73,580 research outputs found
Well-posedness and Stability for Interconnection Structures of Port-Hamiltonian Type
We consider networks of infinite-dimensional port-Hamiltonian systems
on one-dimensional spatial domains. These subsystems of
port-Hamiltonian type are interconnected via boundary control and observation
and are allowed to be of distinct port-Hamiltonian orders .
Wellposedness and stability results for port-Hamiltonian systems of fixed order
are thereby generalised to networks of such. The abstract
theory is applied to some particular model examples.Comment: Submitted to: Control Theory of Infinite-Dimensional System. Workshop
on Control Theory of Infinite-Dimensional Systems, Hagen, January 2018.
Operator Theory: Advances and Applications. (32 pages, 5 figures
Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
We propose a Lie-algebraic duality approach to analyze non-equilibrium
evolution of closed dynamical systems and thermodynamics of interacting quantum
lattice models (formulated in terms of Hubbard-Stratonovich dynamical systems).
The first part of the paper utilizes a geometric Hilbert-space-invariant
formulation of unitary time-evolution, where a quantum Hamiltonian is viewed as
a trajectory in an abstract Lie algebra, while the sought-after evolution
operator is a trajectory in a dynamic group, generated by the algebra via
exponentiation. The evolution operator is uniquely determined by the
time-dependent dual generators that satisfy a system of differential equations,
dubbed here dual Schrodinger-Bloch equations, which represent a viable
alternative to the conventional Schrodinger formulation. These dual
Schrodinger-Bloch equations are derived and analyzed on a number of specific
examples. It is shown that deterministic dynamics of a closed classical
dynamical system occurs as action of a symmetry group on a classical manifold
and is driven by the same dual generators as in the corresponding quantum
problem. This represents quantum-to-classical correspondence. In the second
part of the paper, we further extend the Lie algebraic approach to a wide class
of interacting many-particle lattice models. A generalized Hubbard-Stratonovich
transform is proposed and it is used to show that the thermodynamic partition
function of a generic many-body quantum lattice model can be expressed in terms
of traces of single-particle evolution operators governed by the dynamic
Hubbard-Stratonovich fields. Finally, we derive Hubbard-Stratonovich dynamical
systems for the Bose-Hubbard model and a quantum spin model and use the
Lie-algebraic approach to obtain new non-perturbative dual descriptions of
these theories.Comment: 25 pages, 1 figure; v2: citations adde
Finite-time behavior of inner systems
In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller
- …