ME254/ECE217C,
HW 6
Winter 2009
Due Thursday March 12 at 5pm in the box outside my oce
1. Exercise 1 on page 49 of notes. 2. Consider the stable rst order, input-output LTI system x = x + u y=x (a) Compute the H norm using the frequency domain
ME254/ECE217C,
Due Monday March 2 at 1pm in the box outside my oce
HW 5
Winter 2009
1. Verify carefuly that in the case of the LQR problem, the invariant imbedding equation yields the dierential Ricatti equation. 2. Given the scalar nonlinear opti
ME254/ECE271C Solutions to HW 4
Winter 09
1. Note: These solutions were written several years back, so the terminology may not exactly match that being used in class this quarter, but you should be able to gure things out from context. The techniqu
ME254/ECE217C,
HW 4
Winter 2009
Due Monday Feb 9 at 1pm in Prof. Bamiehs mailbox
1. You are given a control system described by x(t) = u(t), x(0) = 2 2, x(0) = 5 2 ,
which will be steered to the target set = {(x, x) R2 : x2 + x2 = 1} (a ci
18
1 Dierentiability and the calculus of variations
y x
z
Fig. 1.3.
1 0
L=
x2 (t) + y 2 (t) + z 2 (t) dt.
As mentioned in the previous exercise, the extermization of L or L yields the same paths. Work out the E-L equations for L rst, and
1.4 Exercises
17
5. Prove that the shortest path between two points in Rn is a straight line by using the techniques described below. Any path in Rn between two points a and b can be mathematically represented as a vector-valued function p : [0, 1]
ME254/ECE217C, 2009
Final Exam (corrected again and again)
Winter
This is a take home exam, it is due back at 4pm, Thursday 3/19 in Prof. Bamiehs mailbox (sharp deadline). You can consult the notes that have been handed out in class or on the cour
1 Dierentiability and the calculus of variations
We begin with some preliminaries on dierentiation of functions in Rn . Readers familiar with this material should still skim over this section as the concepts are presented in a manner that immediatel
ME254/ECE217C,
Midterm Exam
Winter 2009
This is a take home exam, it is due back at 1pm, Friday 2/13 in Prof. Bamiehs mailbox (sharp deadline). You can consult the notes that have been handed out in class or on the course web page, but no other re
Handout on matrix calculus (ME254/ECE271C, W09)
The following is a useful set of identities in matrix calculus (from Robust and Optimal Control by Zhou, Doyle & Glover). To connect these with the denition of the derivative we have been using in class
Bassam Bamieh
Notes on Optimal Control and Linear Quadratic Problems
(V. 1/22/03)
c Bassam Bamieh, 2001
Preface
The main purpose of these notes is to present a treatment of Linear Quadratic (LQ) problems with possibly indenite quadratic functiona