MEC 560: Advanced Control Systems

Course Description

Analytical methods applied to the design of multivariable linear control systems. Introduction to linear system theory: linearization, solution of linear matrix differential equations, stability, controllability, observability, transformations to canonical forms. Formulation of control objectives. Deterministic state observer. Full-state feedback control based on pole assignment and linear quadratic optimization theory. Linear systems with stochastic inputs and measurement noise. The response of linear systems to random input; stochastic state estimator (Kalman filter); separation principle of stochastic control and estimation; system robustness.

Course Syllabus

Syllabus

References

João P. Hespanha, Linear Systems Theory, 2nd Edition, Princeton University Press, 2018 [Publisher].
Robert L. Williams II and Douglas Lawrence, Linear State-Space Control Systems, Wiley, 2007 [Publisher].
Chi-Tsong Chen, Linear System Theory and Design, 4th Edition, Oxford University Press, 2013 [Publisher].
William L. Brogan, Modern Control Theory, 3rd Edition, Pearson, 1991 [Publisher].
Christopher M. Kellett and Philipp Braun, Introduction to Nonlinear Control: Stability, Control Design, and Estimation, Princeton University Press, 2023 [Publisher].

Course Topics

Chapter 1 - Modeling of Dynamic Systems
Chapter 2 - State-Space Fundamentals
Chapter 3 - Solutions to Linear Systems
Chapter 4 - Internal or Lyapunov Stability
Chapter 5 - Input-Output Stability
Chapter 6 - Controllability and Stabilizability
Chapter 7 - State Feedback Controllers
Chapter 8 - Observability and Detectability
Chapter 9 - Observers and Observer-Based Controllers
Chapter 10 - Feedback Linearization
Chapter 11 - Optimal Control