8,212 research outputs found
On reciprocal systems and controllability
In this paper, we extend classical results on (i) signature symmetric
realizations, and (ii) signature symmetric and passive realizations, to systems
which need not be controllable. These results are motivated in part by the
existence of important electrical networks, such as the famous Bott-Duffin
networks, which possess signature symmetric and passive realizations that are
uncontrollable. In this regard, we provide necessary and sufficient algebraic
conditions for a behavior to be realized as the driving-point behavior of an
electrical network comprising resistors, inductors, capacitors and
transformers
The Dynamics of Group Codes: Dual Abelian Group Codes and Systems
Fundamental results concerning the dynamics of abelian group codes
(behaviors) and their duals are developed. Duals of sequence spaces over
locally compact abelian groups may be defined via Pontryagin duality; dual
group codes are orthogonal subgroups of dual sequence spaces. The dual of a
complete code or system is finite, and the dual of a Laurent code or system is
(anti-)Laurent. If C and C^\perp are dual codes, then the state spaces of C act
as the character groups of the state spaces of C^\perp. The controllability
properties of C are the observability properties of C^\perp. In particular, C
is (strongly) controllable if and only if C^\perp is (strongly) observable, and
the controller memory of C is the observer memory of C^\perp. The controller
granules of C act as the character groups of the observer granules of C^\perp.
Examples of minimal observer-form encoder and syndrome-former constructions are
given. Finally, every observer granule of C is an "end-around" controller
granule of C.Comment: 30 pages, 11 figures. To appear in IEEE Trans. Inform. Theory, 200
Controlling edge dynamics in complex networks
The interaction of distinct units in physical, social, biological and
technological systems naturally gives rise to complex network structures.
Networks have constantly been in the focus of research for the last decade,
with considerable advances in the description of their structural and dynamical
properties. However, much less effort has been devoted to studying the
controllability of the dynamics taking place on them. Here we introduce and
evaluate a dynamical process defined on the edges of a network, and demonstrate
that the controllability properties of this process significantly differ from
simple nodal dynamics. Evaluation of real-world networks indicates that most of
them are more controllable than their randomized counterparts. We also find
that transcriptional regulatory networks are particularly easy to control.
Analytic calculations show that networks with scale-free degree distributions
have better controllability properties than uncorrelated networks, and
positively correlated in- and out-degrees enhance the controllability of the
proposed dynamics.Comment: Preprint. 24 pages, 4 figures, 2 tables. Source code available at
http://github.com/ntamas/netctr
Empirical balanced truncation of nonlinear systems
Novel constructions of empirical controllability and observability gramians
for nonlinear systems for subsequent use in a balanced truncation style of
model reduction are proposed. The new gramians are based on a generalisation of
the fundamental solution for a Linear Time-Varying system. Relationships
between the given gramians for nonlinear systems and the standard gramians for
both Linear Time-Invariant and Linear Time-Varying systems are established as
well as relationships to prior constructions proposed for empirical gramians.
Application of the new gramians is illustrated through a sample test-system.Comment: LaTeX, 11 pages, 2 figure
Optimal control of the state statistics for a linear stochastic system
We consider a variant of the classical linear quadratic Gaussian regulator
(LQG) in which penalties on the endpoint state are replaced by the
specification of the terminal state distribution. The resulting theory
considerably differs from LQG as well as from formulations that bound the
probability of violating state constraints. We develop results for optimal
state-feedback control in the two cases where i) steering of the state
distribution is to take place over a finite window of time with minimum energy,
and ii) the goal is to maintain the state at a stationary distribution over an
infinite horizon with minimum power. For both problems the distribution of
noise and state are Gaussian. In the first case, we show that provided the
system is controllable, the state can be steered to any terminal Gaussian
distribution over any specified finite time-interval. In the second case, we
characterize explicitly the covariance of admissible stationary state
distributions that can be maintained with constant state-feedback control. The
conditions for optimality are expressed in terms of a system of dynamically
coupled Riccati equations in the finite horizon case and in terms of algebraic
conditions for the stationary case. In the case where the noise and control
share identical input channels, the Riccati equations for finite-horizon
steering become homogeneous and can be solved in closed form. The present paper
is largely based on our recent work in arxiv.org/abs/1408.2222,
arxiv.org/abs/1410.3447 and presents an overview of certain key results.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:1410.344
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