Control and Dynamical Systems
CDS 90 abc. Senior Thesis in Control and Dynamical Systems. 9 units (0-0-9); first, second, third terms. Prerequisite: CDS 110 or CDS 112 (may be taken concurrently). Research in control and dynamical systems, supervised by a Caltech faculty member. The topic selection is determined by the adviser and the student and is subject to approval by the CDS faculty. First and second terms: midterm progress report and oral presentation during finals week. Third term: completion of thesis and final presentation. Not offered on a pass/fail basis. Instructor: Staff.
CDS 110. Introduction to Feedback Control Systems. 9 units (3-3-3); third term. Prerequisites: Ma 1abc and Ma 2/102 or equivalents. An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Input/output modeling of dynamical systems using differential equations and transfer functions. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. Design of feedback controllers in state space and frequency domain based on stability, performance and robustness specifications. Instructor: Seinfeld.
CDS 112. Optimal Control and Estimation. 9 units (3-0-6); second term. Prerequisites: CDS 110 (or equivalent) and CDS 131. Optimization-based design of control systems, including optimal control and receding horizon control. Introductory random processes and optimal estimation. Kalman filtering and nonlinear filtering methods for autonomous systems. Instructor: Chung.
CDS 131. Linear Systems Theory. 9 units (3-0-6); first term. Prerequisites: Ma 1b, Ma 2, ACM/IDS 104 or equivalent (may be taken concurrently). Basic system concepts; state-space and I/O representation. Properties of linear systems, including stability, performance, robustness. Reachability, observability, minimality, state and output-feedback. Instructor: Murray.
CDS 141. Network Control Systems. 9 units (3-2-4); third term. Variety of case studies and projects from control, communication and computing in complex tech, bio, neuro, eco, and socioeconomic networks, particularly smartgrid, internet, sensorimotor control, cell biology, medical physiology, and human and animal social organization. Emphasis on leveraging universal laws and architectures but adding domain specific details. Can be taken after CDS 231 (to see applications of the theory) or before (to motivate the theory). Not offered 2019–20.
CDS 190. Independent Work in Control and Dynamical Systems. Units to be arranged; first, second, third terms; maximum two terms. Prerequisite: CDS 110. Research project in control and dynamical systems, supervised by a CDS faculty member.
CDS 231. Robust Control Theory. 9 units (3-2-4); second term. Prerequisites: CMS/ACM/IDS 107, CMS/ACM/IDS 113, and CDS 131 (or equivalents). Linear input/output models (multi-state difference and differential equations). Stability, input/output norms. Uncertainty, including noise, disturbances, parametric uncertainty, unmodeled dynamics, and structured uncertainty (LTI/LTV). Tradeoffs, robustness versus efficiency, conservation laws and hard limits in time and frequency domain. Synthesis of robust control systems. Co-design of sparse and limited (delayed, quantized, saturating, noisy) sensing, communications, computing, and actuation. Layering, localization, and distributed control. Interplay between automation, optimization, control, modeling and system identification, and machine learning. Computational scalability exploiting sparsity and structure, nonlinear dynamics and sum of squares, global stability, regions of attraction. Motivation throughout from case studies from tech, neuro, bio, and socioeconomic networks, explored in more detail in CDS 141. Not offered 2019–20.
CDS 232. Nonlinear Dynamics. 9 units (3-0-6); second term. Prerequisites: CMS/ACM/ IDS107 and CDS 231. This course studies nonlinear dynamical systems beginning from first principles. Topics include: existence and uniqueness properties of solutions to nonlinear ODEs, stability of nonlinear systems from the perspective of Lyapunov, and behavior unique to nonlinear systems; for example: stability of periodic orbits, Poincaré maps and stability/invariance of sets. The dynamics of robotic systems will be used as a motivating example. Instructor: Ames.
CDS 233. Nonlinear Control. 9 units (3-0-6); third term. Prerequisites: CDS 231 and CDS 232. This course studies nonlinear control systems from Lyapunov perspective. Beginning with feedback linearization and the stabilization of feedback linearizable system, these concepts are related to control Lyapunov functions, and corresponding stabilization results in the context of optimization based controllers. Advanced topics that build upon these core results will be discussed including: stability of periodic orbits, controller synthesis through virtual constraints, safety-critical controllers, and the role of physical constraints and actuator limits. The control of robotic systems will be used as a motivating example. Instructor: Ames.
CDS 242. Hybrid Systems: Dynamics and Control. 9 units (3-2-4); third term. Prerequisites: CDS 231 and CDS 232. This class studies hybrid dynamical systems: systems that display both discrete and continuous dynamics. This includes topics on dynamic properties unique to hybrid system: stability types, hybrid periodic orbits, Zeno equilibria and behavior. Additionally, the nonlinear control of these systems will be considered in the context of feedback linearization and control Lyapunov functions. Applications to mechanical systems undergoing impacts will be considered, with a special emphasis on bipedal robotic walking. Not offered 2019–20.
CDS 243. Adaptive Control. 4 units (2-0-2); third term. Prerequisites: CDS 231 AND CDS 232. Specification and design of control systems that operate in the presence of uncertainties and unforeseen events. Robust and optimal linear control methods, including LQR, LQG and LTR control. Design and analysis of model reference adaptive control (MRAC) for nonlinear uncertain dynamical systems with extensions to output feedback. Offered in alternate years. Instructor: Lavretsky.
CDS 244. System Identification. 4 units (2-0-2); third term. Prerequisites: CDS 231 and CDS 232. Mathematical treatment of system identification methods for dynamical systems, with applications. Nonlinear dynamics and models for parameter identification. Gradient and least-squares estimators and variants. System identification with adaptive predictors and state observers. Parameter estimation in the presence of non-parametric uncertainties. Introduction to adaptive control. Offered in alternate years. Not offered 2019–20.
Ae/CDS/ME 251 ab. Closed Loop Flow Control. 9 units; (3-0-6 a, 1-3-5 b). For course description, see Aerospace.
CDS 270. Advanced Topics in Systems and Control. Hours and units by arrangement. Topics dependent on class interests and instructor. May be repeated for credit.
CDS 300 abc. Research in Control and Dynamical Systems. Hours and units by arrangement. Research in the field of control and dynamical systems. By arrangement with members of the staff, properly qualified graduate students are directed in research. Instructor: Faculty.