AI in System Theory: An Observability View,

Abstract

The problem of the construction of a Logic Observer, which generates a sequence of propositions that correctly describe system state properties, is mainly intended to solve the state estimate of finite state machines. Of particular interest is the convergence of the logic-based dynamical system statements (in an appropriate sense) to true characterizations of the system state. This paper demonstrates that this observer can be built within a logic-based framework. It starts with an informal discussion of the nature of logic -- focusing on the predicate calculus -- and discusses the fundamental concepts associated with these formal systems. Later in the paper, the formal definition of the concepts of the logic-based dynamical observer is presented. An arbitrary automaton is selected as an example to understand the simulation and the expert system presented to accomplish the task. In this paper, the assumption is that the automata representation in state space systems is expressed by the quintuple set of states, set of inputs, set of outputs, transition functions and output functions. An automaton is taken as a deterministic input-state-output (finite) system.