Recursive robust filter for discrete-time State-space linear systems

• Grant number: 13/06521-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2013
• End date: January 31, 2014
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: Marco Henrique Terra
• Grantee: Guilherme Machado Gagliardi
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project consists of the study of robust optimum estimates for discrete-time state-space linear dynamic systems which are subject to parametric uncertainties. The development of the quadratic functional which is proposed for the deduction of these estimates is based upon the combination of the techniques of regularized least squares and penalty functions. The Kalman robust estimates and the corresponding Riccati equations are obtained in a more general formulation, as an extension of the well-known results from the literature. Recursive algorithms of the filtered and predictive estimates, along with the corresponding Riccati equations, will be reviewed. The proofs of stability and convergence of the Kalman filter for nominal and uncertain systems will be analyzed. (AU)