Systems and Control - Minor program out-line

3 core courses: Semesters 3, 4 and 5.

1. SC 201 (Semester 3) - Mathematical structures for systems andcontrolPre-requisite: None.Content: Groups (definition, matrix groups - GL(n,R), SO(3), SE(3),the commutator, the Lie algebras so(3) and se(3), applications: robotics,aerospace problems), vector spaces ( definition, linear dependence, basis,subspaces, dual spaces, linear transformations, matrix representations,similarity transformations, eigen values, applications: control and sig-nal processing) and, elements of differential geometry (n-surfaces in Eu-clidean space, tangent vectors, vector fields, co-vector fields, geodesics,covariant derivative, applications: robotics, dynamical systems and con-trol.)Textbooks: 1. Finite Dimensional Vector Spaces - P. R. Halmos, Springer1984, and 2. Elementary Topics in Differential Geometry - J. A. Thorpe,Springer 1979.

2. SC 202 (Semester 4) - Signals and feedback systems.Pre-requisite: SC 201Content: Signals and systems and their interconnections, convolution,differential and difference equations, state variable models, Fourier, Laplaceand z-transforms, regions of convergence, the transfer function, linearfeedback systems, the stability problem, the Routh-Hurwitz and rootlocus method.Textbook: Signals and Systems - S. Haykin and B. Van Veen, John Wi-ley, 2003.Signals and Systems - A. V. Oppenheim and A. S. Willsky, PrenticeHall, 1996.

3. SC 301 (Semester 5) - Linear and nonlinear systemsPre-requisite: SC 201 and 202.Content: Linear state-space models, solutions, controllability, observ-ability, state-feedback (both continuous and discrete domain.) Nonlin-ear state-space models, phase plane diagrams, existence and uniquenessof solutions, Lyapunov stability.Textbook: 1. Linear Systems Theory - C .T. Chen, and 2. NonlinearSystems - H. Khalil, Prentice Hall, 2002.

2 elective courses from the list attached: Semesters 6, 7 and 8.(This list is not exhaustive and we propose to include a few more.)

1

1. SC 627 - Motion Planning and Coordination of Autonomous Ve-hicles

2. SC 624 - Differential Geometric Methods in Control

3. SC 613 - Multivariable Control Systems

4. SC 700 - Embedded Control Systems

5. SC 602 - Control of Nonlinear Dynamical Systems

6. SC 605 - Optimization-based Control of Stochastic Systems

7. SC 607 - Optimization

8. SC 612 - Introduction to Linear Filtering and Beyond

9. SC 616 - Large Scale Systems

10. SC 617 - Adaptive Control Theory

11. SC 623 - Optimal and Robust Control

12. CL 692 - Digital Control

13. CL 686 - Advanced Process Control

14. EE 640 - Multivariable Control Systems

15. EE 636 - Matrix Computations

2