Prof. Emilia Fridman
Engineering
Research work #1:
Constructive methods for averaging with application to extremum seeking control
The existing results on averaging (that have been developed for about 60 years starting from the works of Bogoliubov and Mitropolsky) are qualitative: the original highly oscillating system is stable for small enough values of the parameter if the averaged system is stable. Our recent time-delay approach to averaging has provided the first efficient quantitative bounds on the small parameter making averaging-based control (including vibrational and extremum seeking control, stabilization by fast switching) reliable. The objective of this research is developing of new constructive methods to averaging of various classes of systems (linear/nonlinear ordinary or partial differential equations or time-delay systems) with applications to control problems including the hot topic of extremum seeking (on-line learning).
Extremum seeking is a powerful real-time optimization method that does not require a complete knowledge of the system.
Research work #2:
Constructive methods for control of PDE systems with applications.
Many important plants (e.g. flexible manipulators or heat transfer processes) are governed by partial differential equations (PDEs). PDE models may be useful for decentralized control of multi-agent systems. Some PDEs may not be robust with respect to arbitrary small time-delays in the feedback. Robust finite-dimensional controller design for PDEs is a challenging problem. Our recent constructive method for finite-dimensional observer-based controller design gave the first efficient and easily verifiable
quantitative bounds on observer dimension, the resulting performance and upper bounds on input/output delays that preserve it.
The objective of this research is developing of new constructive methods for robust control of various classes of PDEs with applications (including multi-agent deployment).
Engineering
- School of Electrical Engineering
Research work #1:
Time delays and data sampling are unavoidable in modern control systems that employ digital technology and in networked control systems, where the plant is controlled via communication network. Time-delay is usually a source of instability, but for some systems, the presence of delay can have a stabilizing effect.
My research topics include constructive methods for:
1) robust control of ODE and PDE systems in the presence of delays and data sampling;
2) averaging with application to extremum seeking (on-line learning), switched affine systems, and vibrational control.
Application Deadline: September 28, 2023
Strong background in control theory, applied math, and high computational skills. Good publication list
Good command of English and a passion for research and science.
Research work #2:
The existing results on averaging (that have been developed for about 60 years starting from the works of Bogoliubov and Mitropolsky) are qualitative: the original highly oscillating system is stable for small enough values of the parameter if the averaged system is stable. Our recent time-delay approach to averaging has provided the first efficient quantitative bounds on the small parameter making averaging-based control (including vibrational and extremum seeking control, and stabilization by fast switching) reliable. The objective of this research is developing of new constructive methods for averaging various classes of systems (linear/nonlinear ordinary or partial differential equations or time-delay systems) with applications to control problems, including the hot topic of extremum seeking (online learning).
Extremum seeking is a powerful real-time optimization method that does not require complete knowledge of the system.
The position includes several tasks, such as the derivation of new stability/performance analysis conditions and new controller design. In addition, the position would include scientific paper writing and potential participation in grant proposal preparation.
Application Deadline: October 27, 2023
BSc, MSC in Math or Engineering from the well-known universities. Excellent math and control theory background as well as good numerical skills. Also required are a good command of English, communication and personal relation skills, and a passion for research and science. Publications in the leading control journals are desirable.
Experience in time-delay systems or PDEs is an advantage.
