631 research outputs found
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
Control landscape of measurement-assisted transition probability for a three-level quantum system with dynamical symmetry
Quantum systems with dynamical symmetries have conserved quantities which are
preserved under coherent controls. Therefore such systems can not be completely
controlled by means of only coherent control. In particular, for such systems
maximal transition probability between some pair of states over all coherent
controls can be less than one. However, incoherent control can break this
dynamical symmetry and increase the maximal attainable transition probability.
Simplest example of such situation occurs in a three-level quantum system with
dynamical symmetry, for which maximal probability of transition between the
ground and the intermediate state by only coherent control is , and by
coherent control assisted by incoherent control implemented by non-selective
measurement of the ground state is about , as was previously
analytically computed. In this work we study and completely characterize all
critical points of the kinematic quantum control landscape for this
measurement-assisted transition probability, which is considered as a function
of the kinematic control parameters (Euler angles). This used in this work
measurement-driven control is different both from quantum feedback and
Zeno-type control. We show that all critical points are global maxima, global
minima, saddle points and second order traps. For comparison, we study the
transition probability between the ground and highest excited state, as well as
the case when both these transition probabilities are assisted by incoherent
control implemented by measurement of the intermediate state
Information-theoretic approach to the study of control systems
We propose an information-theoretic framework for analyzing control systems
based on the close relationship of controllers to communication channels. A
communication channel takes an input state and transforms it into an output
state. A controller, similarly, takes the initial state of a system to be
controlled and transforms it into a target state. In this sense, a controller
can be thought of as an actuation channel that acts on inputs to produce
desired outputs. In this transformation process, two different control
strategies can be adopted: (i) the controller applies an actuation dynamics
that is independent of the state of the system to be controlled (open-loop
control); or (ii) the controller enacts an actuation dynamics that is based on
some information about the state of the controlled system (closed-loop
control). Using this communication channel model of control, we provide
necessary and sufficient conditions for a system to be perfectly controllable
and perfectly observable in terms of information and entropy. In addition, we
derive a quantitative trade-off between the amount of information gathered by a
closed-loop controller and its relative performance advantage over an open-loop
controller in stabilizing a system. This work supplements earlier results [H.
Touchette, S. Lloyd, Phys. Rev. Lett. 84, 1156 (2000)] by providing new
derivations of the advantage afforded by closed-loop control and by proposing
an information-based optimality criterion for control systems. New applications
of this approach pertaining to proportional controllers, and the control of
chaotic maps are also presented.Comment: 18 pages, 7 eps figure
ICR ANNUAL REPORT 2019 (Volume 26)[All Pages]
This Annual Report covers from 1 January to 31 December 201
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