47,603 research outputs found
An Exponential Quantum Projection Filter for Open Quantum Systems
An approximate exponential quantum projection filtering scheme is developed
for a class of open quantum systems described by Hudson- Parthasarathy quantum
stochastic differential equations, aiming to reduce the computational burden
associated with online calculation of the quantum filter. By using a
differential geometric approach, the quantum trajectory is constrained in a
finite-dimensional differentiable manifold consisting of an unnormalized
exponential family of quantum density operators, and an exponential quantum
projection filter is then formulated as a number of stochastic differential
equations satisfied by the finite-dimensional coordinate system of this
manifold. A convenient design of the differentiable manifold is also presented
through reduction of the local approximation errors, which yields a
simplification of the quantum projection filter equations. It is shown that the
computational cost can be significantly reduced by using the quantum projection
filter instead of the quantum filter. It is also shown that when the quantum
projection filtering approach is applied to a class of open quantum systems
that asymptotically converge to a pure state, the input-to-state stability of
the corresponding exponential quantum projection filter can be established.
Simulation results from an atomic ensemble system example are provided to
illustrate the performance of the projection filtering scheme. It is expected
that the proposed approach can be used in developing more efficient quantum
control methods
Motion Planning of Uncertain Ordinary Differential Equation Systems
This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems.
Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs.
The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space
Thermodynamic Geometry: Evolution, Correlation and Phase Transition
Under the fluctuation of the electric charge and atomic mass, this paper
considers the theory of the thin film depletion layer formation of an ensemble
of finitely excited, non-empty -orbital heavy materials, from the
thermodynamic geometric perspective. At each state of the local adiabatic
evolutions, we examine the nature of the thermodynamic parameters,
\textit{viz.}, electric charge and mass, changing at each respective
embeddings. The definition of the intrinsic Riemannian geometry and
differential topology offers the properties of (i) local heat capacities, (ii)
global stability criterion and (iv) global correlation length. Under the
Gaussian fluctuations, such an intrinsic geometric consideration is anticipated
to be useful in the statistical coating of the thin film layer of a desired
quality-fine high cost material on a low cost durable coatant. From the
perspective of the daily-life applications, the thermodynamic geometry is thus
intrinsically self-consistent with the theory of the local and global economic
optimizations. Following the above procedure, the quality of the thin layer
depletion could self-consistently be examined to produce an economic, quality
products at a desired economic value.Comment: 22 pages, 5 figures, Keywords: Thermodynamic Geometry, Metal
Depletion, Nano-science, Thin Film Technology, Quality Economic
Characterization; added 1 figure and 1 section (n.10), and edited
bibliograph
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