Cyber-physical Systems

8Dynamics of Cyber‐Physical Systems

This chapter covers key aspects of the dynamics of cyber‐physical systems (CPSs). We will first indicate different paradigms to characterize CPSs including differential and difference equations, stochastic processes, and an agent‐based model. Our aim is to provide a simple overview of different approaches without focusing on the peculiarities of dedicated disciplines like control theory or multiagent systems. As in previous chapters, we rather prefer to study an idealized toy model that is capable of illustrating the main features of the dynamical behavior of CPSs for pedagogical reasons. The exposition will be constructed using a simple elementary cellular automaton (CA) – extensively studied in [1]. By using this idealized model, it will be possible to understand how four classes of behavior can emerge as a result of the internal constitution of the CPS. Possible evaluation metrics and the impact of attacks against the CPS will also be studied following the proposed example.

8.1 Introduction

There are several ways to evaluate the dynamics of different systems, some already presented in previous chapters. The mathematical characterization of dynamical systems using differential equations is probably the best‐known approach in engineering because of the physical laws of classical mechanics, thermodynamics, and electromagnetism. Difference equations, which are roughly speaking a discrete version of differential equations, are also frequently ...