3 papers
math.DS2021
Finding unstable periodic orbits: a hybrid approach with polynomial optimization
Mayur Lakshmi, Giovanni Fantuzzi, Sergei Chernyshenko +1
We present a novel method to compute unstable periodic orbits (UPOs) that optimize the infinite-time average of a given quantity for polynomial ODE systems. The UPO search procedur…
math.DS2019
Finding extremal periodic orbits with polynomial optimisation, with application to a nine-mode model of shear flow
Mayur Lakshmi, Giovanni Fantuzzi, Jesús Fernández-Caballero +2
Tobasco et al. [Physics Letters A, 382:382-386, 2018; see https://doi.org/10.1016/j.physleta.2017.12.023] recently suggested that trajectories of ODE systems that optimize the infi…
math.OC2015
Long-time Average Cost Control of Polynomial Systems: A Sum-of-squares-based Small-feedback Approach
Deqing Huang, Sergei Chernyshenko
The two main contributions of this paper are a proof of concept of the recent novel idea in the area of long-time average cost control, and a new method of overcoming the well-know…