On the Observability of Nonlinear and Switched Systems
Abstract
In this paper, new concept of observability are introduced for both nonlinear systems and switched systems. The new definitions are applicable to a much broader family of problems of estimation including unmeasured state variables, unknown input, and unknown parameters in control systems. It is also taken into account the notion of partial observability which is useful for complex or networked systems. For switched systems, the relationship between the observability and hybrid time trajectories is analyzed. It is proved that a switched system might be observable even when individual subsystems are not. Another topic addressed in this paper is the measure of observability, which is able to quantitatively define the robustness and the precision of observability. It is shown that a system can be perfectly observable in the traditional sense, but in the case of high dimensions, it is practically unobservable (or extremely weekly observable). Moreover, computational algorithm for nonlinear systems is developed to compute the observability with precision. Several examples are given to illustrate the fundamentals and the usefulness of the results.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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