Discrete port-controlled Hamiltonian dynamics and average passivation

Abstract

The paper discusses the modeling and control of port-controlled Hamiltonian dynamics in a pure discrete-time domain. The main result stands in a novel differential-difference representation of discrete port-controlled Hamiltonian systems using the discrete gradient. In these terms, a passive output map is exhibited as well as a passivity based damping controller underlying the natural involvement of discrete-time average passivity.

Interconnection through u-average passivity in discrete time

“…This study is preliminary to the development of new PBC strategies in discrete-time in terms of CbI and IDA-PBC by exploiting the u-average passivity properties of the interconnection. Further understanding of those properties in case of discrete port-Hamiltonian systems [22] is undergoing too.…”

Stabilization of Discrete Port-Hamiltonian Dynamics via Interconnection and Damping Assignment

“…The discrete port-Hamiltonian form we deal with has been recently proposed in [18]. Definition 2.2: A discrete single-input/single-output port-Hamiltonian system with smooth Hamiltonian function H(•) :…”

“…To handle these difficulties, a novel representation of port Hamiltonian dynamics in a purely discrete-time context has been proposed by the authors in [18]. In particular, such form has been shown to be suitably shaped to define a conjugate passivating output relying on the notion of discrete-time average passivity introduced in [19].…”

“…In particular, such form has been shown to be suitably shaped to define a conjugate passivating output relying on the notion of discrete-time average passivity introduced in [19]. An average passivitybased feedback has also been shown in [18] to get asymptotic stability by increasing the damping.…”

“…In the present paper, we further exploit the discrete-time structure proposed in [18] to discuss energy management strategies. More precisely, we set the problem of asymptotic stabilization towards a target equilibrium that corresponds to the energy minimum of a new Hamiltonian function.…”