Genetic algorithms in norm-optimal linear and non-linear iterative learning control

Abstract

In this paper it is analysed whether or not it is possible to apply the norm-optimal iterative learning control algorithm to non-linear plant models. As a new theoretical result it is shown that if the non-linear plant meets a certain technical invertibility condition, the sequence of tracking errors generated by the norm-optimal algorithm will converge geometrically to zero. However, due to the non-linear nature of the plant, it is typically impossible to calculate analytically the sequence of input functions produced by the norm-optimal algorithm. Therefore it is proposed that genetic algorithms can be used as a computational tool to calculate the sequence of norm-optimal inputs. The proposed approach benefits from the design of a low-pass FIR filter. This filter successfully removes unwanted high frequency components of the input signal, which are generated by the genetic algorithm method due to the random nature of the genetic algorithm search. Simulations are used to illustrate the performance of this new approach, and they demonstrate good results in terms of convergence speed and tracking of the reference signal regardless of the nature of the plant.

Acknowledgement

J. Hätönen is supported by the EPSRC contract No GR/R74239/01.