Consistent dynamical system observers for nondeterministic event modeling

This paper describes an approach for constructing consistent observers for dynamic systems based on a formalism of nondeterministic event modeling (NEM). The first part of this paper establishes the definitions of NEM with a main focus on the notion of entropy that is extended for measuring the amount of information from nondeterministic events. The paper demonstrates the importance of the proposed entropy measure in contrast to the classical uncertainty measure when used in dynamic systems. The importance of the information measure stems from a potential failure of the classical uncertainty when observing nondeterministic events. Similar problems, which we describe as unobservable states, are often seen in dynamic systems where an uncertainty measure is used in conjunction with some arbitrary decision process. Based on well-defined dynamic systems concepts, the second part of the paper formulates the notion of consistent observer for nondeterministic event modeling. The consistent observer utilizes the monotonically decreasing entropy function of nondeterministic events. An example will be given in this paper which numerically illustrates the notions of NEM and consistent observer.