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). 

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 (Note that the original file that was posted contained two typos in (14) and (22), "0" should have been "D". This is fixed now)
       

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


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.