A generic impulsive controller for Hamiltonian time-independent systems

Abstract

In a recent work Briozzo (2021) the author introduced an impulsive Floquet controller for periodic orbits in time-periodic Hamiltonian systems, which expresses the control law analytically in terms of the linearized dynamics about the reference orbit and makes full use of the center manifold enhancing performance by minimizing the energy of the actual orbit in the co-moving frame of the reference one. The purpose of the present work is to introduce an equivalent controller for Hamiltonian linear time-periodic systems obtained by linearization of a general time-independent Hamiltonian one about a periodic orbit, so incorporating the presence of a shear manifold associated to energy conservation and the ensuing non-isolation of periodic orbits. Like its preceding version, the controller defines a target subspace akin to the sliding surface of sliding mode controllers, onto which the system state vector is repeatedly sent by control impulses, and is generic in the sense that the target subspace and the control law are explicitly given for any possible decomposition of state space into a shear manifold and saddle, centre, or saddle-focus ones.