Modelling and control of agent’s motion in uncertain environment by idempotent algebra methods

Intelligent nature of agent motion always implies several stages (perception, planning and partial implementation of a plan). That is why it is difficult or even impossible to build mathematical models based on traditional mathematical tools such as algebraic, differential or difference equations over the field of real or complex numbers. Therefore the main subject of the present article is using the methods of idempotent algebra to develop and research the model of agent motion in discrete unbounded uncertain dynamical completely observable environment. The model is formulated in terms of a nonlinear dynamical system over idempotent semi-rings, and, thus, has explicit analytical form.