Control and Dynamical Systems (CDS)

The option in control and dynamical systems (CDS) is open to students with an undergraduate degree in engineering, mathematics, or science. The qualifications of each applicant will be considered individually, and, after being enrolled, the student will arrange their program in consultation with a member of the faculty. In some cases the student may be required to make up undergraduate deficiencies in engineering science courses.

The CDS option, as part of the Computing and Mathematical Sciences department, emphasizes the interdisciplinary nature of modern theory of dynamical systems and control. The curriculum is designed to promote a broad knowledge of mathematical and experimental techniques in dynamical systems theory and control. In addition to taking courses in the CDS option, students must select a focus area (see below).

Students will be admitted to the option who expect to pursue the Ph.D. degree. The master’s degree may be awarded in exceptional cases. The awarding of this degree requires fulfilling the Institute requirements for a master’s degree, satisfying the focus requirements, and receiving a recommendation for awarding of the degree from the candidacy oral examination committee.

Institute requirements for the Ph.D. degree are described in the section on degree requirements. Approximately two years of course work are required, and two or more years are usually needed for preparation of the dissertation.

To be recommended for candidacy for the Ph.D. degree in control and dynamical systems, the student must, in addition to meeting the general Institute requirements, do the following:

• Complete the following courses: CDS 131, CDS 232, and CDS 231 or CDS 233.
• Complete the following CMS/ACM courses: CMS/ACM/IDS 107a, and CMS/ACM/EE 122 or CMS/ACM 117.
• Complete an additional 36 units in CDS or other advanced courses in systems theory, dynamical systems, robotics, and/or applied mathematics.
• Complete the focus requirement, consisting of at least 27 units in a particular area outside of CDS. Courses taken to satisfy the focus must represent a coherent program of advanced study in the chosen area. Possible areas include biological systems, computer science, environmental science, fluid dynamics, information and communications, networking, robotics, and space systems. The program of study must be approved by the student’s counseling committee and the option representative.
• Preliminary examination. Toward the end of the first year, all incoming students must take a preliminary examination administered by the faculty. Its purpose is to ensure a solid and broad knowledge in control and dynamical systems, and in the event of a deficiency, to direct the students to necessary courses and reading.
• Prepare a research progress report.
• Pass an oral examination on the major topic of the student’s research. The oral examination is normally taken no later than the end of the third year of graduate academic residence at the Institute.

In addition, CMS 290 is required for all CDS first year graduate students during each term (fall/winter/spring).

Upon admission, each student is assigned an adviser in the option, who will approve the initial course of study by the student. A preliminary exam given during the first year of study will be used to evaluate the student’s preparation for continued study.

The adviser will be replaced by a research adviser and a candidacy committee when the direction of specialization is determined, not later than the beginning of the second year. The candidacy exam is normally taken during the third year of study. The candidacy committee will be the judge of the completion of the engineering focus requirement, necessary before advancement to candidacy. The student’s candidacy committee may be reconstituted as the thesis committee after the candidacy exam has been successfully completed.

At the early stages of thesis preparation, the student’s thesis committee will meet as needed to advise the student of their progress and to deal with any problems that might have arisen.

A final oral examination will be given after the thesis has been formally completed. The thesis examination will be a defense of the doctoral thesis and a test of the candidate’s knowledge in the specialized field of research. Normally this defense will consist of a one-hour public lecture followed by an examination of the thesis by the thesis committee.

A student majoring in another option at the Institute may elect a subject minor in control and dynamical systems. The student must obtain approval from the CDS faculty of a course of study containing at least 54 units of courses that are required for the CDS Ph.D. (see Advancement to Candidacy) or advanced courses with a CDS listing.