Course web address: http://flyingv.ucsd.edu/krstic/teaching/287/287.html
Instructors: Prof. Miroslav Krstic, 1808 EBUI, 822-1374,
krstic@ucsd.edu
Andrey Smyshlyaev, 1801
EBUI, 822-2406, asmyshly@ucsd.edu
Time and Place: TuTh 5:00-6:50pm, CENTR 201
Office Hours: Mondays 3-4 or by
appointment (e-mail, phone)
Grading:
The level of the course will be informal to accomodate students with very
diverse needs and levels of background. A rough tentative breakdown is
Homework
50%
Final or Project 50%
Topics: Types of PDEs and physical problems they describe. Standard boundary
value problems. Eigenvalues and eigenfunctions. Standard methods of
solution: separation of variables, Laplace and Fourier transforms. Frequency
domain representation. Stability. Motion planning. Backstepping approach to
stabilization problems. Observers. Examples of control design for various
physical problems: strings, beams, fluid flows. Adaptive control (time
permitting).
Course
Notes (slides, prepared after the end of the course, based
on the course notes)
Homework assignments:
Homework1 Due date: Tuesday, October 4
Homework2
Due date: Tuesday, October 11
Homework3
Due date: Thursday, October 20
Homework4
Due date: Tuesday, October 25
Homework5
Due date: Tuesday, November 1
Homework6
Due date: Tuesday, November 8
Homework7
Due date: Tuesday, November 15 (Note three typos (5), (20) and (21) now fixed.)
Homework8
Due date: Tuesday, November 22
Bessel functions handout
GUI to calculate the
eigenvalues of wave equation (unzip the files into the same directory
and type gui_wave in Matlab)
Lecture Notes from 11-08-05 (Jennie Cochran)
Lecture Notes from 11-10-05 (Jennie Cochran)
Control of 3-D NS paper - Cochran, Vazquez, Krstic (Note: some of the equations in section IV are not entirely correct)
1.
A. Smyshlyaev and M.
Krstic, ``Closed form
boundary state feedbacks for a class of 1-D partial integro-differential
equations,'' IEEE Transactions on Automatic Control, vol. 49, pp. 2185-2202, 2004.
2.
A. Smyshlyaev and M.
Krstic, ``Backstepping
observers for a class of parabolic PDEs,’’ Systems and Control Letters, vol. 54, pp. 613-625, 2005.
3.
A. Smyshlyaev and M.
Krstic, ``On control design
for PDEs with space-dependent diffusivity and time-dependent reactivity,’’ Automatica, vol. 41, pp. 1601-1608, 2005.
4.
M. Krstic and A.
Smyshlyaev, ``Backstepping controller and observer designs for the
slender Timoshenko beam,’’ 2006 American Control Conference, submitted.
5.
R. Vazquez and M.
Krstic, ``Explicit
integral operator feedback for local stabilization of nonlinear thermal
convection loop PDEs,’’ Systems and Control Letters, in press.
6. R. Vazquez and M. Krstic, ``A
closed-form feedback controller for stabilization of the linearized 2D
Navier-Stokes Poiseuille flow,’’ under review.
7.
O.-M. Aamo, Andrey
Smyshlyaev, and M. Krstic, ``Boundary
control of the linearized Ginzburg-Landau model of vortex shedding,''
SIAM Journal of Control and Optimization, vol. 43, pp. 1953-1971, 2005.
8. O. M. Aamo, A. Smyshlyaev, M. Krstic, and B. Foss, ``Stabilization
of a Ginzburg-Landau model of vortex shedding by output-feedback boundary
control,’’ under review.
9. M. Krstic, ``Adaptive
boundary control for unstable parabolic PDEs - Part I: Lyapunov design,’’
under review.
10. A. Smyshlyaev and M. Krstic, ``Adaptive
boundary control for unstable parabolic PDEs - Part II: Estimation-based
designs,’’ under review.
11. A. Smyshlyaev and M. Krstic, ``Adaptive
boundary control for unstable parabolic PDEs - Part III: Output-feedback
examples with swapping identifiers,’’ under review.
12. R. Vazquez and M. Krstic, ``Volterra boundary control laws for a class of
nonlinear parabolic partial
differential equations," IFAC Symposium on Nonlinear Control
Systems, 2004.
13. M. Krstic, ``On global stabilization of
Burgers' equation by boundary control,'' Systems and Control Letters, vol.37, p.123-142, 1999.
14. A. Balogh and M. Krstic, ``Burgers' equation with
nonlinear boundary feedback: H^1 stability, well posedness, and simulation,''
Mathematical Problems in Engineering, vol. 6, pp. 189-200, 2000.
15. W.-J. Liu and M. Krstic, ``Backstepping boundary
control of Burgers' equation with actuator dynamics,'' Systems &
Control Letters, vol. 41, pp.
291-303, 2000.
16. W.-J. Liu and M. Krstic, ``Adaptive control of Burgers'
equation with unknown viscosity,'' International Journal of Adaptive
Control and Signal Processing, vol.
15, pp. 745-766, 2001.
17. W.-J. Liu and M. Krstic, ``Stability enhancement by
boundary control in the Kuramoto-Sivashinsky equation,'' Nonlinear
Analysis, vol. 43, pp. 485-583,
2000.
18. W.-J. Liu and M. Krstic, ``Global boundary
stabilization of the Korteweg-de Vries-Burgers equation,'' Computational
and Applied Mathematics, vol. 21,
pp. 315-354, 2002.
19. A. Balogh and M. Krstic, "Boundary control of the
Korteweg--de Vries--Burgers equation: Further results on stabilization and
numerical demonstration," IEEE Transactions on Automatic Control, vol. 45, pp. 1739-1745, 2000.
20. A. Balogh, W.-J. Liu, and M. Krstic, ``Stability enhancement by
boundary control in 2D channel flow'' IEEE Transactions on Automatic Control, vol. 46, pp. 1696-1711, 2001.
21. A. Balogh, O. M. Aamo and M. Krstic, ``Optimal mixing enhancement
in 3D pipe flow,'' IEEE Transactions on Control Systems Technology, vol. 13, pp. 27-41, 2005.
22. C.C. Yuan, M. Krstic, and T. Bewley, ``Active control of jet
mixing,'' IEE Proceedings: Control Theory and Applications, vol. 151, pp. 763-772, 2004.
23. A. Smyshlyaev and M. Krstic, ``Explicit state and output
feedback boundary controllers for partial differential equations,'' Journal
of Automatic Control, University of
Belgrade, vol. 13, pp. 1-9, 2003.
24. D. Boskovic, M. Krstic, and W.-J. Liu, ``Boundary control of an
unstable heat equation via measurement of domain-averaged temperature,''
IEEE Transactions on Automatic Control, vol. 46, pp. 2022-2028, 2001.
25. A. Balogh and M. Krstic, ``Infinite-dimensional
backstepping-style feedback transformations for a heat equation with an
arbitrary level of instability,'' European Journal of Control, vol. 8, pp. 165-177, 2002.
26. D. Boskovic, A. Balogh, and M. Krstic, ``Backstepping in infinite
dimension for a class of parabolic distributed parameter systems,'' Mathematics
of Control, Signals, and Systems,
vol. 16, pp. 44-75, 2003.
27. A. Balogh and M. Krstic, ``Stability of partial
difference equations governing control gains in infinite-dimensional
backstepping,'' Systems and Control Letters, vol. 51, pp. 151-164, 2004.
28. D. Boskovic and M. Krstic, ``Nonlinear stabilization of a
thermal convection loop by state feedback,'' Automatica, vol. 37, pp. 2033-2040, 2001.
29. D. Boskovic and M. Krstic, ``Backstepping control of
chemical tubular reactors,'' Computers and Chemical Engineering, vol. 26, pp. 1077--1085, 2002.
30. D. Boskovic and M. Krstic, ``Stabilization of a solid
propellant rocket instability by state feedback,'' International
Journal of Robust and Nonlinear Control, vol. 13, pp. 483-495, 2003.W.-J. Liu and M. Krstic, "Strong stabilization of
the system of linear elasticity by a Dirichlet boundary feedback, " IMA
Journal of Applied Mathematics, vol.
65, pp. 109-121, 2000
31. O. M. Aamo, M. Krstic, and T. R. Bewley, ``Control of mixing by
boundary feedback in 2D channel flow,'' Automatica, vol. 39, pp. 1597-1606, 2003.
32. E. Schuster and M. Krstic, ``Control of a nonlinear PDE
system arising from non-burning tokamak plasma transport dynamics,'' International
Journal of Control, vol. 76, pp.
1116-1124, 2003.
33. O. M. Aamo and M. Krstic, ``Global stabilization of a
nonlinear Ginzburg-Landau model of vortex shedding,'' European
Journal of Control, vol. 10, pp.
105-116, 2004.
34. O.-M. Aamo and M. Krstic, ``Feedback control of
particle dispersion in bluff body wakes,'' International Journal of
Control, in press.