Identication of fuzzy function via interval analysis

22 pages, accepté Reliable ComputingA number of techniques have been introduced to construct fuzzy models from measured data. One of the most common is the use of mathematical parametric models. In this paper, a new approach based on interval analysis is proposed to compute guaranteed estimates of suitable characteristics of the set of all values of the fuzzy parameter vector such that the error between experimental data and the model outputs belongs to some predefined feasible set. Subpavings consisting of boxes with nonzero width are used to encompass all the acceptable values of the parameter vector. The problem of estimating the parameters of the model is viewed as one of set inversion, which is solved in an approximate but guaranteed way with the tools of interval analysis. The estimation task is formulated here as a constrained optimization problem. Our approach emphasizes the use of interval mathematics for fuzzy representation, which is especially suited to nonlinear models, a situation where most available methods fail to provide any guarantee on the results. An algorithm is proposed, which makes it possible to obtain all fuzzy parameter vectors that are consistent with the data. Properties of this algorithm are established and illustrated on a simple example

A linear programming methodology for approximate dynamic programming

[EN] The linear programming (LP) approach to solve the Bellman equation in dynamic programming is a well-known option for finite state and input spaces to obtain an exact solution. However, with function approximation or continuous state spaces, refinements are necessary. This paper presents a methodology to make approximate dynamic programming via LP work in practical control applications with continuous state and input spaces. There are some guidelines on data and regressor choices needed to obtain meaningful and well-conditioned value function estimates. The work discusses the introduction of terminal ingredients and computation of lower and upper bounds of the value function. An experimental inverted-pendulum application will be used to illustrate the proposal and carry out a suitable comparative analysis with alternative options in the literature.The authors are grateful for the financial support of the Spanish Ministry of Economy and the European Union, grant DPI2016-81002-R (AEI/FEDER, UE), and the PhD grant from the Government of Ecuador (SENESCYT).Diaz, H.; Sala, A.; Armesto Ángel, L. (2020). A linear programming methodology for approximate dynamic programming. International Journal of Applied Mathematics and Computer Science (Online). 30(2):363-375. https://doi.org/10.34768/amcs-2020-0028S36337530

Value Function Estimation in Optimal Control via Takagi-Sugeno Models and Linear Programming

[ES] La presente Tesis emplea técnicas de programación dinámica y aprendizaje por refuerzo para el control de sistemas no lineales en espacios discretos y continuos. Inicialmente se realiza una revisión de los conceptos básicos de programación dinámica y aprendizaje por refuerzo para sistemas con un número finito de estados. Se analiza la extensión de estas técnicas mediante el uso de funciones de aproximación que permiten ampliar su aplicabilidad a sistemas con un gran número de estados o sistemas continuos. Las contribuciones de la Tesis son: -Se presenta una metodología que combina identificación y ajuste de la función Q, que incluye la identificación de un modelo Takagi-Sugeno, el cálculo de controladores subóptimos a partir de desigualdades matriciales lineales y el consiguiente ajuste basado en datos de la función Q a través de una optimización monotónica. -Se propone una metodología para el aprendizaje de controladores utilizando programación dinámica aproximada a través de programación lineal. La metodología hace que ADP-LP funcione en aplicaciones prácticas de control con estados y acciones continuos. La metodología propuesta estima una cota inferior y superior de la función de valor óptima a través de aproximadores funcionales. Se establecen pautas para los datos y la regularización de regresores con el fin de obtener resultados satisfactorios evitando soluciones no acotadas o mal condicionadas. -Se plantea una metodología bajo el enfoque de programación lineal aplicada a programación dinámica aproximada para obtener una mejor aproximación de la función de valor óptima en una determinada región del espacio de estados. La metodología propone aprender gradualmente una política utilizando datos disponibles sólo en la región de exploración. La exploración incrementa progresivamente la región de aprendizaje hasta obtener una política convergida.[CA] La present Tesi empra tècniques de programació dinàmica i aprenentatge per reforç per al control de sistemes no lineals en espais discrets i continus. Inicialment es realitza una revisió dels conceptes bàsics de programació dinàmica i aprenentatge per reforç per a sistemes amb un nombre finit d'estats. S'analitza l'extensió d'aquestes tècniques mitjançant l'ús de funcions d'aproximació que permeten ampliar la seua aplicabilitat a sistemes amb un gran nombre d'estats o sistemes continus. Les contribucions de la Tesi són: -Es presenta una metodologia que combina identificació i ajust de la funció Q, que inclou la identificació d'un model Takagi-Sugeno, el càlcul de controladors subòptims a partir de desigualtats matricials lineals i el consegüent ajust basat en dades de la funció Q a través d'una optimització monotónica. -Es proposa una metodologia per a l'aprenentatge de controladors utilitzant programació dinàmica aproximada a través de programació lineal. La metodologia fa que ADP-LP funcione en aplicacions pràctiques de control amb estats i accions continus. La metodologia proposada estima una cota inferior i superior de la funció de valor òptima a través de aproximadores funcionals. S'estableixen pautes per a les dades i la regularització de regresores amb la finalitat d'obtenir resultats satisfactoris evitant solucions no fitades o mal condicionades. -Es planteja una metodologia sota l'enfocament de programació lineal aplicada a programació dinàmica aproximada per a obtenir una millor aproximació de la funció de valor òptima en una determinada regió de l'espai d'estats. La metodologia proposa aprendre gradualment una política utilitzant dades disponibles només a la regió d'exploració. L'exploració incrementa progressivament la regió d'aprenentatge fins a obtenir una política convergida.[EN] The present Thesis employs dynamic programming and reinforcement learning techniques in order to obtain optimal policies for controlling nonlinear systems with discrete and continuous states and actions. Initially, a review of the basic concepts of dynamic programming and reinforcement learning is carried out for systems with a finite number of states. After that, the extension of these techniques to systems with a large number of states or continuous state systems is analysed using approximation functions. The contributions of the Thesis are: -A combined identification/Q-function fitting methodology, which involves identification of a Takagi-Sugeno model, computation of (sub)optimal controllers from Linear Matrix Inequalities, and the subsequent data-based fitting of Q-function via monotonic optimisation. -A methodology for learning controllers using approximate dynamic programming via linear programming is presented. The methodology makes that ADP-LP approach can work in practical control applications with continuous state and input spaces. The proposed methodology estimates a lower bound and upper bound of the optimal value function through functional approximators. Guidelines are provided for data and regressor regularisation in order to obtain satisfactory results avoiding unbounded or ill-conditioned solutions. -A methodology of approximate dynamic programming via linear programming in order to obtain a better approximation of the optimal value function in a specific region of state space. The methodology proposes to gradually learn a policy using data available only in the exploration region. The exploration progressively increases the learning region until a converged policy is obtained.This work was supported by the National Department of Higher Education, Science, Technology and Innovation of Ecuador (SENESCYT), and the Spanish ministry of Economy and European Union, grant DPI2016-81002-R (AEI/FEDER,UE). The author also received the grant for a predoctoral stay, Programa de Becas Iberoamérica- Santander Investigación 2018, of the Santander Bank.Díaz Iza, HP. (2020). Value Function Estimation in Optimal Control via Takagi-Sugeno Models and Linear Programming [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/139135TESI

Contributions to fuzzy polynomial techniques for stability analysis and control

The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees. The contributions of the thesis are: ¿ Improved domain of attraction estimation of nonlinear systems for both continuous-time and discrete-time cases. An iterative methodology based on invariant-set results is presented for obtaining polynomial boundaries of such domain of attraction. ¿ Extension of the above problem to the case with bounded persistent disturbances acting. Different characterizations of inescapable sets with polynomial boundaries are determined. ¿ State estimation: extension of the previous results in literature to the case of fuzzy observers with polynomial gains, guaranteeing stability of the estimation error and inescapability in a subset of the zone where the model is valid. ¿ Proposal of a polynomial Lyapunov function with discrete delay in order to improve some polynomial control designs from literature. Preliminary extension to the fuzzy polynomial case. Last chapters present a preliminary experimental work in order to check and validate the theoretical results on real platforms in the future.Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773TESI

Proceedings. 24. Workshop Computational Intelligence, Dortmund, 27. - 28. November 2014

Dieser Tagungsband enthält die Beiträge des 24. Workshops "Computational Intelligence" des Fachausschusses 5.14 der VDI/VDE-Gesellschaft für Mess- und Automatisierungstechnik (GMA), der vom 27. - 28. November 2014 in Dortmund stattgefunden hat. Die Schwerpunkte sind Methoden, Anwendungen und Tools für Fuzzy-Systeme, Künstliche Neuronale Netze, Evolutionäre Algorithmen und Data-Mining-Verfahren sowie der Methodenvergleich anhand von industriellen Anwendungen und Benchmark-Problemen

Proceedings. 23. Workshop Computational Intelligence, Dortmund, 5. - 6. Dezember 2013

Dieser Tagungsband enthält die Beiträge des 23. Workshops Computational Intelligence des Fachausschusses 5.14 der VDI/VDE-Gesellschaft für Mess- und Automatisierungstechnik (GMA), der vom 5. - 6. Dezember 2013 in Dortmund stattgefunden hat. Im Fokus stehen Methoden, Anwendungen und Tools für Fuzzy-Systeme, Künstliche Neuronale Netze, Evolutionäre Algorithmen und Data-Mining-Verfahren

System identification and optimal control for mixed-mode cooling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2004."September 2004."Includes bibliographical references (p. 285-294).The majority of commercial buildings today are designed to be mechanically cooled. To make the task of air conditioning buildings simpler, and in some cases more energy efficient, windows are sealed shut, eliminating occupants' direct access to fresh air. Implementation of an alternative cooling strategy-mixed-mode cooling-is demonstrated in this thesis to yield substantial savings in cooling energy consumption in many U.S. locations. A mixed-mode cooling strategy is one that relies on several different means of delivering cooling to the occupied space. These different means, or modes, of cooling could include: different forms of natural ventilation through operable windows, ventilation assisted by low-power fans, and mechanical air conditioning. Three significant contributions are presented in this thesis. A flexible system identification framework was developed that is well-suited to accommodate the unique features of mixed-mode buildings. Further, the effectiveness of this framework was demonstrated on an actual multi- zone, mixed-mode building, with model prediction accuracy shown to exceed that published for other naturally ventilated or mixed-mode buildings, none of which exhibited the complexity of this building. Finally, an efficient algorithm was constructed to optimize control strategies over extended planning horizons using a model-based approach. The algorithm minimizes energy consumption subject to the constraint that indoor temperatures satisfy comfort requirements. The system identification framework was applied to another mixed-mode building, where it was found that the aspects integral to the modeling framework led to prediction improvements relative to a simple model.(cont.) Lack of data regarding building apertures precluded the use of the model for control purposes. An additional contribution was the development of a procedure for extracting building time constants from experimental data in such a way that they are constrained to be physically meaningful.by Henry C. Spindler.Ph.D

Computer science: the hardware software and heart of IT

1st edition, 201