Nonlinear Hamiltonian Systems Under Sampling

• 成果类型: Article
• 署名作者: Monaco, Salvatore; Normand-Cyrot, Dorothee; Mattioni, Mattia; Moreschini, Alessio
• 署名单位: Sapienza University Rome; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3164985
• 发表日期: 2022
• 页码: 4598-4613
• 关键词: Jacobian matrices; Symmetric matrices; Linear systems; instruments; Energy conservation; Damping; computational modeling; computational methods; energy systems; Nonlinear systems; sampled-data control

摘要

This article investigates the transformation of Hamiltonian structures under sampling. It is shown that the exact sampled equivalent model associated to a given port-Hamiltonian continuous-time dynamics exhibits a discrete-time representation in terms of the discrete gradient, with the same energy function but modified damping and interconnection matrices. By construction, the proposed sampled-data dynamics guarantees exact matching of both the state evolutions and the energy-balance at all sampling instants. Its generalization to port-controlled Hamiltonian dynamics leads to characterize a new power conjugate output so recovering the concept of average passivation. On these bases, energy-management control strategies can be proposed. An energetic interpretation of the approach is confirmed by its formulation in the Dirac formalism. Two classical examples are worked out to validate the proposed sampled-data modeling in a comparative way with the literature.