Senior Thesis in Control and Dynamical Systems
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.
Analysis and Design of Feedback Control Systems
Linear Systems Theory
Foundations of Algorithmic Decision-Making: Online Learning, Reinforcement Learning, and beyond
From game-playing agents to Large Language Models, Reinforcement Learning (RL) has become the engine behind many of the most significant breakthroughs in modern AI. This course provides a rigorous introduction to the mathematical foundations of algorithmic decision-making, moving from multi-armed bandits to reinforcement learning and concluding with special topics on how these principles are applied at scale to AI models and complex high-dimensional problems like robotics. Through a mixture of mathematical analysis and algorithmic implementation, students will gain the tools to both understand and develop the next generation of decision-making agents. The course expects students to be comfortable with probability, linear algebra, and basic optimization.
Independent Work in Control and Dynamical Systems
Research project in control and dynamical systems, supervised by a CDS faculty member.
Optimal Control and Reinforcement Learning
Robust Control Theory
Nonlinear Dynamics
Nonlinear Control
Advanced Robotics: Planning
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.
Advanced Robotics: Kinematics
Hybrid Systems: Dynamics and Control
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 2026-27.
Adaptive Control
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 2026-27.
System Identification
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 2026-27.
Data-driven Control
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 2026-27.
Algebraic & Topological Structures in Systems Theory
Closed Loop Flow Control
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 2026-27.
Advanced Topics in Systems and Control
Topics dependent on class interests and instructor. May be repeated for credit. Not offered 2026-27.
Research in Control and Dynamical Systems
Research in the field of control and dynamical systems. By arrangement with members of the staff, properly qualified graduate students are directed in research.