A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

Variable structure control with chattering reduction of a generalized T-S model

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) is presented. The main objective is to obtain an improved performance of highly non-linear unstable systems. New functions for chattering reduction and error convergence without sacrificing invariant properties are proposed. The main feature of the proposed method is that the switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules; together with the state variables. In this work, a tuning of the well known weighting parameters approach is proposed to optimize local and global approximation and modelling capability of the Takagi-Sugeno (T-S) fuzzy model to improve the choice of the performance index and minimize it. The main problem encountered is that the T-S identification method can not be applied when the membership functions are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. The approach developed here can be considered as a generalized version of the T-S method. An inverted pendulum mounted on a cart is chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of the proposed estimation approach in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the estimation method and the robustness of the chattering reduction algorithm. In this paper, we prove that the proposed estimation algorithm converge the very fast, thereby making it very practical to use. The application of the proposed FLC-VSC shows that both alleviation of chattering and robust performance are achieved.

Estimación de modelos borrosos y su aplicación al control óptimo

El objetivo de la presentación es dar a conocer los últimos trabajos del Grupo de Investigación sobre últimos trabajos del Grupo de Investigación sobre Control Borroso. • Obtención de modelos precisos de sistemas no lineales basados en sistemas borrosos – Mamdani – Takagi-Sugeno – Linealización • Generalización del método propuesto por T-S • Identificación iterativa basada en el Filtro de Kalman • Sistemas de control basados en el modelo TS obtenido – LQR

Application of the Extended Kalman filter to fuzzy modeling: Algorithms and practical implementation

Modeling phase is fundamental both in the analysis process of a dynamic system and the design of a control system. If this phase is in-line is even more critical and the only information of the system comes from input/output data. Some adaptation algorithms for fuzzy system based on extended Kalman filter are presented in this paper, which allows obtaining accurate models without renounce the computational efficiency that characterizes the Kalman filter, and allows its implementation in-line with the process

Fuzzy Optimal Control for Double Inverted Pendulum

In this paper a fuzzy optimal control for stabilizing an upright position a double inverted pendulum (DIP) is developed and compared. Modeling is based on Euler-Lagrange equations. This results in a complicated nonlinear fast reaction, unstable multivariable system. Firstly, the mathematical models of double pendulum system are presented. The weight variable fuzzy input is gained by combining the fuzzy control theory with the optimal control theory. Simulation results show that the controller, which the upper pendulum is considered as main control variable, has high accuracy, quick convergence speed and higher precision.

Control of a solar dryer through using a fuzzy logic and low-cost model-based sensor

Solar drying is one of the important processes used for extending the shelf life of agricultural products. Regarding consumer requirements, solar drying should be more suitable in terms of curtailing total drying time and preserving product quality. Therefore, the objective of this study was to develop a fuzzy logic-based control system, which performs a ?human-operator-like? control approach through using the previously developed low-cost model-based sensors. Fuzzy logic toolbox of MatLab and Borland C++ Builder tool were utilized to develop a required control system. An experimental solar dryer, constructed by CONA SOLAR (Austria) was used during the development of the control system. Sensirion sensors were used to characterize the drying air at different positions in the dryer, and also the smart sensor SMART-1 was applied to be able to include the rate of wood water extraction into the control system (the difference of absolute humidity of the air between the outlet and the inlet of solar dryer is considered by SMART-1 to be the extracted water). A comprehensive test over a 3 week period for different fuzzy control models has been performed, and data, obtained from these experiments, were analyzed. Findings from this study would suggest that the developed fuzzy logic-based control system is able to tackle difficulties, related to the control of solar dryer process.

An interactive method of fuzzy probability elicitation in risk analysis

Expert knowledge is used to assign probabilities to events in many risk analysis models. However, experts sometimes find it hard to provide specific values for these probabilities, preferring to express vague or imprecise terms that are mapped using a previously defined fuzzy number scale. The rigidity of these scales generates bias in the probability elicitation process and does not allow experts to adequately express their probabilistic judgments. We present an interactive method for extracting a fuzzy number from experts that represents their probabilistic judgments for a given event, along with a quality measure of the probabilistic judgments, useful in a final information filtering and analysis sensitivity process.

Self-adaptive strategy based on fuzzy control systems for improving performance in wireless sensors networks

The solutions to cope with new challenges that societies have to face nowadays involve providing smarter daily systems. To achieve this, technology has to evolve and leverage physical systems automatic interactions, with less human intervention. Technological paradigms like Internet of Things (IoT) and Cyber-Physical Systems (CPS) are providing reference models, architectures, approaches and tools that are to support cross-domain solutions. Thus, CPS based solutions will be applied in different application domains like e-Health, Smart Grid, Smart Transportation and so on, to assure the expected response from a complex system that relies on the smooth interaction and cooperation of diverse networked physical systems. The Wireless Sensors Networks (WSN) are a well-known wireless technology that are part of large CPS. The WSN aims at monitoring a physical system, object, (e.g., the environmental condition of a cargo container), and relaying data to the targeted processing element. The WSN communication reliability, as well as a restrained energy consumption, are expected features in a WSN. This paper shows the results obtained in a real WSN deployment, based on SunSPOT nodes, which carries out a fuzzy based control strategy to improve energy consumption while keeping communication reliability and computational resources usage among boundaries.

Autonomous classification models in ubiquitous environments

Stream-mining approach is defined as a set of cutting-edge techniques designed to process streams of data in real time, in order to extract knowledge. In the particular case of classification, stream-mining has to adapt its behaviour to the volatile underlying data distributions, what has been called concept drift. Moreover, it is important to note that concept drift may lead to situations where predictive models become invalid and have therefore to be updated to represent the actual concepts that data poses. In this context, there is a specific type of concept drift, known as recurrent concept drift, where the concepts represented by data have already appeared in the past. In those cases the learning process could be saved or at least minimized by applying a previously trained model. This could be extremely useful in ubiquitous environments that are characterized by the existence of resource constrained devices. To deal with the aforementioned scenario, meta-models can be used in the process of enhancing the drift detection mechanisms used by data stream algorithms, by representing and predicting when the change will occur. There are some real-world situations where a concept reappears, as in the case of intrusion detection systems (IDS), where the same incidents or an adaptation of them usually reappear over time. In these environments the early prediction of drift by means of a better knowledge of past models can help to anticipate to the change, thus improving efficiency of the model regarding the training instances needed. By means of using meta-models as a recurrent drift detection mechanism, the ability to share concepts representations among different data mining processes is open. That kind of exchanges could improve the accuracy of the resultant local model as such model may benefit from patterns similar to the local concept that were observed in other scenarios, but not yet locally. This would also improve the efficiency of training instances used during the classification process, as long as the exchange of models would aid in the application of already trained recurrent models, that have been previously seen by any of the collaborative devices. Which it is to say that the scope of recurrence detection and representation is broaden. In fact the detection, representation and exchange of concept drift patterns would be extremely useful for the law enforcement activities fighting against cyber crime. Being the information exchange one of the main pillars of cooperation, national units would benefit from the experience and knowledge gained by third parties. Moreover, in the specific scope of critical infrastructures protection it is crucial to count with information exchange mechanisms, both from a strategical and technical scope. The exchange of concept drift detection schemes in cyber security environments would aid in the process of preventing, detecting and effectively responding to threads in cyber space. Furthermore, as a complement of meta-models, a mechanism to assess the similarity between classification models is also needed when dealing with recurrent concepts. In this context, when reusing a previously trained model a rough comparison between concepts is usually made, applying boolean logic. The introduction of fuzzy logic comparisons between models could lead to a better efficient reuse of previously seen concepts, by applying not just equal models, but also similar ones. This work faces the aforementioned open issues by means of: the MMPRec system, that integrates a meta-model mechanism and a fuzzy similarity function; a collaborative environment to share meta-models between different devices; a recurrent drift generator that allows to test the usefulness of recurrent drift systems, as it is the case of MMPRec. Moreover, this thesis presents an experimental validation of the proposed contributions using synthetic and real datasets.