Cyber-physical Systems

3Uncertainty

This chapter focuses on uncertainty and the means to evaluate it through a mathematical theory of probability. Our objective here is to pedagogically present such a theory as a way to operate with random variables and random processes with special attention to well‐defined systems following the demarcation process presented in Chapter 2. In this case, uncertainty can be related to either internal or external aspects of a given particular system, as well as to its articulation with its environment. We will introduce this theoretical field in an accessible manner with an explicit intention of reinforcing foundational concepts instead of detailing mathematical techniques and derivations. Such concepts are the raw material needed to understand the definition of information to be presented in Chapter 4. For readers with interest in the mathematics, the original book by Kolmogorov is a must [1]. Engineers and engineering students could also refer to [2] and readers with interest in complex systems to [3].

3.1 Introduction

The word “uncertainty” refers to aspects of a phenomenon, an object, a process, or a system that are totally or partly unknown, either in relative or absolute terms. For example, it is uncertain to me how many people will read this book, or if I will be able to travel to Brazil in the summer vacations. It is also uncertain to me who will win the lottery this evening; however, I am certain that I will not win because I have no ticket. Other phenomena ...