State estimation of switched nonlinear systems and systems with bounded inputs: Entropy and bit rates
Sibai, Hussein Mohamad Ali
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https://hdl.handle.net/2142/99265
Description
Title
State estimation of switched nonlinear systems and systems with bounded inputs: Entropy and bit rates
Author(s)
Sibai, Hussein Mohamad Ali
Issue Date
2017-12-15
Director of Research (if dissertation) or Advisor (if thesis)
Mitra, Sayan
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
State estimation
Bit rates
Topological entropy
Switched systems
Nonlinear systems
Abstract
State estimation is a fundamental problem when monitoring and controlling dynamical systems. Engineering systems interconnect sensing and computing devices over shared bandwidth-limited channels, and therefore, estimation algorithms should strive to use bandwidth optimally. Often, the dynamics of these systems are affected by external factors. In certain cases, these factors would lead the system to switch between different modes. In other cases, they would affect the dynamics of the system continuously in time without leading to explicit mode transitions. In this thesis, we present two notions of entropy for state estimation of nonlinear switched and non-autonomous dynamical systems as lower bounds on the average number of bits needed to be sent from the sensors to the estimators to estimate the states with deterministic (worst case) error bounds. Our approach relies on the notion of topological entropy and uses techniques from control under limited information. Since the computation of these entropies is hard in general, we compute corresponding upper bounds. Additionally, we design a state estimation algorithm for switched systems when their modes cannot be observed. We show that the average bit rate used by the algorithm is optimal in the sense that the efficiency gap is within an additive constant from the gap between the entropy of the considered system and its computed upper-bound. Finally, we apply our theory and algorithms to linear and nonlinear models of systems such as a glycemic index for diabetic patients, a controller of a Harrier jet and a Pendulum.
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