Employing Interpolation to Enable Higher Order Fuzzy Logic Controllers on Resource Constrained Embedded Devices Christian Wagner The Computational Intelligence Centre Department of Computing and Electronic Systems University of Essex Wivenhoe Park, Colchester, CO4 3SQ United Kingdom chwagn @ essex.ac.uk Hani Hagras The Computational Intelligence Centre Department of Computing and Electronic Systems University of Essex Wivenhoe Park, Colchester, CO4 3SQ United Kingdom hani @ essex.ac.uk Abstract It has been shown recently that higher order Fuzzy Logic Controllers (FLCs) such as type- 2 FLCs have the potential to outperform type- 1 FLCs. However, the high computational cost associated with such higher order FLCs is still impeding their widespread use in real world applications where the computational and memory resources are limited. In this paper we will present a simple framework that allows to tie together the advantages of using higher order FLCs while keeping computational costs at a minimum. The proposed technique is based on the offline computation of high-quality control surfaces which are sparsely sampled and reproduced through interpolation on the actual embedded device. The proposed technique will be described in detail and we will present some example applications and results achieved using the proposed system. 1 Introduction The last 30 years have witnessed the wide deployment of Fuzzy Logic Controllers (FLCs) in a vast number of real world applications. The motivation for this is that the FLC is credited with being an adequate methodology for designing robust systems that are able to deliver good performance in the face of uncertainty and imprecision ubiquitous in real world applications. In addition, FLCs facilitate the construction of control algorithms in a user- friendly way closer to human thinking and perception. The vast majority of fuzzy systems research and applications employ type-1 FLCs. However, type-1 FLCs cannot fully handle or accommodate the high levels of linguistic and numerical uncertainties associated with dynamic real world applications and environments as type-1 FLCs use the crisp and precise type-1 fuzzy sets. However, advances in technology and fuzzy logic theory have made it possible to research and apply more complex, i.e. higher order forms of fuzzy logic such as type-2 fuzzy logic. It has been shown that interval type-2 fuzzy systems can provide superior performance when compared to type-1 fuzzy systems with the same amount of rules as a result of the additional degrees of freedom provided by only the footprint of uncertainty [1], [2]. A major drawback of such higher order FLCs has nevertheless been the significant increase of computational complexity which has considerably narrowed the possibility for real world application of such controllers. Recently, a series of advances such as [3],[4], [5], [6] have been made in trying to reduce the computational complexity associated with the currently most complex used form of FLCs – general type-2 FLCs, in order to facilitate and enable their practical usage. In [4] a novel form of representing general type-2 fuzzy sets using geometric concepts such as polygons and poly-lines was presented. In [5], [6] new forms of representation were suggested based on the concepts of zSlices and α-cuts. Both representations aim towards devising new representations which enable the implementation of general type-2 FLCs while relying on the existing theory of interval type-2 FLCs. As such, the complexity of general type-2 fuzzy logic should become manageable and its application will be greatly facilitated. The work presented in this paper aims to enable the utilization of the benefits provided by higher order FLCs while minimizing the computational requirements. In particular we are trying to enable the application of higher order FLCs on the small, resource-constrained embedded systems present in the vast majority of real world applications. This will enable such real world applications to benefit from the various advantages and control performance