Extended Kalman Filter Design for Semilinear Distributed Parameter Systems with Application to Anaerobic Digestion


  • Ivan Francisco Yupanqui Tello University of Mons
  • Daniel Coutinho Universidade Federal de Santa Catarina
  • Alain Vande Wouwer Université de Mons




State estimation, Ricatti equation, Process monitoring, Biochemical systems


This paper is concerned with the online state estimation of a class of one-dimensional semilinear partial differential equation (PDE) systems considering piecewise measurements over the spatial domain. In the context of infinite-dimensional linear systems, it is well-known that the Kalman filter minimizes the mean square estimation error. For semilinear infinite-dimensional systems, the extended Kalman filter (EKF) is a widely used extension relying on successive linearizations of the estimation error dynamics. In this paper, we propose a computationally tractable implementation of the EKF using a sample-and-hold approach for which the optimal output injection operator associated to the proposed estimator is computed at each sampling time via the approximate solution of the infinite-dimensional Riccati equation. The performance of the observer is exemplified through numerical experiments which demonstrate the efficiency of the proposed approach.


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How to Cite

“Extended Kalman Filter Design for Semilinear Distributed Parameter Systems with Application to Anaerobic Digestion”, Syst. Theor. Control Comput. J., vol. 1, no. 1, pp. 95–103, Jun. 2021, doi: 10.52846/stccj.2021.1.1.18.