1,616 research outputs found
Criteria for reachability of quantum states
We address the question of which quantum states can be inter-converted under
the action of a time-dependent Hamiltonian. In particular, we consider the
problem applied to mixed states, and investigate the difference between pure
and mixed-state controllability introduced in previous work. We provide a
complete characterization of the eigenvalue spectrum for which the state is
controllable under the action of the symplectic group. We also address the
problem of which states can be prepared if the dynamical Lie group is not
sufficiently large to allow the system to be controllable.Comment: 14 pages, IoP LaTeX, first author has moved to Cambridge university
([email protected]
Control of complex networks requires both structure and dynamics
The study of network structure has uncovered signatures of the organization
of complex systems. However, there is also a need to understand how to control
them; for example, identifying strategies to revert a diseased cell to a
healthy state, or a mature cell to a pluripotent state. Two recent
methodologies suggest that the controllability of complex systems can be
predicted solely from the graph of interactions between variables, without
considering their dynamics: structural controllability and minimum dominating
sets. We demonstrate that such structure-only methods fail to characterize
controllability when dynamics are introduced. We study Boolean network
ensembles of network motifs as well as three models of biochemical regulation:
the segment polarity network in Drosophila melanogaster, the cell cycle of
budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in
Arabidopsis thaliana. We demonstrate that structure-only methods both
undershoot and overshoot the number and which sets of critical variables best
control the dynamics of these models, highlighting the importance of the actual
system dynamics in determining control. Our analysis further shows that the
logic of automata transition functions, namely how canalizing they are, plays
an important role in the extent to which structure predicts dynamics.Comment: 15 pages, 6 figure
Controllability Canonical Forms of Linear Ensemble Systems
Ensemble control, an emerging research field focusing on the study of large
populations of dynamical systems, has demonstrated great potential in numerous
scientific and practical applications. Striking examples include pulse design
for exciting spin ensembles in quantum physics, neurostimulation for relieving
neurological disorder symptoms, and path planning for steering robot swarms.
However, the control targets in such applications are generally large-scale
complex and severely underactuated ensemble systems, research into which
stretches the capability of techniques in classical control and dynamical
systems theory to the very limit. This paper then devotes to advancing our
knowledge about controllability of linear ensemble systems by integrating tools
in modern algebra into the technique of separating points developed in our
recent work. In particular, we give an algebraic interpretation of the dynamics
of linear systems in terms of actions of polynomials on vector spaces, and this
leads to the development of the functional canonical form of matrix-valued
functions, which can also be viewed as the generalization of the rational
canonical form of matrices in linear algebra. Then, leveraging the technique of
separating points, we achieve a necessary and sufficient characterization of
uniform ensemble controllability for time-invariant linear ensemble systems as
the ensemble controllability canonical form, in which the system and control
matrices are in the functional canonical and block diagonal form, respectively.
This work successfully launches a new research scheme by adopting and tailoring
finite-dimensional methods to tackle control problems involving
infinite-dimensional ensemble systems, and lays a solid foundation for a more
inclusive ensemble control theory targeting a much broader spectrum of control
and learning problems in both scientific research and practice
Control and Synchronization of Neuron Ensembles
Synchronization of oscillations is a phenomenon prevalent in natural, social,
and engineering systems. Controlling synchronization of oscillating systems is
motivated by a wide range of applications from neurological treatment of
Parkinson's disease to the design of neurocomputers. In this article, we study
the control of an ensemble of uncoupled neuron oscillators described by phase
models. We examine controllability of such a neuron ensemble for various phase
models and, furthermore, study the related optimal control problems. In
particular, by employing Pontryagin's maximum principle, we analytically derive
optimal controls for spiking single- and two-neuron systems, and analyze the
applicability of the latter to an ensemble system. Finally, we present a robust
computational method for optimal control of spiking neurons based on
pseudospectral approximations. The methodology developed here is universal to
the control of general nonlinear phase oscillators.Comment: 29 pages, 6 figure
Asymptotic ensemble stabilizability of the Bloch equation
In this paper we are concerned with the stabilizability to an equilibrium
point of an ensemble of non interacting half-spins. We assume that the spins
are immersed in a static magnetic field, with dispersion in the Larmor
frequency, and are controlled by a time varying transverse field. Our goal is
to steer the whole ensemble to the uniform "down" position. Two cases are
addressed: for a finite ensemble of spins, we provide a control function (in
feedback form) that asymptotically stabilizes the ensemble in the "down"
position, generically with respect to the initial condition. For an ensemble
containing a countable number of spins, we construct a sequence of control
functions such that the sequence of the corresponding solutions pointwise
converges, asymptotically in time, to the target state, generically with
respect to the initial conditions. The control functions proposed are uniformly
bounded and continuous
Effect of correlations on network controllability
A dynamical system is controllable if by imposing appropriate external
signals on a subset of its nodes, it can be driven from any initial state to
any desired state in finite time. Here we study the impact of various network
characteristics on the minimal number of driver nodes required to control a
network. We find that clustering and modularity have no discernible impact, but
the symmetries of the underlying matching problem can produce linear, quadratic
or no dependence on degree correlation coefficients, depending on the nature of
the underlying correlations. The results are supported by numerical simulations
and help narrow the observed gap between the predicted and the observed number
of driver nodes in real networks
Quantum control theory and applications: A survey
This paper presents a survey on quantum control theory and applications from
a control systems perspective. Some of the basic concepts and main developments
(including open-loop control and closed-loop control) in quantum control theory
are reviewed. In the area of open-loop quantum control, the paper surveys the
notion of controllability for quantum systems and presents several control
design strategies including optimal control, Lyapunov-based methodologies,
variable structure control and quantum incoherent control. In the area of
closed-loop quantum control, the paper reviews closed-loop learning control and
several important issues related to quantum feedback control including quantum
filtering, feedback stabilization, LQG control and robust quantum control.Comment: 38 pages, invited survey paper from a control systems perspective,
some references are added, published versio
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