726 research outputs found
Equivalence of hybrid dynamical systems
A common theme in theoretical computer science (in particular, the theory of distributed processes and computer-aided verification) and in systems and control theory is to charac-terize systems which are ‘externally equivalent’. The intuitive idea is that we only want to distinguish between two systems if the distinction can be detected by an external syste
A geometric approach to differential Hamiltonian systems and differential Riccati equations
Motivated by research on contraction analysis and incremental
stability/stabilizability the study of 'differential properties' has attracted
increasing attention lately. Previously lifts of functions and vector fields to
the tangent bundle of the state space manifold have been employed for a
geometric approach to differential passivity and dissipativity. In the same
vein, the present paper aims at a geometric underpinning and elucidation of
recent work on 'control contraction metrics' and 'generalized differential
Riccati equations'
Port-Hamiltonian systems: an introductory survey
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 immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian systems is based on the canonical symplectic structure of the phase space or on a Poisson structure that is obtained by (symmetry) reduction of the phase space, in the case of a port-Hamiltonian system the geometric structure derives from the interconnection of its sub-systems. This motivates to consider Dirac structures instead of Poisson structures, since this notion enables one to define Hamiltonian systems with algebraic constraints. As a result, any power-conserving interconnection of port-Hamiltonian systems again defines a port-Hamiltonian system. The port-Hamiltonian description offers a systematic framework for analysis, control and simulation of complex physical systems, for lumped-parameter as well as for distributed-parameter models
A port-Hamiltonian approach to modeling and interconnections of canal systems
We show how the port-Hamiltonian formulation of distributed parameter systems, which incorporates energy flow through the boundary of the spatial domain of the system, can be used to model networks of canals and study interconnections of such systems. We first formulate fluid flow with 1-d spatial variable whose dynamics are given by the well-known shallow water equations, with respect to a Stokes-Dirac structure, and then consider a slightly more complicated case where we have a modified (a non-constant) Stokes-Dirac structure. We also explore the existence of Casimir functions for such systems and highlight their implications on control of fluid dynamical systems.
Structure-preserving model reduction of physical network systems by clustering
In this paper, we establish a method for model order reduction of a certain
class of physical network systems. The proposed method is based on clustering
of the vertices of the underlying graph, and yields a reduced order model
within the same class. To capture the physical properties of the network, we
allow for weights associated to both the edges as well as the vertices of the
graph. We extend the notion of almost equitable partitions to this class of
graphs. Consequently, an explicit model reduction error expression in the sense
of H2-norm is provided for clustering arising from almost equitable partitions.
Finally the method is extended to second-order systems
Geometry of Thermodynamic Processes
Since the 1970s contact geometry has been recognized as an appropriate
framework for the geometric formulation of the state properties of
thermodynamic systems, without, however, addressing the formulation of
non-equilibrium thermodynamic processes. In Balian & Valentin (2001) it was
shown how the symplectization of contact manifolds provides a new vantage
point; enabling, among others, to switch between the energy and entropy
representations of a thermodynamic system. In the present paper this is
continued towards the global geometric definition of a degenerate Riemannian
metric on the homogeneous Lagrangian submanifold describing the state
properties, which is overarching the locally defined metrics of Weinhold and
Ruppeiner. Next, a geometric formulation is given of non-equilibrium
thermodynamic processes, in terms of Hamiltonian dynamics defined by
Hamiltonian functions that are homogeneous of degree one in the co-extensive
variables and zero on the homogeneous Lagrangian submanifold. The
correspondence between objects in contact geometry and their homogeneous
counterparts in symplectic geometry, as already largely present in the
literature, appears to be elegant and effective. This culminates in the
definition of port-thermodynamic systems, and the formulation of
interconnection ports. The resulting geometric framework is illustrated on a
number of simple examples, already indicating its potential for analysis and
control.Comment: 23 page
A Finite Dimensional Approximation of the shallow water Equations: The port-Hamiltonian Approach
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 finite elements for the approximation of geometric variables (forms) describing a infinite-dimensional system, to spatially discretize the system and obtain a finite-dimensional port-Hamiltonian system. In particular we take the example of a special case of the shallow water equations.
Stability of dynamical distribution networks with arbitrary flow constraints and unknown in/outflows
A basic model of a dynamical distribution network is considered, modeled as a
directed graph with storage variables corresponding to every vertex and flow
inputs corresponding to every edge, subject to unknown but constant inflows and
outflows. We analyze the dynamics of the system in closed-loop with a
distributed proportional-integral controller structure, where the flow inputs
are constrained to take value in closed intervals. Results from our previous
work are extended to general flow constraint intervals, and conditions for
asymptotic load balancing are derived that rely on the structure of the graph
and its flow constraints.Comment: published in proceeding of 52nd IEEE Conference on Decision and
Control (CDC 2013). arXiv admin note: text overlap with arXiv:1403.5198,
arXiv:1403.520
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