A comparison of two methods for energy efficient tracking control using filtered basis functions

This paper presents and compares two methods for trading off energy efficiency and feedforward tracking accuracy using filtered basis functions. In the regular filtered basis function (FBF) approach, the control input to the system is expressed as a linear combination of basis functions. The basis functions are forward filtered using the dynamics of the system and their coefficients selected such that a performance index which penalizes tracking errors is minimized. It is shown that, in the regular FBF approach, varying the number of basis functions can be used to tradeoff energy efficiency (control energy) and tracking accuracy. Another way of achieving the same goal using FBFs is to minimize a weighted sum of tracking and control energy objectives (i.e., linear quadratic tracking) using a fixed number of basis functions. Simulation-based examples are used to compare both approaches with regard to their degree of tradeoff between tracking accuracy and energy efficiency.