Stable genetic adaptive controllers for multivariable systems using a two-degree-of-freedom topology

This paper introduces an adaptive reference tracking controller based on the online genetic estimation of the parameters of the system. The main novelty of the paper relies on the fact that the stability of the genetic adaptive scheme is analytically proved and not simply validated by means of simulation as it is customary in the literature. The resulting set-up is flexible enough to be integrated within a great variety of genetic estimation algorithms, which can in many cases outperform traditional estimation procedures. The goal is achieved by using a certain two-degree-of-freedom (2-DOF) based implementation of the control law in which the reference tracking property is separated from the closed-loop stability. Within this framework, the here-presented procedure for the genetic controller synthesis just affects two time-varying pre-filter blocks that do not compromise the closed-loop stability under weak conditions. In this manner, the power and versatility of genetic algorithms can be safely used to achieve tracking performance disregarding stability, which is delegated to a static feedback controller designed on the basis of robust control theory.