative study of auto-tuning algorithms for PID controllers. Results of the 2010-2011 match of the control engineering group of CEA

In this paper three PID auto-tuning algorithms which are mainly focused on the disturbance rejection problem are compared. The algorithms differ in both the experiments carried out to obtain information of the process dynamic and the methods for calculating the controller parameters. The algorithms were presented in the 2010-2011 Match of the Control Engineering Group of CEA. The comparison is based on an evaluation methodology that takes into account the experimental phase as well as the closed loop performance during the control phase. © 2011 CEA. Publicado por Elsevier España, S.L