15,479 research outputs found
Quantum Markovian Subsystems: Invariance, Attractivity, and Control
We characterize the dynamical behavior of continuous-time, Markovian quantum
systems with respect to a subsystem of interest. Markovian dynamics describes a
wide class of open quantum systems of relevance to quantum information
processing, subsystem encodings offering a general pathway to faithfully
represent quantum information. We provide explicit linear-algebraic
characterizations of the notion of invariant and noiseless subsystem for
Markovian master equations, under different robustness assumptions for
model-parameter and initial-state variations. The stronger concept of an
attractive quantum subsystem is introduced, and sufficient existence conditions
are identified based on Lyapunov's stability techniques. As a main control
application, we address the potential of output-feedback Markovian control
strategies for quantum pure state-stabilization and noiseless-subspace
generation. In particular, explicit results for the synthesis of stabilizing
semigroups and noiseless subspaces in finite-dimensional Markovian systems are
obtained.Comment: 16 pages, no figures. Revised version with new title, corrected
typos, partial rewriting of Section III.E and some other minor change
A Tractable Fault Detection and Isolation Approach for Nonlinear Systems with Probabilistic Performance
This article presents a novel perspective along with a scalable methodology
to design a fault detection and isolation (FDI) filter for high dimensional
nonlinear systems. Previous approaches on FDI problems are either confined to
linear systems or they are only applicable to low dimensional dynamics with
specific structures. In contrast, shifting attention from the system dynamics
to the disturbance inputs, we propose a relaxed design perspective to train a
linear residual generator given some statistical information about the
disturbance patterns. That is, we propose an optimization-based approach to
robustify the filter with respect to finitely many signatures of the
nonlinearity. We then invoke recent results in randomized optimization to
provide theoretical guarantees for the performance of the proposed filer.
Finally, motivated by a cyber-physical attack emanating from the
vulnerabilities introduced by the interaction between IT infrastructure and
power system, we deploy the developed theoretical results to detect such an
intrusion before the functionality of the power system is disrupted
Dynamic Energy Management
We present a unified method, based on convex optimization, for managing the
power produced and consumed by a network of devices over time. We start with
the simple setting of optimizing power flows in a static network, and then
proceed to the case of optimizing dynamic power flows, i.e., power flows that
change with time over a horizon. We leverage this to develop a real-time
control strategy, model predictive control, which at each time step solves a
dynamic power flow optimization problem, using forecasts of future quantities
such as demands, capacities, or prices, to choose the current power flow
values. Finally, we consider a useful extension of model predictive control
that explicitly accounts for uncertainty in the forecasts. We mirror our
framework with an object-oriented software implementation, an open-source
Python library for planning and controlling power flows at any scale. We
demonstrate our method with various examples. Appendices give more detail about
the package, and describe some basic but very effective methods for
constructing forecasts from historical data.Comment: 63 pages, 15 figures, accompanying open source librar
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