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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, CDS 112 or CDS 140 (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: Murray.

CDS 101. Design and Analysis of Feedback Systems. 6 units (2-2-2); first term. Prerequisites: Ma 1 and Ma 2 or equivalents. An introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear vs. nonlinear models, and local vs. global behavior. This course is taught concurrently with CDS 110, but is intended for students who are interested primarily in the concepts and tools of control theory and not the analytical techniques for design and synthesis of control systems. Instructor: Burdick.

CDS 110. Introduction to Feedback Control Systems. 12 units (3-3-6); first 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: Burdick.

CDS 112. Control System Design. 9 units (3-2-4); second term. Prerequisites: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. Instructor: Doyle.

CDS 140. Introduction to Dynamics. 9 units (3-0-6); third term. Prerequisites: Ma 2/102 or equivalent, ACM 104. Basics topics in dynamics for continuous state systems in continuous and discrete time, using linear and nonlinear differential equations and maps. Topics include equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructor: Doyle.

CDS 190. Independent Work in Control and Dynamical Systems. Units to be arranged; first, second, third terms; maximum two terms. Prerequisite: CDS 110 or CDS 140. Research project in control and dynamical systems, supervised by a CDS faculty member.

CDS 212. Introduction to Modern Control. 9 units (3-2-4); second term. Prerequisites: Ma 2/102, ACM/CMS 104, CDS 110. Introduction to modern control systems with emphasis on the role of control in overall system analysis and design. Examples drawn from throughout engineering and science. Open versus closed loop control. State-space methods, time and frequency domain, stability and stabilization, realization theory. Time-varying and nonlinear models. Uncertainty and robustness. Instructor: Doyle.

CDS 213. Robust Control. 9 units (3-0-6); third term. Prerequisites: CDS 212. Linear systems, realization theory, time and frequency response, norms and performance, stochastic noise models, robust stability and performance, linear fractional transformations, structured uncertainty, optimal control, model reduction, m analysis and synthesis, real parametric uncertainty, Kharitonov's theorem, uncertainty modeling. Not offered 2016-17.

CDS 240. Nonlinear Dynamical Systems. 9 units (3-0-6); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Not offered 2016-17.

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: Staff.