Data-driven stabilization of non-zero equilibrium for polynomial systems

Abstract

Most existing work on direct data-driven stabilization considers the equilibrium at the origin. When the desired equilibrium is not the origin, existing data-driven approaches often require performing coordinate transformation, or adding integrator action to the controller. As an alternative, this work addresses data-driven state feedback stabilization of any given assignable equilibrium via dissipativity theory. We show that for a polynomial system, if a data-driven stabilizer can be designed to render the origin globally asymptotically stable, then by modifying the stabilizer, we obtain a stabilizer for any given assignable equilibrium.