Instructor: Igor Zelenko
Office: Milner 324
Office hours (subject to change): Mon 2:00 p.m.- 3:00 p.m., Wed 2:00 p.m.-3:00 p.m., Fri 2:00 p.m. -3:00 p.m., or by appointment.
e-mail: zelenko"at"math.tamu.edu
Home-page: /~zelenko
Class hours: MWF 11:30-12:20 ZACH119D
Text:.
Course Description.
The course will mainly consist of 2 parts:
i. Controllability: orbits
of families of vector fields (Nagano-Sussmann, Rashevsky-Chow, and
Frobenius theorems), the structure of attainable sets for
bracket-generating systems (accessibility, relaxation, Poisson
stability) with application to control of rigid body and control of
configurations. This corresponds to chapters 1, 2, 3, 5, 6, 7, and 8 of
the book;
ii. Optimal Control Theory:
existence theorems (Filippov theorem), Pontryagin Maximum Principle
with applications, linear time-optimal problems, linear- quadratic
problems, dynamic programming and Hamilton-Jacobi equation. Thi
corresponds to chapters 10, 12, 13, 15, 16, 17. If the time permit we
will discuss second order optimality conditions ( second variation and Jacobi fields , chapters 20 and 21)
If the time permit we also will discuss state-feedback equivalence
of control systems: state and state-feedback linearizability (chapters
4 and 9) and Hamiltonian approach to Differential Geometry
of control systems (chapter 23) (this part does not require any
preliminary background in Differential Geometry).
Prerequisite:
Grading. Your grade will be determined by biweekly home assignments
(70%) and final take-home exam or project (30%). The grade will be given according to the following percentage:
85%-100%=A,
75%-84%=B , 65%-74%=C, 55%-64%=D, less than 55%=F
Copyright policy: All printed materials disseminated in class or on the web are protected by Copyright laws. One xerox copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.
Americans with Disabilities Act (ADA) Policy Statement.
The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides
comprehensive civil rights protection for persons with disabilities. Among other things, this legislation
requires that all students with disabilities be guaranteed a learning environment that provides for
reasonable accommodation of their disabilities. If you believe you have a disability requiring an
accommodation, please contact Disability Services, in Cain Hall, Room B118, or call 845-1637. For
additional information visit http://disability.tamu.edu.