Introduction

Especially because the circuitry of the cerebellum is strikingly uniform and has been relatively well characterized anatomically and physiologically, many investigators have been prompted to devise theories to explain its function. Over the centuries, many conceptions of cerebellar function have been put forward, and it still cannot be said that a consensus view has been achieved. However, despite their seeming diversity, theories of cerebellar function have converged significantly. Useful summaries and reviews of the more historical ideas can be found in several places (Llinas, 1981; Pellionisz, 1985; Thach et al., 1992). In order to afford better quantitative analysis and to take advantage of our growing computer simulation capabilities, models of cerebellar function have been formulated increasingly in mathematical terms. This chapter focuses on these models and attempts to introduce them from a qualitative engineering perspective, with a bare mimimum of mathematical detail. Specifically, it reviews the basic character of cerebellar function, describing it as an adaptive modulator or ‘controller’ of movement, rather than as a principal driver of movement. It then describes the types of signal processing that are thought to occur in the cerebellum and the essential features of the neuronal architecture that would implement these proposed types of computation. The central theoretical principles of controller design that are used to understand and evaluate cerebellar models are then outlined. Specifically, feedforward, feedback, internal model-based, and discontinuous control strategies are discussed. Finally, several specific mathematical models have been selected to highlight important concepts in the evolution of the quantitative thinking about the cerebellum.