Convergence of fractional adaptive systems using gradient approach

Javier A Gallegos; Manuel A Duarte-Mermoud

doi:10.1016/j.isatra.2017.04.021

Convergence of fractional adaptive systems using gradient approach

ISA Trans. 2017 Jul:69:31-42. doi: 10.1016/j.isatra.2017.04.021. Epub 2017 May 5.

Authors

Javier A Gallegos¹, Manuel A Duarte-Mermoud²

Affiliations

¹ Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago, Chile; Advanced Mining Technology Center, University of Chile, Av. Tupper 2007, Santiago, Chile. Electronic address: jgallego@ing.uchile.cl.
² Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago, Chile; Advanced Mining Technology Center, University of Chile, Av. Tupper 2007, Santiago, Chile. Electronic address: mduartem@ing.uchile.cl.

PMID: 28483272
DOI: 10.1016/j.isatra.2017.04.021

Abstract

Conditions for boundedness and convergence of the output error and the parameter error for various Caputo's fractional order adaptive schemes based on the steepest descent method are derived in this paper. To this aim, the concept of sufficiently exciting signals is introduced, characterized and related to the concept of persistently exciting signals used in the integer order case. An application is designed in adaptive indirect control of integer order systems using fractional equations to adjust parameters. This application is illustrated for a pole placement adaptive problem. Advantages of using fractional adjustment in control adaptive schemes are experimentally obtained.

Keywords: Adaptive systems; Fractional systems; Gradient method.