Robust Kalman Filtering for Systems Subject to Polytopic Uncertainties

Author(s)

Rocha, Kaio D. T. ; Bueno, Jose Nuno A. D. ; Marcos, Lucas B. ; Terra, Marco H. ; IEEE

• Document type: Journal article
• Source: 2022 30TH MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION (MED); v. N/A, p. 6-pg., 2022-01-01.

Abstract

Measuring the entire state vector of a dynamic system in practical applications is often infeasible due to various factors. State estimation is usually adopted to overcome this issue. However, the system model inevitably undergoes the degrading effects of parametric uncertainties. Hence, it is crucial to estimate the state irrespective of such unknown parameter variations. In this paper, we address the robust filtering problem regarding linear discrete-time systems subject to polytopic uncertainties. We formulate a min-max optimization problem whose cost function weights the polytope vertices altogether. The solution yields a robust recursive filter as a Kalman-like correction-prediction algorithm, suitable for real-time applications. We further provide stability conditions for the steady-state filter. Furthermore, we validate our approach with a numerical example, comparing the results with other methods from the literature on robust filtering. (AU)

• FAPESP's process: 14/50851-0 - INCT 2014: National Institute of Science and Technology for Cooperative Autonomous Systems Applied in Security and Environment
• Grantee: Marco Henrique Terra
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 21/08103-0 - Cooperative autonomous control of heterogeneous vehicle systems
• Grantee: Lucas Barbosa Marcos
• Support Opportunities: Scholarships in Brazil - Technical Training Program - Technical Training
• FAPESP's process: 17/16346-4 - Communication network fault tolerant control for coordinated movement of heterogeneous robots
• Grantee: Kaio Douglas Teófilo Rocha
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)