Sliding Mode Control and Geometrization Conjecture in Seismic Response

Abstract

The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov functions, the first associated with slipping in a finite period of time and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to minimization of the displacements of the floors.

Keywords

• Ricci flow
• Ricci solitons
• geodesics
• seismic waves