Variable Structure Systems Theory Based Training Strategies for Computationally Intelligent Systems Mehmet Önder Efe Okyay Kaynak Carnegie Mellon University Bogazici University Electrical and Computer Engineering Department Electrical and Electronic Engineering Department Pittsburgh, PA 15213-3890 Bebek, 80815, Istanbul U.S.A. TURKEY efemond@andrew.cmu.edu kaynak@boun.edu.tr Abstract − Variable Structure Systems (VSS) Theory, which is particularly well developed for tracking control of uncertain nonlinear systems, has inspired the scientists in developing solutions to ill-posed problems like the design of training criteria under a set of conditions and performance metrics. The underlying idea has been to exploit the invariance properties introduced by the theory together with the parametric flexibility of the architectures of computational intelligence. Since the traditional approaches utilizing the gradient information are oversensitive against disturbances, the robustification becomes an inevitable need, and as a powerful tool for handling the nonlinearity, time-delays, saturations and similar system specific difficulties, VSS theory becomes a good candidate for safely expanding the search space. The tutorial focuses on the architectures of common use, and postulates several tuning laws based on the VSS theory. I. INTRODUCTION Twentieth century has witnessed widespread innovations in all disciplines of engineering sciences. Two snapshots from early 1900s and late 1990s differ particularly in terms of the active role of humans in performing complicated tasks. The trend during the last century had the goal of implementing systems having some degrees of intelligence to cope with the problem specific difficulties that are likely to arise during the normal operation of the system. Today, it is apparent that the trend towards the development of autonomous machinery will maintain its importance as the tasks and the systems are getting more and more complicated. A natural consequence of the increase in the complexity of the task and physical hardware is to observe an ever-widening gap between the mathematical models and the physical reality to which the models correspond. Having this picture in front of us, what now becomes evident is the need for research towards the development of approaches having the capability of self-organization under the changing conditions of the task and the environment. Computational Intelligence (CI) is a framework offering various solutions to handle the complexity and the difficulties of information-limited operating environments. The diversity in the solution space is a remarkable advantage that the designer utilizes either in the sense of algorithm-oriented manner or in the sense of architecture-oriented manner, hence, the result is an autonomous system exploiting these advantages. Autonomy is one of the most important characteristics required from a computationally intelligent system. A basic requirement in this context is the ability to refresh and to refine the information content of the dynamics of the system. It therefore requires a careful consideration in the realm of engineering practice. From a systems and control engineering point of view, the designer is motivated by the time-varying nature of structural and environmental conditions to realize controllers that can accumulate the experience and improve the mapping precision [1-2]. Methodologies imitating the inference mechanism of the human brain are good in achieving the former and those imitating the massively interconnected structure of the human brain are good in achieving the latter. In the literature, the linguistic aspects of intelligence are discussed in the area Fuzzy Logic (FL) while the connectionist aspects are scrutinized in the area Neural Networks (NN). The integration of these methodologies that exploit the strength of each collectively and synergistically is a driving force to synthesize hybrid intelligent systems. Being not limited to what is mentioned, methods mimicking the process of evolution, which are discussed under the title Genetic Algorithms (GA), and those adapted from artificial intelligence constitute other branches of CI and fall beyond the focus of the approaches presented in this chapter. NN are well known with their property of representing complex nonlinear mappings. Earlier works on the mapping properties of these architectures have shown that NN are universal approximators [3-5]. The mathematical power of intelligence is commonly attributed to the neural systems because of their structurally complex interconnections and fault tolerant nature. Various architectures of neural systems are studied in the literature. Feedforward and Recurrent Neural Networks (FNN, RNN) [6], Radial Basis Function Neural Networks (RBFNN) [1,6], dynamic neural networks [7], and Runge-Kutta neural networks [8] constitute typical topologically different models. FL is the most popular constituent of the CI area since fuzzy systems are able to represent human expertise in the form of IF antecedent THEN consequent statements. In this domain, the system behavior is modeled through the use of linguistic descriptions. Although the earliest work by Prof. Zadeh on fuzzy systems [9] has not been paid as much attention as it deserved in the early 1960s, since then the methodology has become a well- developed framework. The typical architectures of Fuzzy Inference Systems (FIS) are those introduced by Wang [10], Takagi and Sugeno [11] and Jang, Sun and Mizutani [1]. In [10], a fuzzy system having Gaussian membership functions, product inference rule and weighted average defuzzifier is constructed and has become the standard method in most applications. Takagi and Sugeno change the defuzzification procedure where dynamic systems are used in the defuzzification stage. The potential advantage of the method is that under certain constraints, the stability of the system can be studied. Jang et al [1] propose an adaptive neuro-fuzzy inference system, in which polynomials are used in the defuzzifier. This structure is commonly referred to as ANFIS in the related literature. When the applications of NN and FL are considered the process of learning gains a vital importance. Although there is IECON'01: The 27th Annual Conference of the IEEE Industrial Electronics Society 0-7803-7108-9/01/$10.00 (C)2001 IEEE 1563