ECE6554: Homework #1
Due: Jan. 22, 2016
Problem 1. [6 pts] Using the sample code for using ode45 put up online, modify it to implement the simple
adaptive controller from the notes (beginning chapter)
ECE6554: Homework #2
Due: Feb. 5, 2016
Problem 1. [6 pts]
Find the Lipschitz constant on the region x [1, ) or prove none for f (x) = 1/x.
Problem 2. [6 pts]
Show that f1 + f2 is locally Lipschitz, wh
ECE6554: Homework #3
Due: Feb. 19, 2016
T
Problem 1. [8 pts] A gradient system is a dynamical system where x = grad V (x) for grad V (x) [DV (x)]
and V : D Rn R is C 2 (D; R).
1. Show that V (x) 0, x
12
Lipschitz Continuity
Calculus required continuity, and continuity was supposed to require
the innitely little, but nobody could discover what the innitely
little might be. (Russell)
12.1 Introducti
Homework 4 Solutions
1. For each of the following initial value problems y + p(t)y : g(t)7 y(t0) 2 yo use the existence and unique-
ness theorem for linear lst order ODEs to determine the largest time