Courses 2025-26 | Caltech Academic Catalog

CDS 90 abc

Senior Thesis in Control and Dynamical Systems

9 units (0-0-9) | first, second, third terms

Prerequisites: 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: Ames

CDS 110

Analysis and Design of Feedback Control Systems

9 units (3-3-3) | third term

Prerequisites: Ma 1 abc and Ma 2/102 or equivalents.

An introduction to analysis and design of feedback control systems in the time and frequency domain, with an emphasis on state space methods, robustness, and design tradeoffs. Linear input/output systems, including input/output response via convolution, reachability, and observability. State feedback methods, including eigenvalue placement, linear quadratic regulators, and model predictive control. Output feedback including estimators and two-degree of freedom design. Input/output modeling via transfer functions and frequency domain analysis of performance and robustness, including the use of Bode and Nyquist plots. Robustness, tradeoffs and fundamental limits, including the effects of external disturbances and unmodeled dynamics, sensitivity functions, and the Bode integral formula.

Instructor: Mazumdar

CDS 131

Linear Systems Theory

12 units (3-0-9) | second term

Prerequisites: Ma 1 b, 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. Brief introduction to optimal control and control of networked and nonlinear systems. Motivating case studies from tech, biology, neuroscience, and medical systems.

Instructor: Chung

CDS 190

Independent Work in Control and Dynamical Systems

Units to be arranged | first, second, third terms

Prerequisites: CDS 110.

Research project in control and dynamical systems, supervised by a CDS faculty member.

Instructor: Staff

CDS 212

Optimal Control and Reinforcement Learning

9 units (3-0-6) | third term

Prerequisites: CDS 110 (or equivalent) and CDS 131.

Advanced topics in optimization-based design of control, optimal control, and estimation/filtering. Optimal control theory using calculus of variations, Hamilton-Jacobi-Bellman equation, Pontryagin's maximum principle, and optimal control applications including reinforcement learning and model predictive control. Kalman filtering, Bayesian filtering, and nonlinear filtering methods for autonomous systems.

Instructor: Chung

CDS 231

Robust Control Theory

9 units (3-2-4) | third term

Prerequisites: CMS/ACM/IDS 107, CMS/ACM/EE 122, and CDS 131 (or equivalents).

Scalable analysis and synthesis of robust control systems. Motivation throughout from case studies in tech, neuro, bio, med, and socioeconomic networks. Co-design of sparse and limited (delayed, localized, quantized, saturating, noisy) sensing, communications, computing, and actuation using System Level Synthesis (SLS). Layering, localization, and distributed control. Computational scalability exploiting sparsity and structure. 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. Advanced topics, depending on class interest, can include interplay between automation, optimization, control, modeling and system identification, and machine learning, and nonlinear dynamics and sum of squares, global stability, regions of attraction.

Instructor: Staff

CDS 232

Nonlinear Dynamics

9 units (3-0-6) | second term

Prerequisites: CMS/ACM/IDS 107 or equivalent.

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, Poincare 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 131 and CDS 232.

This course studies control synthesis for 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 (CLF), and corresponding stabilization results in the context of optimization-based controllers. This leads to control barrier functions (CBFs), which enforce safety on nonlinear systems via safety filters. The interplay between stability (CLFs) and safety (CBFs) will be studied from a variety of perspectives. Advanced topics that build upon these core results will be discussed, including: robust, adaptive and event-triggered control, layered control architectures, model-predictive control and hybrid systems. The control of robotic systems will be used as a motivating example.

Instructor: Ames

ME/CDS/EE 234 ab

Advanced Robotics: Planning

9 units (3-3-3) | second, third terms

Prerequisites: ME/CS/EE 133 b, or equivalent. ME/CS/EE 133 a preferred.

Advanced topics in robotic motion planning and navigation, including inertial navigation, simultaneous localization and mapping, Markov Decision Processes, Stochastic Receding Horizon Control, Risk-Aware planning, robotic coverage planning, and multi-robot coordination. Course work will consist of homework, programming projects, and labs. Given in alternate years. Not offered 2025-26.

ME/CDS/EE 235 ab

Advanced Robotics: Kinematics

9 units (3-3-3) | second, third terms

Prerequisites: ME/CS/EE 133 a, or equivalent.

Advanced topics in robot kinematics and robotic mechanisms. Topics include a Lie Algebraic viewpoint on kinematics and robot dynamics, a review of robotic mechanisms, and a detailed development of robotic grasping and manipulation. Given in alternate years.

Instructor: Burdick

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 2025-26.

Instructor: Staff

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. Given in alternate years. Not offered 2025-26.

Instructor: Staff

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. Not offered 2025-26.

Instructor: Staff

CDS 245

Data-driven Control

9 units (3-0-6) | second term

Prerequisites: CDS 131 and CDS 232.

Mathematical treatment of data-driven machine learning methods for controlling robotic and dynamical systems with various uncertainties. Gradient and least-squares estimators and variants for dynamical systems for system identification and residual learning. Adaptive control methods for online adaptation and combination with deep learning. Learning-based control certificates such as neural Lyapunov functions and neural contraction metrics. Not offered 2025-26.

Instructor: Staff

Ae/CDS/ME 251 ab

Closed Loop Flow Control

9 units (3-0-6 a, 1-6-1 b) | second, third term

Prerequisites: ACM 100 abc, Ae/APh/CE/ME 101 abc or equivalent.

This course seeks to introduce students to recent developments in theoretical and practical aspects of applying control to flow phenomena and fluid systems. Lecture topics in the second term drawn from: the objectives of flow control; a review of relevant concepts from classical and modern control theory; high-fidelity and reduced-order modeling; principles and design of actuators and sensors. Third term: laboratory work in open- and closed-loop control of boundary layers, turbulence, aerodynamic forces, bluff body drag, combustion oscillations and flow-acoustic oscillations. Not offered 2025-26.

CDS 270

Advanced Topics in Systems and Control

Hours and units by arrangement; third term

Topics dependent on class interests and instructor. May be repeated for credit. Not offered 2025-26.

Instructor: Staff

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: Staff

Published Date: Aug. 28, 2025