Elsevier

Applied Soft Computing

Volume 7, Issue 3, June 2007, Pages 728-738
Applied Soft Computing

Modeling and control of non-linear systems using soft computing techniques

https://doi.org/10.1016/j.asoc.2005.12.005Get rights and content

Abstract

This work is an attempt to illustrate the utility and effectiveness of soft computing approaches in handling the modeling and control of complex systems. Soft computing research is concerned with the integration of artificial intelligent tools (neural networks, fuzzy technology, evolutionary algorithms, …) in a complementary hybrid framework for solving real world problems. There are several approaches to integrate neural networks and fuzzy logic to form a neuro-fuzzy system. The present work will concentrate on the pioneering neuro-fuzzy system, Adaptive Neuro-Fuzzy Inference System (ANFIS). ANFIS is first used to model non-linear knee-joint dynamics from recorded clinical data. The established model is then used to predict the behavior of the underlying system and for the design and evaluation of various intelligent control strategies.

Introduction

The current trend in intelligent systems or soft computing research is concerned with the integration of artificial intelligent tools (neural networks, fuzzy technology, evolutionary algorithms, …) in a complementary hybrid framework for solving complex problems.

Fuzzy logic offers the important concept of fuzzy set theory, fuzzy if-then rules and approximate reasoning which deals with imprecision and information granularity. Neural networks have on their side the capability for learning and adaptation by adjusting the interconnections between layers, while genetic algorithms make use of a systemized random search and are important for optimization.

Neuro-fuzzy techniques have emerged from the fusion of Artificial Neural Networks (ANN) and Fuzzy Inference Systems (FIS) and form a popular framework for solving real world problems. A neuro-fuzzy system is based on a fuzzy system which is trained by a learning algorithm derived from neural network theory. While the learning capability is an advantage from the viewpoint of FIS, the formation of linguistic rule base will be advantageous from the viewpoint of ANN. There are several approaches to integrate ANN and FIS and very often the choice depends on the application [1], [2].

The growing interest in the field is demonstrated by the ever-increasing applications in various areas extending from image and pattern recognition to identification and control applications.

Intelligent control emerged as a viable alternative to conventional model-based control schemes. This is because with fuzzy logic and neural networks issues such as uncertainty or unknown variations in plant parameters and structure can be dealt with more effectively and hence improving the robustness of the control system.

The present work will concentrate on the pioneering neuro-fuzzy system, Adaptive Neuro-Fuzzy Inference System (ANFIS) [3], which is presently available in MatLab®. ANFIS belongs to the class of rules extracting systems using a decompositional strategy, where rules are extracted at the level of individual nodes within the neural network and then aggregating these rules to form global behavior descriptions. The objective of this research work is to explore a number of control strategies for Functional Electrical Stimulation (FES) induced gait.

FES is a rehabilitative technology that can restore muscle activity to people who have suffered spinal cord injury and become paralyzed. The technique consists of applying a variable pulsewidth input signal in order to alter the level of contraction of the quadriceps muscle group to perform the motion of the shank. The output signal of the system is the angle between the thigh and shank.

High performance FES control system design relies heavily on the availability of a precise knee-joint model. ANFIS like systems have proven to be able to deliver very accurate models and are therefore suitable candidates for such applications [4].

The non-linear, time-variant behavior of the knee-joint dynamics under FES has led us to investigate various control strategies based on neural networks and adaptive neuro-fuzzy approaches.

It has been shown that with the aid of ANFIS, it is possible to create a Fuzzy Inference System that emulates the behavior of the neuromuscular system on the basis of available recorded real-time data.

For controller design and performance evaluation purposes this ANFIS based knee-joint model will be is used in the simulation study.

Section snippets

Neuro-fuzzy modeling approach

Conventional approaches to system modeling rely heavily on mathematical tools which emphasizes a precise description of the physical quantities involved. By contrast, modeling approaches based on neural networks and fuzzy logic are becoming a viable alternative where the former conventional techniques fail to achieve satisfactory results.

Neuro-fuzzy modeling is concerned with the extraction of models from numerical data representing the behavioral dynamics of a system.

This modeling approach has

Neural networks based control

Neural networks (NN) represent an important paradigm for classifying patterns or approximating complex non-linear process dynamics. These properties clearly indicate that NN exhibit some intelligent behavior, and are good candidate models for non-linear processes, for which no perfect mathematical model is available.

Neural networks have been applied very successfully in the identification and control of dynamic systems. The universal approximation capabilities of the Multi-Layer Perceptron

ANFIS based control

Due to the adaptive capability of ANFIS, its application to adaptive and learning control is immediate. The most common design techniques for ANFIS controllers are derived directly from neural networks counterpart's methodologies. However, certain design techniques are exclusively dedicated to ANFIS [11].

Overview of the controllers performance and robustness

The control methods presented in this paper are grouped in two parts. The first part deals with NN based controllers while the second part addresses some typical ANFIS based control structures.

NN control has focused on direct inverse control, adaptive direct inverse control, direct inverse with specialized learning control and IMC. Since these control strategies all require a well-trained inverse and/or forward, inaccuracies may result in the implementation stage unless an integral action is

Conclusions

Intelligent control is a promising field in modern control technology typically dedicated to highly complex and uncertain systems.

FES is one type of such complex systems and hence may be considered as a challenging system for evaluating the soft computing based control techniques proposed in this work. The aim of the controllers is to adjust the stimulating electrical current to control the knee-joint swing angle.

Neural network-based control has been successfully applied and the potential

Acknowledgment

The author is grateful to the Deutscher Akademischer Austauschdienst (DAAD) for the financial support of this research work.

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