Error Covariance Bounds for Suboptimal Filters with Lipschitzean Drift and Random Sampling

Abstract

We propose suboptimal filters for a class of continuous-time nonlinear stochastic systems when the measurements are assumed to arrive randomly at discrete times under a Poisson distribution. The proposed filter is a dynamical system with a differential equation and a reset map which updates the estimate whenever a new measurement is received. We analyze the performance of the proposed filter by computing the expected value of the error covariance which is described by a differential equation. We study throughly the conditions under which the error covariance remains bounded, which depend on the system data and the mean sampling rate associated with the measurement process. We also study the particular cases when the error covariance is seen to decrease with the increase in the sampling rate. For the particular case of linear filters, we can also compare the error covariance bounds with the case when the measurements are continuously available.

Biography

Aneel Tanwani received the mechatronics engineering degree from the National University of Sciences and Technology, Islamabad, Pakistan, in 2005, followed by D.E.A. in automatique-productique from the Institute National Polytechnique de Grenoble, France in 2006. He graduated from University of Illinois at Urbana-Champaign, USA in 2011 where he obtained the M.S. degree in applied mathematics, and the M.S. and Ph.D. degrees in electrical engineering. He held postdoctoral positions at INRIA and Gipsa-lab in Grenoble, France, and then in the Department of Mathematics, Technical University Kaiserslautern, Germany. Since 2015, he has been a CNRS Associate Researcher with the LAAS, Toulouse, France. His research interests include switched and hybrid dynamical systems, stochastic processes, nonlinear control, variational analysis, and control with limited information. Dr. Tanwani was a recipient of the Fulbright scholarship in 2006. He is serving as an associate editor for IFAC Journal of Automatica since 2018, and for IEEE Transactions on Automatic Control since 2020. He has been an International Program Committee member for ACM Conference on Hybrid Systems: Computation and Control (2021), an associate editor for Conference Editorial Board of IEEE Control Systems Society (2016–2020) and European Control Association (2021), and a technical associate editor for IFAC World Congress 2020.