Asymptotic Tracking of Periodic Operation Based on Control Contraction Metrics*

Periodic operations can be beneficial to chemical and biological systems, leading to better efficiency and plant economy compared to steady state operation. In this paper, the tracking control of desired periodic operation based on control contraction metrics is considered. A relaxation method is proposed to convert the nonconvex control synthesis problem into a convex sum-of-squares programming. Finally, an application to a Lotka-Volterra system of sustained oscillating chemical reactions is presented for illustration. The main advantages of this approach include: (1) the feedback information is geodesics, which is a general deviation considering local nonlinearity; (2) the differential state feedback control law is reference trajectory independent; (3) the control design can be carried out via numerical optimization.