CDS 110 ab . Introduction to Control of Physical Systems. 9 units (3-0-6); first, second terms. Prerequisites: AMa 95 abc. Application of feedback analysis and design to physical systems, including classical control theory in the frequency and time domains. Stability; performance; methods based on Bode, Nyquist, and root-locus diagrams. Representation in state space. Analog and discrete dynamical systems. Introduction to multivariable control.

CDS 111. Applications of Control Technology. 9 units (3-3-3); third term. Prerequisite: CDS 110 or equivalent. Application of modern control design techniques to physical systems. The goal of this course is to teach students how to design and implement feedback controllers on physical systems, and to allow students to evaluate different control design methodologies on experimental hardware. (Not offered 1998-1999)

CDS 140. Introduction to Dynamics. 9 units (3-0-6); first term. Prerequisite: AMa 95 (or AM 114) Basic topics in dynamical systems in Euclidean space, including equilibria, stability, Liapunov functions, periodic solutions, Poincare-Bendixon theory, Poincare maps. Attractors and structural stability. The Euler-Lagrange equations, energy as a Liapunov function, conservation laws. Introduction to simple bifurcations; eigenvalue crossing conditions. Discussion of bifurcations in applications.

CNS/CDS 177. Special Topics in Computation and Neural Systems and Control and Dynamical Systems. Units to be arranged; first, second, or third terms. Students may register with permission of the responsible faculty member.

CDS 201 Applied Operator Theory. 9 units (3-0-6) first term. Prerequisites: AM 95, AM 114, or equivalent. Invariant subspaces, Jordan form, Cayley-Hamilton theorem, matrix exponential, singular value decompoisiton, some Banach and Hilbert spaces, operators, duals, the inverse and implicit function theorems.

CDS 202 Geometry of Nonlinear Systems. 9 units (3-0-6) second term. Prerequisites: CDS 201, or AM 125. Basic differential geometry oriented toward applications in control and dynamical systems. Topics include smooth manifolds and mappings, tangent and normal bundles, transversality. Vector fields and flows. Distributions and Frobenius' theorem. Matrix LIe groups and Lie algebras. Exterior differential forms, Stokes' theorem.

CDS 205 Geometric Mechanics. 9 units (3-0-6) third term. Prerequisites: CDS 202, CDS 140. The geometry and dynamics of Lagrangian and Hamiltonian systems, including symplectic and Poisson manifolds, variational principles, Lie groups, momentum maps, rigid-body dynamics, Euler-Poincare equations, stability, and an introduction to reducion theory. More advanced topics will include (taught in a course the following year) reduction theory, fluid dynamics, the energy momentym method, geometric phases, bifurcation theory for mechanical systems, and nonholonomic systems.

CDS 212 Introduction to Modern Control. 9 units (3-0-6) first term. Prerequisites: AMa 95, AM 114, or equivalent; CDS 110ab or equivalent. 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 modesl. Uncertainty and robustness.

CDS 213 Robust Control. 9 units (3-0-6) second term. Prerequisites: CDS 212, CDS 201. 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, $\mu$ analysis and synthesis, real parametric uncertainty, Kharitonov's theorem, uncertainty modeling.

CDS 221 Control of Nonlinear Systems. 9 units (3-0-6) third term (alternate years). Prerequisites: CDS 140, CDS 201, CDS 202 or Am 125a, CDS 212. Analysis and design of nonlinear control systems using Lyapunov theory and differential geometric methods. Controllability, observability, feedback linearization, invariant distributions, disturbance decoupling. Second-order systems, describing functions, direct and indirect method of Lyapunov, I/O stability, adaptive control.

CDS 224 System Identification. 9 units (3-0-6) third term (alternate years). Prerequisites: CDS 201, CDS 212. Review of probability, statistics, and stochastic processes. Optimal predictors for input-output and state-space models. Nonparametric, prediction-error, and correlation methods. Asymptotic analysis. Computational aspects. Recursive identification. Experiment design. Model validation and closed-loop identification.

CDS 240 Nonlinear Dynamical Systems and Chaos. 9 units (3-0-6); second term. Prerequisite: CDS 140. Normal form theory, center manifold theory, codimension two and larger bifurcation theory, normally hyperbolic invar iant manifolds, nonlinear resonance, the KAM theorem, method of averaging, symbolic dynamics, the Smale horseshoe, Melnikov's method, homoclinic and heteroclinic orbits, chaos, Liapunov exponents, strange attractors, global bifurcations.

CDS 242. Hamiltonian Dynamics. 9 units (3-0-6); third term (alternate years). Prerequisites: CDS 240. Hamiltonian stability and bifurcation theory, Poincare-Birkhoff normal forms, KAM theory, Nekhoroshev theory, Arnold diffusion.

CDS 270. Advanced Topics in Systems and Control. Prerequisite: CDS 102. Topics dependent on class interests and instructor. Can be repeated for credit.

CDS 280. Advanced Topics in Dynamical Systems Theory. Prerequisite: consent of instructor. Topics will vary according to student and instructor interest. Examples include chaotic transport theory, invariant manifold techniques, multidimensional geometric perturbation theory, the dynamics of coupled oscillators, rigid-body dynamics, numerical methods in dynamical systems theory. Can be repeated for credit.

CDS 300abc. 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.