Control + Dynamical Systems

Control and Dynamical Systems is a multidisciplinary program offered by the California Institute of Technology that provides students with a comprehensive understanding of the principles and applications of systems control and dynamical analysis. This program is designed to prepare students for careers in research, development, and engineering across a broad range of fields including robotics, aerospace, electrical engineering, mechanical engineering, and applied physics. The curriculum combines rigorous coursework in mathematics, physics, and engineering, with hands-on research opportunities that enable students to apply theoretical concepts to real-world problems. Students gain proficiency in modeling complex systems, analyzing their stability and behavior, and designing control strategies to guide system performance. The program emphasizes both foundational theories and emerging technologies, ensuring graduates are well-equipped to innovate and lead in rapidly evolving technological landscapes. Core courses cover topics such as system theory, control design, dynamical systems, and signal processing. Advanced electives allow exploration in specialized areas such as nonlinear control, robotics, bioengineering, and computational methods. The program also fosters a collaborative research environment, encouraging students to work with faculty on cutting-edge projects that often have significant interdisciplinary components. Through seminars, workshops, and industry collaborations, students develop critical problem-solving skills, gain insight into current research trends, and prepare for careers in academia, industry, or entrepreneurship. Graduates of the Control and Dynamical Systems program leave with a solid foundation in analysis and design of complex systems, making them valuable contributors to technological innovation and scientific discovery.

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.

• Admission to Candidacy. 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:
  1. Complete the following courses: CMS/ACM 107, CMS/ACM 113, CMS/ACM 117; CDS 140 and CDS 212.
  2. Complete an additional 45 units in CDS or other advanced courses in systems theory, dynamical systems, and/or applied mathematics.
  3. Complete the focus requirement, consisting of at least 27units 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.
  4. Prepare a research progress report.
  5. 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 CMS/ACM/CDS/CS first year graduate students during each term (fall/winter/spring).

• Advising and Thesis Supervision. 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 his or her 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 onehour public lecture followed by an examination of the thesis by the thesis committee.
• Subject Minor. A student majoring in another option at the Institute may elect a subject minor in control and dynamical systems. He or she 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

Requirements

• Statement of Purpose
• Include payment of the application fee or submit a fee waiver request. 
• Three letters of recommendation from individuals familiar with your academic and/or work performance are required for all applicants. 
• Transcripts from all colleges or universities attended are required. Transcripts may be sent directly from the Registrar of the institution you attended or transcripts issued directly to the applicant, and so marked, are acceptable, and can be submitted online following the electronic submission process. If you attended Caltech as an undergraduate, you must request an official transcript from the Office of the Registrar. We cannot obtain one on your behalf. 
• Attach a CV or resume
• TOEFL

The California Institute of Technology (Caltech) offers a comprehensive financial aid program to support students pursuing the Control and Dynamical Systems degree. Undergraduate students primarily benefit from a need-based financial aid system, which includes grants, scholarships, work-study opportunities, and loans. The Institute is committed to meeting 100% of demonstrated financial need for admitted students, ensuring that financial barriers do not prevent talented individuals from enrolling. Financial aid packages are determined through a thorough assessment of family income, assets, and other relevant factors, coordinated by Caltech’s Office of Financial Aid.

Graduate students enrolled in the Control and Dynamical Systems program also have access to various funding opportunities. These include fellowships, research assistantships, teaching assistantships, and departmental scholarships. Many graduate students finance their studies through a combination of these sources, with stipends provided to support living expenses. Caltech emphasizes a merit-based approach for graduate funding, awarding fellowships based on academic achievement and research potential, which do not require repayment.

In addition to institutional aid, students may explore external sources of funding such as government scholarships, private foundations, and industry sponsorships. The Institute's close ties with industry partners also facilitate internship and research opportunities that can supplement academic funding. Foreign students are eligible for the same financial aid options, with additional support available through specific programs aimed at international students.

Caltech’s financial aid process for prospective students begins early, with clear application procedures and deadlines. For undergraduates, prospective students submit the Free Application for Federal Student Aid (FAFSA) and the College Scholarship Service (CSS) Profile to determine eligibility. Graduate applicants typically indicate their funding preferences during the application process, and the department works with prospective students to identify suitable funding sources.

Overall, Caltech’s financing studies are designed to make education accessible and sustainable, providing comprehensive financial support to capable students regardless of their economic background. This ensures a diverse and vibrant academic community committed to advancing control and dynamical systems research and education.

Control and Dynamical Systems at the California Institute of Technology is an interdisciplinary program that focuses on the mathematical modeling, analysis, and control of complex dynamical systems across engineering and scientific disciplines. This program prepares students to address real-world challenges involving the design, analysis, and optimization of systems that evolve over time, such as robotic systems, aerospace vehicles, biological systems, and networked systems. The curriculum combines coursework in control theory, dynamical systems, applied mathematics, engineering principles, and computer science, providing students with a solid foundation in both theoretical and practical aspects of system control and analysis.

Students in this program gain expertise in diverse topics, including nonlinear control, stochastic processes, system identification, optimization, signal processing, and real-time control systems. The program emphasizes an interdisciplinary approach, encouraging collaboration across different fields to develop innovative solutions to complex challenges. Participants frequently engage in research projects that involve modeling complex phenomena, developing control algorithms, and implementing solutions in experimental or simulated environments.

The faculty involved in Control and Dynamical Systems at Caltech are leading experts in their fields, guiding students through cutting-edge research and fostering an environment of innovation. Typically, the program offers a combination of coursework, research opportunities, seminars, and workshops aimed at enhancing students' analytical and practical skills. Graduates of the program are well-equipped for careers in academia, industry, and government agencies, where skills in control systems and dynamical analysis are highly valued.

The program also emphasizes the importance of computational tools, including simulation software and programming languages, to analyze and design advanced control systems. Interdisciplinary collaboration is facilitated through joint projects with other engineering and science departments on campus, enabling students to apply their knowledge to real-world problems. Overall, the Control and Dynamical Systems program at Caltech is designed to produce highly skilled professionals capable of advancing the understanding and application of control theory in various technological contexts.