Port-Hamiltonian formulation of shallow water equations with Coriolis force and topography (2008)
Pasumarthy, R., Ambati, V.R., Van Der Schaft, A.J.
We look into the problem of approximating the shallow water equations with Coriolis forces and topography. We model the system as an infinite-dimensional port-Hamiltonian system which is represented...
Parametrization of the regular equivalences of the canonical controller (2008)
Julius, A.A., Polderman, J.W., Van Der Schaft, A.J.
We study control problems for linear systems in the behavioral framework. Our focus is a class of regular controllers that are equivalent to the canonical controller. The canonical controller is a...
Parametrization of the regular equivalences of the canonical controller and its applications (2007)
Julius, A. A., Polderman, J. W., Van Der Schaft, A. J.
We study control problems for linear systems in the behavioral framework. Our focus is a class of regular controllers that are equivalent to the canonical controller. The canonical controller is a...
Composition of infinite-dimensional Dirac structures (2006)
Kurula, M., Van Der Schaft, A.J., Zwart, H.J.
In this paper, we define the Dirac structure and give some fundamental tools for its study.We then proceed by defining composition of ``split Dirac structures''. In the finite-dimensional case,...
Equivalence of switching linear systems by bisimulation (2006)
Pola, G., Van Der Schaft, A.J., Benedetto Di, M.D.
A general notion of hybrid bisimulation is proposed for the class of switching linear systems. Connections between the notions of bisimulation-based equivalence, state-space equivalence, algebraic...
Port-Hamiltonian systems: an introductory survey (2006)
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems...
Matching in the method of controlled Lagrangians and IDA-passivity based control (2006)
Blankenstein, G., Ortega, R., Van Der Schaft, A.J.
This paper reviews the method of controlled Lagrangians and the interconnection and damping assignment passivity based control (IDA-PBC)method. Both methods have been presented recently in the...
Sakamoto, N., Van Der Schaft, A.J.
In this report, a method for approximating the stabilizing solution of the Hamilton-Jacobi equation for integrable systems is proposed using symplectic geometry and a Hamiltonian perturbation...
A finite-dimensional approximation of the shallow-water equation: a port-Hamiltonian approach (2006)
Pasumarthy, R., Van Der Schaft, A.J.
We look into the problem of approximating a distributed parameter port-Hamiltonian system which is represented by a non-constant Stokes-Dirac structure. We here employ the idea where we use different...
Port Representations of the Telegrapher's Equations (2005)
Villegas, J.A., Zwart, H.J., Van Der Schaft, A.J.
This article studies the telegrapher's equations with boundary port variables. Firstly, a link is made between the telegrapher's equations and a skew-symmetric linear operator on a spatial domain....
Tools for analysis of Dirac structures on Hilbert spaces (2004)
Golo, G., Iftime, O.V., Zwart, H.J., Van Der Schaft, A.J.
In this paper tools for the analysis of Dirac structures on Hilbert spaces are developed. Some properties are pointed out and two natural representations of Dirac structures on Hilbert spaces are...
Fluid dynamical systems as Hamiltonian boundary control systems (2001)
Maschke, B.M.J., Van Der Schaft, A.J.
It is shown how the geometric framework for distributed-parameter port-controlled Hamiltonian systems, as recently obtained by the authors, can be adapted to formulate ideal adiabatic fluids with...
Hamiltonian formulation of distributed-parameter systems with boundary energy flow (2001)
Maschke, B.M.J., Van Der Schaft, A.J.
A Hamiltonian formulation of classes of distributed-parameter systems is presented, which incorporates the energy flow through the boundary of the spatial domain of the system, and which allows to...
Port controlled Hamiltonian representation of distributed parameter systems (2000)
Maschke, B.M.J., Van Der Schaft, A.J.
A port controlled Hamiltonian formulation of the dynamics of distributed parameter systems is presented, which incorporates the energy flow through the boundary of the domain of the system, and which...
Compositionality issues in discrete, continuous and hybrid systems (2000)
Van Der Schaft, A.J., Schumacher, J.M.
Models of complex dynamical systems are often built by connecting submodels of smaller parts. The key to this method is the operation of ``interconnection'' or ``composition'' which serves to define...
Discretization of control law for a class of variable structure control systems (2000)
Golo, G., Van Der Schaft, A.J., Milosavljević, Č.
A new method for the discretization of a class of continuous-time variable structure control systems, based on the linear complementarity theory, is proposed. The proposed method consists two steps....
Golo, G., Breedveld, P.C., Maschke, B.M.J., Van Der Schaft, A.J.
This paper deals with the extraction of input-output equations that describe a generalized junction structure. This is done by associating a Dirac structure to the generalized junction structure....
Symmetry and reduction in implicit generalized Hamiltonian systems (1999)
Blankenstein, G., Van Der Schaft, A.J.
In this paper the notion of symmetry for implicit generalized Hamiltonian systems will be studied and a reduction theorem, generalizing the `classical' reduction theorems of symplectic and...
Characterization of well-posedness of piecewise linear systems (1998)
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for...
Linearization of Hamiltonian and Gradient Systems (1984)
Necessary and sufficient conditions are derived in order to transform a nonlinear Hamiltonian or gradient system by a change of coordinates of its state space into a linear Hamiltonian or gradient...