Theoretical Results for describing Expert Systems in the Supervision of the Adaptation Transients of a Planar Robot M. de la Sen *† , J.J. Miñambres * , Aitor J. Garrido *‡ , A. Almansa ** and J.C. Soto *** * Instituto de Investigación y Desarrollo de Procesos (IIDP). Dpto. de Ingeniería de Sistemas y Automática. Facultad de Ciencias, Universidad del País Vasco, Leioa (Bizkaia), Apdo. 644 de Bilbao, 48080. SPAIN. http://www.ehu.es/IIDP. ** Dept. Materials and Production Engineering. Bereich Werkstoffe und Produktionstechnik. ARC Seibersdorf Research GmbH. A-2444 Seibersdorf. AUSTRIA. *** Dpto. de Matemática Aplicada. E.U. de Ingeniería Técnica Industrial. Universidad del País Vasco, Bilbao (Bizkaia), Pza. de la Casilla, 3, 48012. SPAIN. Abstract. The objective of expert systems is the use of Artificial Intelligence tools so as to solve problems within specific prefixed applications. This paper deals with the development of an expert system valid to optimize the adaptation transients arising in adaptive control using a logic formalism previously described. Its structure is composed by a supervisor based on an expert network organization and designed to improve the transient performances in the adaptive control of a planar robot. Apart form the basic adaptation scheme consisting of an estimation algorithm plus an adaptive controller, two additional coordinated expert systems are used to update an adaptation gain and the sampling period with a master expert system coordinating both above expert systems. Keywords. AI and expert systems, Supervisory control, Neural-adaptive control systems, Intelligent mechatronics, Knowledge based systems, Intelligent automation, Adaptive Sampling. † wepdepam@lg.ehu.es . http://www.ehu.es/IIDP/delasen.htm. ‡ ispgahea@lg.ehu.es (corresponding author). 1. Introduction The term expert system was originally used to denote systems using a significant amount of expert information about a particular domain in order to solve problems within that domain (SASS, 1984, Buchanan and Shortliffe, 1984, Scarl et al., 1984, Gorgeoff, 1983). Due to the important role of knowledge in such systems, they have also been called knowledge-based systems (see Gorgeoff, 1983, Gorgeoff and Firschein, 1985). However, since the terminology has been applied to so many diverse systems, it has essentially evolved into two uses of the term that need to be differentiated. First, the term is often used to describe any system constructed with special kinds of “expert-systems” programming languages and tools; these include production systems, rule-based systems, frame-based systems, “blackboard” architectures, and various languages like Lisp or Prolog. The other important feature is that, since they are usually non-deterministic, a large number of modules may be “applicable” (candidates for activation) at any given moment. Thus, it is necessary a criterion to determine how to select which of the applicable modules must be executed next, and what to do after selection. This second is the more appropriate job of an expert system in the sense that it is a system that “reasons” about a problem in much the same way humans do. Expert systems are of great interest in complex specific applications like, for instance, production systems and Space Station Automation systems (Gorgeoff and Firschein, 1985, Scarl et al., 1984, Gorgeoff, 1983). Also, these tools are very useful in real-time problems, in which monitoring is essentially dependent on preceding experience over similar examples and/or on the previous system performance in its current task (see, for instance, Hagras et al., 1999, Stonier and Mohammadian, 1996, Raju and J. Zhou, 1993, Raju et al., 1991 and De la Sen and Miñambres, 1987). Although a great experimental effort together with some theoretical issues have been employed in the last years to investigate the completeness and consistency of rule-based systems, and to partition of systems by assemblies (see SASS, 1984, Buchanan and Shortliffe, 1984, Scarl et al., 1984, De la Sen and Miñambres, 1987, Soto et al., 1988, Jackson, 1999 and Veloso and Wooldridge, 1999), there is often a gap in the formalism which allows structuring of expert-system programming towards expert system design. A first attempt to deal with this problem from a formal-logic point of view was described by De la Sen, 1987. In this paper, that formalism is first generalized and then applied to the improvement of the adaptation transients by using knowledge-based tools so as to adaptively update the tracking error of model reference adaptive control systems. The method is applied for supervising the adaptation transients in a planar robot. The two mechanisms involved in the supervision are the use of time-varying sampling periods obtained from adaptive sampling laws and the on-line adjustment of one of the free-design parameters of the