531 research outputs found
Models and Feedback Stabilization of Open Quantum Systems
At the quantum level, feedback-loops have to take into account measurement
back-action. We present here the structure of the Markovian models including
such back-action and sketch two stabilization methods: measurement-based
feedback where an open quantum system is stabilized by a classical controller;
coherent or autonomous feedback where a quantum system is stabilized by a
quantum controller with decoherence (reservoir engineering). We begin to
explain these models and methods for the photon box experiments realized in the
group of Serge Haroche (Nobel Prize 2012). We present then these models and
methods for general open quantum systems.Comment: Extended version of the paper attached to an invited conference for
the International Congress of Mathematicians in Seoul, August 13 - 21, 201
Switching Quantum Dynamics for Fast Stabilization
Control strategies for dissipative preparation of target quantum states, both
pure and mixed, and subspaces are obtained by switching between a set of
available semigroup generators. We show that the class of problems of interest
can be recast, from a control--theoretic perspective, into a
switched-stabilization problem for linear dynamics. This is attained by a
suitable affine transformation of the coherence-vector representation. In
particular, we propose and compare stabilizing time-based and state-based
switching rules for entangled state preparation, showing that the latter not
only ensure faster convergence with respect to non-switching methods, but can
designed so that they retain robustness with respect to initialization, as long
as the target is a pure state or a subspace.Comment: 15 pages, 4 figure
Stabilizing feedback controls for quantum systems
No quantum measurement can give full information on the state of a quantum
system; hence any quantum feedback control problem is neccessarily one with
partial observations, and can generally be converted into a completely observed
control problem for an appropriate quantum filter as in classical stochastic
control theory. Here we study the properties of controlled quantum filtering
equations as classical stochastic differential equations. We then develop
methods, using a combination of geometric control and classical probabilistic
techniques, for global feedback stabilization of a class of quantum filters
around a particular eigenstate of the measurement operator
Non-smooth Control Barrier Functions for Stochastic Dynamical Systems
Uncertainties arising in various control systems, such as robots that are
subject to unknown disturbances or environmental variations, pose significant
challenges for ensuring system safety, such as collision avoidance. At the same
time, safety specifications are getting more and more complex, e.g., by
composing multiple safety objectives through Boolean operators resulting in
non-smooth descriptions of safe sets. Control Barrier Functions (CBFs) have
emerged as a control technique to provably guarantee system safety. In most
settings, they rely on an assumption of having deterministic dynamics and
smooth safe sets. This paper relaxes these two assumptions by extending CBFs to
encompass control systems with stochastic dynamics and safe sets defined by
non-smooth functions. By explicitly considering the stochastic nature of system
dynamics and accommodating complex safety specifications, our method enables
the design of safe control strategies in uncertain and complex systems. We
provide formal guarantees on the safety of the system by leveraging the
theoretical foundations of stochastic CBFs and non-smooth safe sets. Numerical
simulations demonstrate the effectiveness of the approach in various scenarios
Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance
Issued as Progress report, and Final report, Project no. E-21-67
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