10,418 research outputs found
System Level Synthesis
This article surveys the System Level Synthesis framework, which presents a
novel perspective on constrained robust and optimal controller synthesis for
linear systems. We show how SLS shifts the controller synthesis task from the
design of a controller to the design of the entire closed loop system, and
highlight the benefits of this approach in terms of scalability and
transparency. We emphasize two particular applications of SLS, namely
large-scale distributed optimal control and robust control. In the case of
distributed control, we show how SLS allows for localized controllers to be
computed, extending robust and optimal control methods to large-scale systems
under practical and realistic assumptions. In the case of robust control, we
show how SLS allows for novel design methodologies that, for the first time,
quantify the degradation in performance of a robust controller due to model
uncertainty -- such transparency is key in allowing robust control methods to
interact, in a principled way, with modern techniques from machine learning and
statistical inference. Throughout, we emphasize practical and efficient
computational solutions, and demonstrate our methods on easy to understand case
studies.Comment: To appear in Annual Reviews in Contro
Quantum and classical resources for unitary design of open-system evolutions
A variety of tasks in quantum control, ranging from purification and cooling to quantum stabilisation and open-system simulation, rely on the ability to implement a target quantum channel over a specified time interval within prescribed accuracy. This can be achieved by engineering a suitable unitary dynamics of the system of interest along with its environment, which, depending on the available level of control, is fully or partly exploited as a coherent quantum controller. After formalising a controllability framework for completely positive trace-preserving quantum dynamics, we provide sufficient conditions on the environment state and dimension that allow for the realisation of relevant classes of quantum channels, including extreme channels, stochastic unitaries or simply any channel. The results hinge on generalisations of Stinespring's dilation via a subsystem principle. In the process, we show that a conjecture by Lloyd on the minimal dimension of the environment required for arbitrary open-system simulation, albeit formally disproved, can in fact be salvaged, provided that classical randomisation is included among the available resources. Existing measurement-based feedback protocols for universal simulation, dynamical decoupling and dissipative state preparation are recast within the proposed coherent framework as concrete applications, and the resources they employ discussed in the light of the general results
Optimal Control of Two-Player Systems with Output Feedback
In this article, we consider a fundamental decentralized optimal control
problem, which we call the two-player problem. Two subsystems are
interconnected in a nested information pattern, and output feedback controllers
must be designed for each subsystem. Several special cases of this architecture
have previously been solved, such as the state-feedback case or the case where
the dynamics of both systems are decoupled. In this paper, we present a
detailed solution to the general case. The structure of the optimal
decentralized controller is reminiscent of that of the optimal centralized
controller; each player must estimate the state of the system given their
available information and apply static control policies to these estimates to
compute the optimal controller. The previously solved cases benefit from a
separation between estimation and control which allows one to compute the
control and estimation gains separately. This feature is not present in
general, and some of the gains must be solved for simultaneously. We show that
computing the required coupled estimation and control gains amounts to solving
a small system of linear equations
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
Galerkin approximations for the optimal control of nonlinear delay differential equations
Optimal control problems of nonlinear delay differential equations (DDEs) are
considered for which we propose a general Galerkin approximation scheme built
from Koornwinder polynomials. Error estimates for the resulting
Galerkin-Koornwinder approximations to the optimal control and the value
function, are derived for a broad class of cost functionals and nonlinear DDEs.
The approach is illustrated on a delayed logistic equation set not far away
from its Hopf bifurcation point in the parameter space. In this case, we show
that low-dimensional controls for a standard quadratic cost functional can be
efficiently computed from Galerkin-Koornwinder approximations to reduce at a
nearly optimal cost the oscillation amplitude displayed by the DDE's solution.
Optimal controls computed from the Pontryagin's maximum principle (PMP) and the
Hamilton-Jacobi-Bellman equation (HJB) associated with the corresponding ODE
systems, are shown to provide numerical solutions in good agreement. It is
finally argued that the value function computed from the corresponding reduced
HJB equation provides a good approximation of that obtained from the full HJB
equation.Comment: 29 pages. This is a sequel of the arXiv preprint arXiv:1704.0042
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