AERE/EE/ME/MATH 574
Optimal Control
Spring, 2014
MWF 9:00-9:50 am
1344 Howe Hall
Instructor
Prof. Ping Lu
2335 Howe Hall
Tel. (515) 294-6956
[email protected]
Text:
Notes (Typed notes will be made available throughout the
semester)
References:
See attached
Lecture 22
Introduction
Minimum-fuel (or fuel-optimal) problem shares some
similarity with the minimum-time problem, but also has
distinctive characteristics in solution structure
It is a very important class of problems in engineering
applications from
FINITE-HORIZON TRACKING PROBLEM
Lecture 30
Optimal Control
AER E 574 XE Cross Listed: E E/MATH/M E
Professor Ping Lu
Introduction
In Chapter 11, we will discuss a number of problems
closely related to LQR problem
Finite-horizon tracking problem
Infinit
OPTIMAL CONTROL WITH STATE INEQUALITY
CONSTRAINTS
Lecture 34
Optimal Control
AER E 574 XE Cross Listed: E E/MATH/M E
Professor Ping Lu
Introduction
Often times an optimal control problem has inequality constraints
imposed on the state throughout the enti
Lecture 20
Chapter 7: Minimum-Time Problem
General Statement
Given nonlinear affine system with state equation
=
where :
Denote
and
=
,
+
=
and :
,
are
may be nonlinear functions of
Control is constrained
=
, = 1,
AERE/EE/ME/Math 574
,
,
Prof
LINEAR QUADRATIC PROBLEMS
Lecture 25
Optimal Control
AER E 574 XE Cross Listed: E E/MATH/M E
Professor Ping Lu
Introduction
Linear quadratic (LQ) problems are the most widely used
and successful in the area of optimal control
There are many variations i
INFINITE-HORIZON LQR EXAMPLES
Lecture 28
Optimal Control
AER E 574 XE Cross Listed: E E/MATH/M E
Professor Ping Lu
Solution to Infinite-Horizon LQR Problem
Optimal Control
AER E 574 XE Cross Listed: E E/MATH/M E
Professor Ping Lu
Example 1:
The double-int
Lecture 2
Lecture Overview
Absolute/Global versus Relative /Local minimum
Proper/Strong versus Improper/Weak minimum
Sufficient Condition
Iowa State University
Professor Ping
Professor Ping LuLu
Definitions
, defined
on the closed interval x [ , ], has
AN APPLICATION EXAMPLE IN AEROSPACE
ENGINEERING
Lecture 19
Optimal Control
AER E 574 XE Cross Listed: E E/MATH/M E
Professor Ping Lu
Aerocapture Problem in Space Exploration
Aerocapture is a nearly propellant-free maneuver to capture of an
interplanetary
Lecture 6
Formal Problem Statement
Consider the minimization problem
min
subject to
where :
=
Iowa State University
and h:
=0
are
,
Professor Ping Lu
< , and
Necessary Conditions (Theorem I)
Define an auxiliary function called the Lagrangian
=
+
Lecture 9
Optimal Control of Continuous-Time Systems
Problem Statement
=
, , ,
=
,
,
state equation
initial conditions( is given)
=0
( , )=
terminal conditions
,
control constraints
Minimize a performance index
=
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,
+
,
,
Profe
Lecture 3
Lecture Overview
Fundamentals
Notation
Interior and Boundary Points
Sylvesters Criterion
Stationary, Boundary, and Saddle Points
Iowa State University
Professor Ping Lu
Professor Ping Lu
Fundamentals
Unconstrained problem:
min = ( )
is an
AERE/EE/ME/MATH 574
Home Work # 3
Spring 2014
1. Solve the following problem by hand by applying the KKT conditions
2. Consider the quadratic programming problem
Show, by applying the sufficient condition for general NLP problems, that if Q is
positive de