2017-18 Catalog

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.

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

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. Motivating case studies from tech, neuro, bio, and socioeconomic networks. Additional topics (as time permits): polytime scalability, sparsity, structure; layering and architecture; delay versus warning; communication and computing limits, quantization; actuator saturation, nonlinear dynamics, sum of squares, global stability, regions of attraction.

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.

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.

Emphasis on case studies from complex tech, bio, neuro, eco, and socioeconomic networks, particularly energy, internet, sensorimotor control, cell biology, medical physiology, and human and animal social organization. Layered architectures and distributed control. Tradeoffs, synthesis, and co-design due to parse and limited sensing, communications, computing, and actuation. Interplay between automation, optimization, control, modeling and system identification, and machine learning.

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.

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.

Topics dependent on class interests and instructor. May be repeated for credit.

Research in the field of control and dynamical systems. By arrangement with members of the staff, properly qualified graduate students are directed in research.