J.M. Tarela

Efficient Hardware/Software Implementation of an Adaptive Neuro-Fuzzy System

This paper describes the development of efficient hardware/software (HW/SW) neuro-fuzzy systems. The model used in this work consists of an adaptive neuro-fuzzy inference system modified for efficient HW/SW implementation. The design of two different on-chip approaches are presented: a high-performance parallel architecture for offline training and a pipelined architecture suitable for online parameter adaptation. Details of important aspects concerning the design of HW/SW solutions are given. The proposed architectures have been implemented using a system-on-a-programmable-chip. The device contains an embedded-processor core and a large field programmable gate array (FPGA). The processor provides flexibility and high precision to implement the learning algorithms, while the FPGA allows the development of high-speed inference architectures for real-time embedded applications.

Digital Hardware Implementation of High Dimensional Fuzzy Systems

This paper presents an algorithm to compute high dimensional piecewise linear (PWL) functions with simplicial division of the input domain, and introduces the circuit scheme for its implementation in a FPGA. It is also investigated how to modify this algorithm and implementation to compute a class of PWL fuzzy systems.

Consequences of the digitization on the performance of a fuzzy logic controller

The consequences of the finite wordlength on the performance of a digital fuzzy logic controller (FLC) based on Mamdanis inference algorithm are investigated. Digital implementations of FLCs involve three main types of errors due to the finiteness of the wordlength: analog-to-digital errors, membership function errors, and arithmetic errors. First, a statistical evaluation of the consequences of these errors is performed. The effects of the digital resolution on the controller response are discussed. Then, the dynamic behavior of a closed-loop fuzzy system composed of a digitized FLC and a second-order plant is evaluated; a qualitative evaluation of time-domain parameters as a function of the universe discretization is carried out. The results show that, as in the case of conventional control strategies, bias effects and limit cycles are generated as a consequence of the digitization. Although these distortions diminish when the discretization is sufficiently refined, they are very difficult to predict because of the nonlinear nature of both quantization and fuzzy operation. In this sense, the availability of computer-aided design (CAD) tools that permit the specification of the wordlength is essential to validate the design.

Optimised PWL recursive approximation and its application to neuro-fuzzy systems

In this work, a piecewise-linear (PWL) function approximation is described by a lattice algebra. The maximum (@?) and minimum (@?) lattice operators have been modified to incorporate interpolation capability of generated PWL function vertexes. As a result of that, a new recursive method called centred recursive interpolation (CRI) based on such operators is proposed and analysed for successive function smoothing and more accurate approximation. The resultant computational scheme is accurate but simple, as few parameters are needed for function definition. The method is tested by applying it to the optimum approximation of some sample functions, and it turns out to be a natural quadratic approximation. Due to its advantageous characteristics and the properties that Gaussian-like function based neuro-fuzzy systems show, optimised approximation of programmable Gaussian functions has been studied in detail. A table of optimum parameters has been obtained for approximating the function through different design schemes. This constitutes a previous theoretical work for the future hardware implementation of function generators in neuro-fuzzy systems.

Issues concerning the analysis and implementation of a class of fuzzy controllers

This paper presents some important aspects concerning the analysis and implementation of a piecewise linear (PWL) fuzzy model with universal approximation capability. The main advantages of PWL models are the availability of well-established analysis methods and their suitability for simple hardware and software implementations. As an example, the development of a two-input single-output fuzzy controller is presented. Special attention is paid to the analysis of the system stability using piecewise quadratic Lyapunov functions. In addition, two implementations are addressed: one based on a Digital Signal Processor (DSP) and the other based on a Programmable Logic Device (PLD).

IMPLEMENTATION OF INTELLIGENT CONTROLLERS ON DIGITAL SIGNAL PROCESSORS

This paper introduces the use of digital signal processors DSPs to implement intelligent control ICT algorithms. We show that DSPs, which are CISC microprocessors designed for real-time processing of digital signals, are also suitable for the implementation of ICT algorithms, such as neural networks and fuzzy systems. These systems are very close to signal processing applications in many aspects. For example, both involve multiply and multiply-accumulate operations, and both require an intensive data treatment and efficient I O peripherals. A detailed description of the software implementation of a feedforward neural network and a fuzzy inference algorithm is included. The performance achieved in both implementations is provided. The main advantages of the proposed alternative are low cost, complete flexibility in the selection of algorithms, and high processing speed in comparison with a standard microprocessor or microcontroller embedded system.

Gaussian Function Approximation in Neuro-Fuzzy Systems

Using smooth membership functions and activation functions presuma- bly enhances the performance of neural, fuzzy and neuro-fuzzy systems. In this work we present some results based on the efficient generation of gaussian piece- wise-linear approximations and its application to neural/fuzzy parallel computing systems. The application of approximations to the gaussian nodes of radial basis function networks (RBFN), and the observation of the approximation capabilities of the networks after applying various learning algorithms, is revealing. We use the equivalence theorem between RBFNs and certain fuzzy inference systems for extracting conclusions applicable to de fuzzy world.

Design and Synthesis of Piecewise-Linear Fuzzy Systems

The main advantages of piecewise linear approximations are the availability of mature and precise analysis methods, and their suitability for simple hardware implementa- tions. The control surface of a large number of practical fuzzy controllers is well approxi- mated by means of PWL functions. In this work a design methodology for PWL fuzzy con- trollers is presented. As an example, the development of a two-input single-output fuzzy controller is presented and its stability in the phase plane is investigated. The closed-loop system trajectories in the phase plane are simulated and the system stability is assured by means of a globally quadratic Lyapunov function. In addition, two efficient hardware im- plementations are presented.

Quantisation Errors in Digital Implementations of Fuzzy Controllers

Fuzzy Logic Controllers (FLCs) have proven useful in the control of complex and nonlinear processes. Unlike conventional control, which is based on a precise model of a process, fuzzy control is able to handle linguistic information in the form of IF-THEN rules. These rules usually encapsulate the experience of human operators and engineers. At present, most FLCs are implemented digitally. Microprocessors, digital signal processors (DSPs), and application specific integrated circuits (ASICs) are used to cope with real time fuzzy control. Therefore, the quantisation noise due to the finite length of digital words is to be taken into account in designing fuzzy systems. Digital implementations of FLCs involve three main types of quantisation errors: the analogue-to-digital (A/D) errors, the membership function errors, and the arithmetic errors. The consequences of these errors on the behaviour of a typical FLC are analysed and the problem of the selection of a digital format for fuzzy information is addressed.

Automatic implementation of different inference architectures for fuzzy control on PLDs

Abstract In this paper a software design tool for implementing Fuzzy Logic Controllers (FLCs) on Programmable Logic Devices (PLDs) is presented. The designer is able to choose between three different inference architectures which implement the max-min inference method, and to configure the implementation by defining a digital format for fuzzy information. Available architectures introduce different degrees of parallelism in the processing of rules and membership values. The developed software generates a representation of the selected architecture in a hardware description language which is accepted by a PLD development system. Our software, together with the PLD development system, constitute a very powerful environment for the implementation of fuzzy controllers on PLDs. The main characteristics of the proposed solution are low development costs, much shorter design time than other ASIC solutions, and the possibility of reprogramming the devices. A comparative performance analysis of different implementation examples is given.