MAE 287 - Control of Distributed Parameter Systems (Fall 2005)

Department of MAE, UCSD

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)


Primary Literature (several of these papers will be required reading)

  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.

Secondary Literature (contain important problem formulations or models)

  1. M. Krstic, ``On global stabilization of Burgers' equation by boundary control,'' Systems and Control Letters, vol.37, p.123-142, 1999.
  2. 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.
  3. W.-J. Liu and M. Krstic, ``Backstepping boundary control of Burgers' equation with actuator dynamics,'' Systems & Control Letters, vol. 41, pp. 291-303, 2000.
  4. 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.
  5. W.-J. Liu and M. Krstic, ``Stability enhancement by boundary control in the Kuramoto-Sivashinsky equation,'' Nonlinear Analysis, vol. 43, pp. 485-583, 2000.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.

Mildly Relevant (helpful to trace the historic development of the techniques)

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. D. Boskovic and M. Krstic, ``Nonlinear stabilization of a thermal convection loop by state feedback,'' Automatica, vol. 37, pp. 2033-2040, 2001.
  6. D. Boskovic and M. Krstic, ``Backstepping control of chemical tubular reactors,''  Computers and Chemical Engineering, vol. 26, pp. 1077--1085, 2002.
  7. 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
  8. 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.
  9. 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.
  10. 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.
  11. O.-M. Aamo and M. Krstic, ``Feedback control of particle dispersion in bluff body wakes,''  International Journal of Control, in press.