A Finite State Machine Model to Support the Visualization of Complex Dynamic Systems.
Brian J. d’Auriol · MSV · 2006
Linear and non-linear controllable systems are commonly found in many engineering problems and are examples of models that involve complex high-dimensional spatially-related data sets. Such systems range in size and complexity from small-scale systems of a few state variables to large-scale systems comprising many state variables that evolve in complex ways. Particular evolution trajectories and regionalized evolutionary behavior of such complex systems are often non-intuitive and may reflect bifurcations in the system. A state space discretization approach leading to a novel structure termed Orthogonal Organized Finite State Machines (OOFSM) is proposed as a modeling technique to support visualizations of the properties of these types of complex systems. Linear and non-linear controllable systems are commonly found in many engineering problems [1]. Such systems range in size and complexity from small-scale systems of a few state variables to large-scale systems comprising many state variables that evolve in complex ways. Particular evolution trajectories and regionalized evolutionary behavior of such complex systems are often non-intuitive and may reflect bifurcations in the system. For largescale systems in particular, the state space exists in high dimensional spaces and many of the transitions are expected to be intra-dimensional. Understanding the operation and behavior of the system together with the details about specific evolution trajectories and how such relates with other trajectories or with the system as a whole may provide insight into the underlying dynamics of the system as it evolves towards desired or undesired behavior. In addition, this may also facilitate decision making by policy makers who are involved in control operations. An orthogonal organized finite state machine (OOFSM) is proposed in this paper as a discrete state space abstraction of the evolutionary behavior of dynamic systems. A lattice partitioning applied to the state space discretizes the state space. A discrete vector field that abstracts the intersection of trajectories with the boundaries of the discretized state space provides for the abstraction of the evolutionary behavior. This paper formalizes the OOFSM as a finite state machine abstraction of the discretized state space with the discrete vector field abstraction. The rest of this paper is organized as follows. The discretization approach and the OOFSM are described in Section I. Applications of this abstraction are presented in Section II. Conclusions are given in Section III. I. DYNAMIC SYSTEM DISCRETIZATION Finite state machines (FSMs) as models for dynamic systems have previously been considered in the literature. There is a lot of literature concerning FSM modeling of Discrete Event Systems (DES), see for example [2]; also, hybrid systems. In [3], an FSM models discrete event systems so as to take into account the issue of partial observability. The work presented here however is based on discretizing a continuous system. A more general treatment of finite state modeling of continuous systems is described in [4]. The approach taken in this paper is to derive a spatially organized finite state machine. In the literature, the term “Orthogonal finite-State Machine (OFSM)” [5] is introduced in 2002. The model presented here is similar, but derived specifically from an analysis of complex dynamic systems and therefore is intended to wholly represent and support the modeling of these systems, including, the visualization of properties of these systems. The term ”organized finite state machine” also appears