Homework 7 - Modeling Hybrid Systems

Due 11/12/21 at 11am

Instructions

Submit these in slide format (ppt, pptx, or pdf) with each section on a different slide. Please do not put your name on the PDF, so that we can anonymize grading in Canvas. Number the questions/question parts. Questions in blue are optional/questions for you to think about to yourself.

You are graded on good-faith effort, not correctness. This means that you should attempt to answer every question, and if you did not reach an answer, you should describe your process and where you got stuck.

Ordinary Differential Equations

Read this PDF that gives an overview of ODEs. You can also optionally read Lee/Seshia chapter 2, but this chapter gives a much less gentle introduction to the concepts.

1. Post any questions you have on Ed

2. (6 pts) Do Lee/Seshia Chapter 2, exercise 1 a/b. If you get stuck or confused, make a note of it on the homework and you will get full credit. I will be looking through the homework before class to see how much math we need to review before proceeding with the rest of the lecture.

Hybrid systems

Read Lee/Seshia Chapter 4, sections 4.1, 4.2.1, and example 4.7 only. Make sure you understand Example 4.3. The top part of the diagrams (the box with lines coming in and out) just illustrates a system with inputs (to the left) and outputs (to the right). You do not need to understand this notation any farther, but if you would like more context, you can refer to chapter 2.

1. Post any questions you have on Ed

2. (10 pts) Do Lee/Seshia Chapter 4, exercise 2a. Don’t worry about avoiding “imprecise or sloppy notation.” Explain how you got your answer. Hint: Graph what happens to r(t) and s(t) over time, as in Figure 4.6