\( \textcolor{blue}{OP}\textcolor{black}{timization} \quad \textcolor{blue}{O}\textcolor{black}{riented} \quad \textcolor{blue}{C}\textcolor{black}{ontrol} \)
Our recent research by Swapnil Tripathi, Mahmut Kudeyt, Alkım Gökçen, Savaş Şahin, and Özkan Karabacak has been accepted for publication. The paper proposes a novel semidefinite programming approach to certify local phase synchronization in generalized Kuramoto models on arcs, using the trace parametrization of trigonometric polynomials and Putinar’s Positivstellensatz.
The method establishes forward invariance on arcs and provides SDP certificates for stability, with examples verified using our arcSOS-t solver.
Our latest research by Alkım Gökçen, Savaş Şahin, Mahmut Kudeyt, Swapnil Tripathi, and Özkan Karabacak presents a novel dual Lyapunov-based closed-loop synchronization method for nonlinear chaotic systems.
Using semidefinite programming and sum-of-squares polynomials, we compute nonlinear state feedback to synchronize the Rössler system to a reference model, replacing chaotic behavior with a stable limit cycle. The approach is validated through simulations with 100 random initial conditions, bifurcation diagrams, and phase portraits.
This work demonstrates how the method can be adapted for more complex systems and opens new directions in synchronization control research.