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Fuzzy logic in control: truck backer-upper problem revisited

The truck backer-upper problem, considered an acknowledged benchmark in nonlinear system identification, is an excellent test-bed for fuzzy control systems. A fuzzy controller, formulated on the basis of human understanding of the process or identified from measured control actions, can be regarded as an emulator of human operator. Controller design, however, may become difficult, especially if the number of state variables is large. In the paper, a supervisory control system is proposed that reduces the complexity of the control problem and enhances control. This is demonstrated with backing simulations in comparison with other fuzzy control techniques.

Transparent Fuzzy Systems in Modelling and Control

This chapter deals with low-level transparency of fuzzy systems that is necessary to ensure reliable interpretation of linguistic information provided by fuzzy systems. It is shown that for different types of fuzzy systems different definitions of transparency apply. Particular attention is paid to transparency protection mechanisms for data-driven optimisation algorithms such as gradient descent and genetic algorithms that otherwise would destroy the semantics of fuzzy systems in the course of optimisation. The need for transparency in fuzzy control is discussed and further illustrated by a control application of truck backer-upper.

Identification of transparent, compact, accurate and reliable linguistic fuzzy models

Transparency, accuracy, compactness and reliability all appear to be vital (even though somewhat contradictory) requirements when it comes down to linguistic fuzzy modeling. This paper presents a methodology for simultaneous optimization of these criteria by chaining previously published various algorithms - a heuristic fully automated identification algorithm that is able to extract sufficiently accurate, yet reliable and transparent models from data and two algorithms for subsequent simplification of the model that are able to reduce the number of output parameters as well as the number of fuzzy rules with only a marginal negative effect to the accuracy of the model.

Interpretability of Fuzzy Systems and Its Application to Process Control

The paper reviews the concept of fuzzy system interpretability and concludes that known interpretability constraints work mostly for the internal consistency of the system, thus are insufficient that we could really benefit from interpretability in practice. In particular, reliability of system rules is an often overlooked property. The latter is a phenomenon of external consistency and thus is largely a responsibility of the optimization algorithm that is used to finalize the system. The modeling algorithm that is suggested in current paper has special regard for model reliability. We then proceed with a methodology for extracting a process controller from the identified process model. Controller design is guided by a automatic linguistic inversion technique. The approach is successfully tested on a fed-batch fermentation benchmark.

Adaptability, interpretability and rule weights in fuzzy rule-based systems

This paper discusses interpretability in two main categories of fuzzy systems - fuzzy rule-based classifiers and interpolative fuzzy systems. Our goal is to show that the aspect of high level interpretability is more relevant to fuzzy classifiers, whereas fuzzy systems employed in modeling and control benefit more from low-level interpretability. We also discuss the interpretability-accuracy tradeoff and observe why various rule weighting schemes that have been brought into play to increase adaptability of fuzzy systems rather just increase computational overhead and seriously compromise interpretability of fuzzy systems.

Car navigation and collision avoidance system with fuzzy logic

A navigation control and collision avoidance system for delivering a car to the arbitrarily positioned loading dock is designed, based on the fuzzy trajectory mapping unit (TMU). Simulated driving experiments in different environmental conditions demonstrate that the designed system shows good performance. Modular structure of the control system facilitates both efficient control knowledge acquisition (which is encapsulated in TMU) as well as further development of the control system to accomplish more demanding tasks.

Interpretability improvement of fuzzy systems: Reducing the number of unique singletons in zeroth order Takagi-Sugeno systems

This paper addresses one specific aspect of complexity reduction/interpretability improvement in fuzzy systems — how to limit the number of unique singletons in 0-th order Takagi-Sugeno (TS) systems, where the common practice is to assign an unique singleton to each rule. While abundance of free parameters makes 0-th order TS systems effective in data-driven identification, it also presents a computational load and an obstacle for interpretability and reliability of fuzzy rules. The developed reduction algorithm that utilizes singleton mapping matrix, subtractive clustering and least squares estimation algorithms, is able to bring the number of unique singletons down to the desired level without substantial accuracy loss.

An integrated approach for the identification of compact, interpretable and accurate fuzzy rule-based classifiers from data

This paper presents three very simple and computationally undemanding symbiotic algorithms for the identification of compact fuzzy rule-based classifiers from data. The problem of interpretability is specifically addressed, resulting in a conclusion that due to the characteristics of classification tasks a major well-known interpretability condition — distinguishability — can be discarded. It is shown that despite the interpretability-accuracy tradeoff, accuracy of identified classifiers stands out to comparison. All obtained properties can be very useful in practical problems. The proposed method is validated on Iris, Wine and Wisconsin Breast Cancer data sets.

Interpretability, interpolation and rule weights in linguistic fuzzy modeling

Linguistic fuzzy modeling that is usually implemented using Mamdani type of fuzzy systems suffers from the lack of accuracy and high computational costs. The paper shows that product-sum inference is an immediate remedy to both problems and that in this case it is sufficient to consider symmetrical output membership functions. For the identification of the latter, a numerically efficient method is suggested and arising interpretational aspects are discussed. Additionally, it is shown that various rule weighting schemes brought into the game to improve accuracy in linguistic modeling only increase computational overhead and can be reduced to the proposed model configuration with no loss of information.

Fuzzy Knowledge-Based Control for Backing Multi-Trailer Systems

This paper embraces the problem of controlling backward movements of multi-trailer systems (in present case trucks with three and four trailers) by the means of fuzzy logic. It is shown that decomposition of the problem is a great help when finding the solution, however, as the number of trailers increases, it becomes increasingly complex to find a satisfying solution as the control object itself becomes less and less controllable.