Why Is It Important to Study Stochastic-Dynamic Systems?

LECTURE # 1

Course Overview

Why is it important to study stochastic-dynamic systems?

• Real world problems include variables whose values are uncertain. Examples: rainfall at a TTU site on January 15, 2001; tomorrow's average temperature at Cookeville, Tennessee.
• Most systems of interest to the engineer contain components whose response to certain input varies in time (dynamic). Examples: the rainfall-runoff transformation of a hydrologic prediction model; the building stresses under earthquake forcing.

Systems with dynamic components that contain uncertain parameters, variables, or accept uncertain input will be referred to as stochastic-dynamic systems.

The course provides basic techniques for the analysis and synthesis of such systems. The material in this course can be used to solve three main classes of problems: Estimation, Prediction and Optimal Control of systems that are observed remotely or directly. For example, consider the problem of precipitation estimation from multiple sensors, the problem of flood prediction, and the problem of optimal control of a multipurpose reservoir system.

CLASS DISCUSSION ON:

1. The existence of uncertainty sources in aforementioned and other examples (shown in italics).
2. Introduction of individual’s research project
3. Overview of topics to be covered

TRIVIA#1 (Actually, this can be mind-boggling)

Sometime around the fifth century BC, the Greek philosopher Zeno posed a paradox that now bears his name. Suppose that Achilles and a tortoise are to run a footrace. Let’s assume Achilles is exactly twice as fast as the tortoise. To make things fair, the tortoise will get a head start of 1000 meters. After the start of the race, by the time Achilles runs 1000 meters, the tortoise is still ahead by 500 meters. However, Achilles, being a superior athlete, easily covers that extra 500 meters ahead of him. During that time, the tortoise has managed, however, (much to Achilles’ dismay), to go another 250 meters. We can repeat the process for an infinite number of time slices while always finding the tortoise just a bit ahead of Achilles. So now the trivial question, folks, WILL ACHILLES EVER CATCH UP TO THE TORTOISE?

Comment: Under ordinary circumstances, if I had just ONLY mentioned the actual running speeds of Achilles and the tortoise, you could have easily given me a ‘deterministic’ (hard coded) answer through a few lines of algebraic manipulation. I hope I have managed to confuse you enough with my line of differential and definitely valid reasoning. Anyone who can give an equally mind-boggling answer shall receive extra credit. Remind me to give you an explanation that reconciles with apparently two conflicting logical reasonings.
LECTURE# 1 Figure

UNCERTAINTY IN ENGINEERING MODELS