Neural - fuzzy approach for system identification

Most real-world processes have nonlinear and complex dynamics. Conventional methods of constructing nonlinear models from first principles are time consuming and require a level of knowledge about the internal functioning of the system that is often not available. Consequently, in such cases a nonlinear system identification procedure from observational data is a more attractive alternative. If the model structures to be investigated are purely chosen from a set of mathematically convenient structures, without incorporation of knowledge about the internal functioning, this is called black-box modeling. In case that some qualitative a priori information can be used in the above modeling procedure, it is sometimes referred to as gray-box modeling.Artificial neural network models and fuzzy models are typical examples of black-box and gray-box modeling, respectively. They have the same property of parallel processing and both serve as universal function approximators to perform nonlinear mapping. Each of them has its own weak and strong points. The fuzzy model has a transparent knowledge representation but has restricted learning ability. A neural network model can easily learn from new data, but it is difficult to interpret the information contained in its internal configuration.This thesis investigates how to construct an integrated neural-fuzzy model that can perform approximation of an unknown system via a set of given input-output observations. The result is the integrated neural-fuzzy model NUFZY, which combines the advantages of the above two paradigms, and concurrently compensates for their weaknesses. Thus, it has a transparent network structure and a self-explanatory representation of fuzzy rules.The NUFZY system is a special type of neural network, which is characterized by partial connections in its first and second layers. Through its network connections the NUFZY system carries out a particular type of fuzzy reasoning. Also, the NUFZY system is functionally equivalent to a zero th -order Takagi-Sugeno fuzzy model, so that it is an universal function approximator as well.Two existing learning methods, i.e., the orthogonal least squares and the prediction error algorithms, can be applied directly to the developed NUFZY model. The former method, referred to as batch learning, can be used to detect redundant fuzzy rules from the prototype rule base and to find the weight parameters of the NUFZY model by one-pass estimation. The latter, referred to as recursive learning, allows a fast adaptation of parameters of the NUFZY model. Several practical examples with real data of agricultural problems, which address the tomatoes growth and the greenhouse temperature, have been presented in this thesis, showing the capability of the NUFZY system for modeling nonlinear dynamic systems.Two questions concerning the integrated neural-fuzzy model are addressed by studying the equivalent T-S fuzzy model: how to obtain a linguistic interpretation of fuzzy rules deduced by learning from training examples, and how to incorporate a priori knowledge into the T-S fuzzy model.It is found out that it is possible to have linguistic interpretations of the crisp consequent of the T-S fuzzy rules by transforming them into Mamdani - like fuzzy rules. A new parameter set, the consequent significance level, is associated to the consequent of each Mamdani fuzzy rule to form an extended Mamdani fuzzy model. This model has a more flexible modeling ability than the ordinary Mamdani fuzzy model and has a comparable model accuracy as that of the T-S fuzzy model.Regarding the second question, an optimization approach is employed to systematically incorporate the a priori knowledge into the T-S fuzzy model. If the knowledge about the system behavior outside the identification data range is expressed in the form of a qualitative Mamdani fuzzy model, then this model can be incorporated in the objective function of the parameter estimation problem as an additional penalty term. Thus, the estimation of the parameters of the T-S fuzzy model from the identification data is constrained by the involvement of a priori knowledge. As a consequence, the resultant fuzzy model becomes more robust in the extrapolation domain. This approach can be extended to neural -fuzzy modeling without difficulty.To conclude, the beauty of the integrated neural-fuzzy model, NUFZY, developed in this thesis is that it is a neural network, enabling the implementation of efficient learning algorithms in an easy way, and that it is a fuzzy model at the same time, allowing incorporation of priori knowledge and transparent interpretation of its internal network structure. So, among the various methods of nonlinear system identification, the NUFZY model can serve as an attractive alternative.See alsohttp://www.math.utwente.nl/disc/dissertations/tien.html</A

Neuro-fuzzy modelling and control of robotic manipulators

The work reported in this thesis aims to design and develop a new neuro-fuzzy control system for robotic manipulators using Machine Learning Techniques, Fuzzy Logic Controllers, and Fuzzy Neural Networks. The main idea is to integrate these intelligent techniques to develop an adaptive position controller for robotic manipulators. This will finally lead to utilising one or two coordinated manipulators to perform upper-limb rehabilitation. The main target is to benefit from these intelligent techniques in a systematic way that leads to an efficient control and coordination system. The suggested control system possesses self-learning features so that it can maintain acceptable performance in the presence of uncertain loads. Simulation and modelling stages were performed using dynamical virtual reality programs to demonstrate the ideas of the control and coordination techniques. The first part of the thesis focuses on the development of neuro-fuzzy models that meet the above requirement of mimicking both kinematics and dynamics behaviour of the manipulator. For this purpose, an initial stage for data collection from the motion of the manipulator along random trajectories was performed. These data were then compacted with the help of inductive learning techniques into two sets of if-then rules that form approximation for both of the inverse kinematics and inverse dynamics of the manipulator. These rules were then used in fuzzy neural networks with differentiation characteristics to achieve online tuning of the network adjustable parameters. The second part of the thesis introduces the proposed adaptive neuro-fuzzy joint-based controller. To achieve this target, a feedback Fuzzy-Proportional-Integral-Derivative incremental controller was developed. This controller was then applied as a joint servo-controller for each robot link in addition to the main neuro-fuzzy feedforward controller used to compensate for the dynamics interactions between robot links. A feedback error learning scheme was applied to tune the feedforward neuro-fuzzy controller online using the error back-propagation algorithm. The third part of the thesis presents a neuro-fuzzy Cartesian internal model control system for robotic manipulators. The neuro-fuzzy inverse kinematics model of the manipulator was used in addition to the joint-based controller proposed and the forward mathematical model of the manipulator in an adaptive internal model controller structure. Feedback-error learning scheme was extended to tune both of the joint-based neuro-fuzzy controller and the neuro-fuzzy internal model controller online. The fourth part of the thesis suggests a simple fuzzy hysteresis coordination scheme for two position-controlled robot manipulators. The coordination scheme is based on maintaining certain kinematic relationships between the two manipulators using reference motion synchronisation without explicitly involving the hybrid position/force control or modifying the existing controller structure for either of the manipulators. The key to the success of the new method is to ensure that each manipulator is capable of tracking its own desired trajectory using its own position controller, while synchronizing its motion with the other manipulator motion so that the differential position error between the two manipulators is reduced to zero or kept within acceptable limits. A simplified test-bench emulating upper-limb rehabilitation was used to test the proposed coordination technique experimentally

Neurofuzzy Approximator based on Mamdani's Model

Neurofuzzy approximators can take on numerous alternatives, as a consequence of the large body of options available for defining their basic operations. In particular, the extraction of the rules from numerical data can be conveniently based on clustering algorithms. The large number of clustering algorithms introduces a further flexibility. Neurofuzzy approximators can treat both numerical and linguistic sources. The analysis of approximator sensitivity to the previous factors is important in order to decide the best solution in actual applications. This task is carried out in the present paper by recurring to illustrative examples and exhaustive simulations. The results of the analysis are used for comparing different learning algorithms. The underlying approach to the determination of the optimal approximator architecture is constructive. This approach is not only very efficient, as suggested by learning theory, but it is also particularly suited to combat the effect of noise that can deteriorate the numerical data