2018-19 Catalog: Control & 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.

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.

Basic system concepts; state-space and I/O representation. Properties of linear systems, including stability, performance, robustness. Reachability, observability, minimality, state and output-feedback.

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).

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. 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.

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.

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.

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.