Reduction of a Wave-Variable biological Arm Control Model

This paper describes a systematic approach to reducing the order of a recently proposed biological arm control model. The single-joint Wave Variable Intermediate Cerebellar Arm Control Model (WVI-CACM), developed by Massaquoi [9, 10] on the basis of previous work by Neimeyer and Slotine [13], proposes that the cerebellum enables stable linear servo control of simple arm movements in the presence of neural signal transmission delays via a transformation of variables. A reduction strategy based on balanced truncation was applied to the WVICACM, which generated reduced order models as a function of the WVICACM parameters. While being analytically much simpler than the WVICACM, these approximate models retain a very large portion of its stability and performance characteristics over a wide range of parameter values, including those which render the WVICACM unstable. The strategy employed here may be generally useful for retaining the excellent model matching capabilities of the balanced truncation method in situations where the original system is potentially not stable.