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

Adaptive Non-singleton Type-2 Fuzzy Logic Systems: A Way Forward for Handling Numerical Uncertainties in Real World Applications

Real world environments are characterized by high levels of linguistic and numerical uncertainties. A Fuzzy Logic System (FLS) is recognized as an adequate methodology to handle the uncertainties and imprecision available in real world environments and applications. Since the invention of fuzzy logic, it has been applied with great success to numerous real world applications such as washing machines, food processors, battery chargers, electrical vehicles, and several other domestic and industrial appliances. The first generation of FLSs were type-1 FLSs in which type-1 fuzzy sets were employed. Later, it was found that using type-2 FLSs can enable the handling of higher levels of uncertainties. Recent works have shown that interval type-2 FLSs can outperform type-1 FLSs in the applications which encompass high uncertainty levels. However, the majority of interval type-2 FLSs handle the linguistic and input numerical uncertainties using singleton interval type-2 FLSs that mix the numerical and linguistic uncertainties to be handled only by the linguistic labels type-2 fuzzy sets. This ignores the fact that if input numerical uncertainties were present, they should affect the incoming inputs to the FLS. Even in the papers that employed non-singleton type-2 FLSs, the input signals were assumed to have a predefined shape (mostly Gaussian or triangular) which might not reflect the real uncertainty distribution which can vary with the associated measurement. In this paper, we will present a new approach which is based on an adaptive non-singleton interval type-2 FLS where the numerical uncertainties will be modeled and handled by non-singleton type-2 fuzzy inputs and the linguistic uncertainties will be handled by interval type-2 fuzzy sets to represent the antecedents’ linguistic labels. The non-singleton type-2 fuzzy inputs are dynamic and they are automatically generated from data and they do not assume a specific shape about the distribution associated with the given sensor. We will present several real world experiments using a real world robot which will show how the proposed type-2 non-singleton type-2 FLS will produce a superior performance to its singleton type-1 and type-2 counterparts when encountering high levels of uncertainties.</jats:p

Nature-Inspired Learning Models

Intelligent learning mechanisms found in natural world are still unsurpassed in their learning performance and eficiency of dealing with uncertain information coming in a variety of forms, yet remain under continuous challenge from human driven artificial intelligence methods. This work intends to demonstrate how the phenomena observed in physical world can be directly used to guide artificial learning models. An inspiration for the new learning methods has been found in the mechanics of physical fields found in both micro and macro scale. Exploiting the analogies between data and particles subjected to gravity, electrostatic and gas particle fields, new algorithms have been developed and applied to classification and clustering while the properties of the field further reused in regression and visualisation of classification and classifier fusion. The paper covers extensive pictorial examples and visual interpretations of the presented techniques along with some testing over the well-known real and artificial datasets, compared when possible to the traditional methods

A methodological approach for algorithmic composition systems' parameter spaces aesthetic exploration

Algorithmic composition is the process of creating musical material by means of formal methods. As a consequence of its design, algorithmic composition systems are (explicitly or implicitly) described in terms of parameters. Thus, parameter space exploration plays a key role in learning the system's capabilities. However, in the computer music field, this task has received little attention. This is due in part, because the produced changes on the human perception of the outputs, as a response to changes on the parameters, could be highly nonlinear, therefore models with strongly predictable outputs are needed. The present work describes a methodology for the human perceptual (or aesthetic) exploration of generative systems' parameter spaces. As the systems' outputs are intended to produce an aesthetic experience on humans, audition plays a central role in the process. The methodology starts from a set of parameter combinations which are perceptually evaluated by the user. The sampling process of such combinations depends on the system under study and possible on heuristic considerations. The evaluated set is processed by a compaction algorithm able to generate linguistic rules describing the distinct perceptions (classes) of the user evaluation. The semantic level of the extracted rules allows for interpretability, while showing great potential in describing high and low-level musical entities. As the resulting rules represent discrete points in the parameter space, further possible extensions for interpolation between points are also discussed. Finally, some practical implementations and paths for further research are presented.Peer ReviewedPostprint (author's final draft

Learning Opposites with Evolving Rules

The idea of opposition-based learning was introduced 10 years ago. Since then a noteworthy group of researchers has used some notions of oppositeness to improve existing optimization and learning algorithms. Among others, evolutionary algorithms, reinforcement agents, and neural networks have been reportedly extended into their opposition-based version to become faster and/or more accurate. However, most works still use a simple notion of opposites, namely linear (or type- I) opposition, that for each $x\in[a,b]$ assigns its opposite as $\breve{x}_I=a+b-x$. This, of course, is a very naive estimate of the actual or true (non-linear) opposite $\breve{x}_{II}$, which has been called type-II opposite in literature. In absence of any knowledge about a function $y=f(\mathbf{x})$ that we need to approximate, there seems to be no alternative to the naivety of type-I opposition if one intents to utilize oppositional concepts. But the question is if we can receive some level of accuracy increase and time savings by using the naive opposite estimate $\breve{x}_I$ according to all reports in literature, what would we be able to gain, in terms of even higher accuracies and more reduction in computational complexity, if we would generate and employ true opposites? This work introduces an approach to approximate type-II opposites using evolving fuzzy rules when we first perform opposition mining. We show with multiple examples that learning true opposites is possible when we mine the opposites from the training data to subsequently approximate $\breve{x}_{II}=f(\mathbf{x},y)$.Comment: Accepted for publication in The 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2015), August 2-5, 2015, Istanbul, Turke