In this Project, we designed a control approach for chaotic systems which have an unknown governing equations and only one of the states of the system is measurable. We have used embedding theorem to elicit the dynamics of the system to reconstruct an auxiliary system. With some learning algorithm on the auxiliary system, we were able to find a proper controller for the original unknown system.
This project was done on both continuous-time and discrete-time system. Currently, I am supervising a M.Sc. student to apply this approach in designing heart pacemaker.
Publications:
Kaveh, H., H. Salarieh, and R. Hajiloo, On the control of unknown continuous time chaotic systems by applying Takens embedding theory. Chaos, Solitons & Fractals, 2018. 109: p. 53-57.
Kaveh, H. and H. Salarieh, Control of Continuous Time Chaotic Systems With Unknown Dynamics and Limitation on State Measurement. Journal of Computational and Nonlinear Dynamics, 2018. 14(1): p. 011007-011007-5.
Kaveh, H. and H. Salarieh, A New Approach To Design a Robust Control for Unknown Discrete Time Chaotic Systems Using Takens' Embedding Theorem . Applied mathematical modeling, (Under review process).