Hamiltonian discretization of boundary control systems

A fundamental problem in the simulation and control of complex physical systems containing distributed-parameter components concerns finite-dimensional approximation. Numerical methods for partial differential equations (PDEs) usually assume the boundary conditions to be given, while more often than not the interaction of the distributed-parameter components with the other components takes place precisely via the boundary. On the other hand, finite-dimensional approximation methods for infinite-dimensional input-output systems (e.g., in semi-group format) are not easily relatable to numerical techniques for solving PDEs, and are mainly confined to linear PDEs. In this paper we take a new view on this problem by proposing a method for spatial discretization of boundary control systems based on a particular type of mixed finite elements, resulting in a finite-dimensional input-output system. The approach is based on formulating the distributed-parameter component as an infinite-dimensio...

• Type: Journal
• Year: 2004
• Where: AUTOMATICA
• Authors: Goran Golo, Viswanath Talasila, Arjan van der Schaft, Bernhard Maschke
• Keywords: AUTOMATICA 2004, Distributed-parameter Component, Finite-dimensional Approximation, Mixed Finite Elements