Passivity preserving balanced reduction for the finite and infinite dimensional port Hamiltonian systems

Abstract : In this thesis we have developed different structure preserving reduction methods for finite and infinite dimensional port Hamiltonian systems by using a balanced model reduction approach. In the first part we have defined a descriptor representation of port Hamiltonian systems with constraints. The balanced realization of the descriptor system has been used for reducing the port Hamiltonian descriptor system and conserving explicitly the constraint equations. In the second part, conditions have been derived on the weighting matrices of the LQG control problem such that the dynamical LQG controller is passive and has a port Hamiltonian realization. Two passive LQG control design methods have been suggested and one of them allows us to define a LQG balanced realization. Based on this realization, the effort constraint method has been used to reduce the LQG balanced port Hamiltonian system and obtain a reduced order passive LQG controller. In this way the closed-loop system is derived from the interconnection of 2 port Hamiltonian systems, hence the Hamiltonian structure has been preserved. In the third part, the proceeding results have been extended to a class of infinite dimensional port Hamiltonian system with bounded input operator. A passive LQG control design method for infinite dimensional port Hamiltonian system has been derived as by Control by Interconnection (CbI). Based on the balanced realization associated with this passive LQG control design, a finite dimensional approximation has been achieved and a reduced order passive LQG controller has been derived. As a consequence, the system in closed-loop with this reduced order LQG controller again admits a port Hamiltonian structure and satisfies the passivity
Document type :
Theses
Complete list of metadatas

Cited literature [86 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-01287237
Contributor : Abes Star <>
Submitted on : Saturday, March 12, 2016 - 2:34:06 PM
Last modification on : Saturday, May 18, 2019 - 1:39:44 AM
Long-term archiving on : Monday, June 13, 2016 - 1:54:18 PM

File

TH2015WuYongxin.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01287237, version 1

Citation

Yongxin Wu. Passivity preserving balanced reduction for the finite and infinite dimensional port Hamiltonian systems. Automatic. Université Claude Bernard - Lyon I, 2015. English. ⟨NNT : 2015LYO10278⟩. ⟨tel-01287237⟩

Share

Metrics

Record views

376

Files downloads

396