AA/ME/EE 583: Nonliner control systems, Autumn 2023

Course logistics:

  • Schedule: Tuesday & Thursday 4:00 PM - 5:20 PM (In person)
  • Description: Analysis of nonlinear systems and nonlinear control system design
  • Prerequisite: linear algebra, differential equations, elementary analysis (more details below)

How will your grade be calculated?

  • Homeworks: 60%
  • Final exam (or change it to final presentation): 40%

References:

Course objectives:

  • Review elementary methods for the analysis of nonlinear systems (phase portrait and linearization)
  • Learn about nonlinear differential equations and how to analyze them
  • Learn about Lyapunov method and use it to study stability of nonlinear systems and their long-term behaviour
  • Learn about Passivity and how it is used for control design in inter-connected network of systems
  • Learn about optimal control design for nonlinear systems
  • Develop analytical skills to perform mathematical analysis
  • Go beyond what you learned in the course by exploring new topics or applications of your interest

What Math do you need to know for this course?

  • vector spaces, space of functions, p-norms and L_p norms
  • spectral analysis of matrices, spectrum of symmetric matrices, matrix norms
  • limits, convergence of sequences, open and closed sets

Look at this notes on mathematical preliminaries.

Handwritten Lecture notes

  1. What is this course about? (pendulum code)
  2. Phase portrait method (supplementary note, SIS simulation,pendulum simulation)
  3. Linearization (hand-out,Taylor expansion)
  4. Differential equations and Lipschitz functions (I)
  5. Differential equations and Lipschitz functions (II)
  6. Perturbation error analysis
  7. Lyapunov method for stability
  8. Exponential Stability
  9. Lyapunov method for linear systems
  10. Stability of nearly linear systems
  11. Lassalle invariance principle
  12. Gradient flows for optimization (A. Wilson PhD thesis , 2nd order methods)
  13. Input Output Stability
  14. small gain theorem and passivity
  15. passivity theorems
  16. Review session
  17. Review + Control Lyapunov functions
  18. Control Lyapunov and barrier functions (Sontag’s universal formula, CBF)
  19. Guest Lecture: Structured Neural-PI Control for Networked Systems

AA/EE 547: Linear Systems Theory, Winter 2024

Course logistics:

  • Schedule: Tuesday & Thursday 2:30 PM - 4:20 PM (In person)
  • Description: Analysis of controlled linear systems
  • Prerequisite: linear algebra, differential equations

How will your grade be calculated?

  • Homeworks: 60%
  • Final presentation: 40%

References:

Course objectives:

  • General form of the solution to a linear system (2 weeks)
  • Stability analysis of linear systems (1-2 weeks)
  • Controllability and feedback control design (1-2 weeks)
  • Observability and linear observer design (1-2 weeks)
  • Duality and minimum realization (1-2 week)
  • Linear quadratic regulator and Kalman filter (depending on time)

What Math do you need to know for this course?

  • Solid understanding of linear algebra: vector spaces, Linear dependence and independence, Subspaces and bases and dimensions, change of basis, image and null space, eigenvalues and eigenvectors, diagonalization, Symmetric matrices, Positive definite matrices

Handwritten Lecture notes: TBA

AA/EE 549: Estimation And System Identification, Spring 2023

Course logistics:

  • Schedule: Tuesday & Thursday 10:00 AM - 11:20 AM (In person)
  • Prerequisite: Linear system theory, undergraduate probability

How will your grade be calculated?

  • Homeworks: 60%
  • Final presentation: 40%

References:

  • Class notes and HW assignments
  • K. Law, A. Stuart “Data assimilation: a mathematical introduction”
  • Y. Bar-Shalom, “Estimation with Applications to Tracking and navigation: Theory, Algorithms, Software”

Course outline:

  • Background on probability theory
  • Conditional expectation
  • Filtering equations
  • Kalman filter
  • Extensions of Kalman filter
  • Sequential Monte-Carlo methods
  • Particle filters
  • Ensemble Kalman filter
  • Optimal transport/coupling viewpoint

Handwritten Lecture notes: TBA

AA 447: Control In Aerospace Systems, Spring 2024

Course logistics:

  • Schedule: Tuesday & Thursday 8:30 AM - 10:20 AM(In person)

How will your grade be calculated?

  • Homeworks: 50%
  • Midterm exam: 20%
  • Final exam: 30%

References:

  • Class notes and HW assignments
  • Feedback Systems, K.J. Astrom and R.M. Murray
  • Feedback control of dynamic systems, G. Franklin, J. Powell, A. Emami-Naeini
  • Control System Engineering, Norman S. Nise

Course objecrtives:

  • What is feedback control and why is it important?
  • How do dynamical systems behave under feedback?
  • How do I mathematically analyze stability and sensitivity of feedback systems?
  • How do I design a feedback controllers?
  • How all of these may be applied to real world applications?

Course outline:

  • Introduction to feedback control systems
  • Control of first-order and second-order systems
  • Block-diagram manipulations
  • Nyquist stability method
  • Stability margins
  • PID controller
  • lead/lag controller
  • Loop shaping

Handwritten Lecture notes: TBA