Prediction Capability Analysis for a Particular Type of Mimetic Models of Nonlinear Dynamic Systems

The main purpose of the paper is to provide the description of the conditions applicable to the usage of a certain systems modeling technique, called mimetic modeling technique. The paper describes and provides the proof for the mimetic modeling technique developed in the attempt to provide a management modeling instrument for economic, technological and other types of systems. Such systems are described by the evolution of their parameter values in time seen as the system's trajectory in the extended state space. The approximating model is built gradually based on the observed trajectory. Though based on similar approximation techniques to a previous approach (Pascadi M. 2015), the approximating model presented in this paper is not built in an iterative manner, its descriptor parameters being partly determined based on solving an n-dimensional equation and partly being sized based on additional imposed conditions, in one step. The theoretical results are confirmed by numerical simulations. The paper then analyses and presents certain conclusions regarding the prediction capabilities and their limits based on the given mimetic modeling technique. The analysis refers to the density/quantity/quality of data gathered so that predictions may be made based on the model, the restrictions related to the domain of evolution of the modeled system and behavioral limitations of the modeled system that may determine the impossibility to make predictions. A large variety of systems may benefit of a ”from the outside” modeling capacity without actually having data regarding the modeled system. For all such cases, it is important to be able to decide regarding the situations where the technique is successfully applicable and the ones it is not. The paper brings newly developed results regarding the applicability conditions of the mimetic modeling technique and provides a step further in defining the applicability of the method based on pre-modeling analysis criteria of the to-be-modeled systems. As the learning phase of the mimetic technique may be large (and based on large data), time consumption and risks (related to improper application of the modeling technique) may be avoided.