EML 6350
Fall 2013
Hw 3: OFB Control
1. Consider the system
a
x + bx + csin(x) = u
where a, b, c are unknown positive constants, and only x(t) is measurable. Given e =
x(t) xd where xd is a known positive constant, design u(t) to minimize the error.
2. Is
EAS 6939: Spring 2008
Adaptive, Robust, Feedback Linearization and Backstepping
Test #2.
Consider the following system
mx + ax + x2 = y
y = u + sgn(y)
where m, a R are unknown positive constants.
1. (30 points) Assuming that x(t), x(t),
and y(t) are all m
EAS 6939: Spring 2008
Adaptive, Robust, Feedback Linearization and Backstepping Homework.
1. Using any controller possible, prove that your controller yields GES for the following system
m
q + g(q) = km qm
J qm + kf q = u
where
m, km , J, kf R are known
EML 6350
Fall 2013
1. (20 pts) Consider the following dynamic system
x 1 = x1 + x2 cosh2 (t)
x 2 = x1 x2
= x1 cosh2 (t)
where x1 , x2 , R, and the plot of cosh2 (t) is given below.
Consider the Lyapunov function candidate
1
1
1
V (x) = x21 + x22 + 2 .
2
EML 6350: Fall 2011 Test 2
Name
Instructions. This is a 50 minute closed-book, closed-notes test. No calculators and other such
electronic devices are allowed. Point values for each problem are listed.
1. (25 points) Consider the system
ax bx c sinx u
whe
EAS 6939: Fall 2004 Test1
Name
Instructions. This is a 50 minute closed-book, closed-notes test. No calculators and other such electronic
devices are allowed. Point values for each problem are listed.
1. (40 points) Consider the following dynamic system
x
Nonlinear Control: Spring 2010 Test1
Name
Instructions. This is a open-book, open-notes test. No interaction with any students, faculty, or controls
related researchers is allowed. The work is intended to be completely independent.
1. Consider the followi
EML 6350
Fall 2013
Test 2
1. (25 pts) Consider the system
x = y + tanh(ax)
y = u
where a is an unknown positive constant, and x(t) and y(t) are measurable. Design
u(t) to prove that x 0 as t if possible. If not, derive the best possible result
that you ca
EML 6350
Fall 2015
Hw 1: Autonomous Systems
1. Consider the following dynamic system
x 1 = x2
x 2 = x1.
Given a Lyapunov function candidate
1
1
V (x) = x21 + x22
2
2
what is the best can you prove about the equilibrium point?
Ans:
V (x) = x1 (x2 ) x2 x1
V
EML 6350
Fall 2013
Hw 1: Autonomous and Nonautonomous Systems
1. Consider the following dynamic system
x 1 = x1 + x2
x 2 = x1.
Given a Lyapunov function candidate
1
1
V (x) = xT1 x1 + xT2 x2
2
2
what is the best can you prove about the equilibrium point?
EML 6350
Fall 2013
Test 3: OFB Control
1. (50 points) Consider the system
x = ax2 + bu + sin(cx)
where a, b, c are unknown positive constants, and only x(t) is measurable. Design
u(t) to prove that x(t) is at least semi-globally uniformly ultimately bound
Nonlinear Control: Spring 2010 Test 3
Name
Instructions. This is a open-book, open-notes test. No interaction with any students, faculty, or controls
related researchers is allowed. The work is intended to be completely independent.
1. Given the following
EML 6350 Fall 2011
Test #3.
Name
Instructions. This is a take home open-book, open-notes test - you should not talk with colleagues and will fail the course if I consider you cheating on this exam. Point values for each problem are
listed. More credit is
EAS 6939: Spring 2008
Test #3.
Name
Instructions. This is a take home open-book, open-notes test - you should not talk with colleagues and will fail the course if I consider you cheating on this exam. Point values for each problem are
listed. More credit
EML 6350
Fall 2013
Hw 2: Robust and Adaptive Control
1. Consider the system
a
x + bx + csin(x) = u
where a, b, c are unknown positive constants, and x(t), x(t)
are measurable. Design
u(t) to prove that x 0 as t . Also, what can you say about the ability o