1,038 research outputs found
Time-Minimal Control of Dissipative Two-level Quantum Systems: the Generic Case
The objective of this article is to complete preliminary results concerning
the time-minimal control of dissipative two-level quantum systems whose
dynamics is governed by Lindblad equations. The extremal system is described by
a 3D-Hamiltonian depending upon three parameters. We combine geometric
techniques with numerical simulations to deduce the optimal solutions.Comment: 24 pages, 16 figures. submitted to IEEE transactions on automatic
contro
A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations in Infinite Horizon
A linear-quadratic (LQ, for short) optimal control problem is considered for
mean-field stochastic differential equations with constant coefficients in an
infinite horizon. The stabilizability of the control system is studied followed
by the discussion of the well-posedness of the LQ problem. The optimal control
can be expressed as a linear state feedback involving the state and its mean,
through the solutions of two algebraic Riccati equations. The solvability of
such kind of Riccati equations is investigated by means of semi-definite
programming method.Comment: 40 page
Time-minimal control of dissipative two-level quantum systems: The Integrable case
The objective of this article is to apply recent developments in geometric
optimal control to analyze the time minimum control problem of dissipative
two-level quantum systems whose dynamics is governed by the Lindblad equation.
We focus our analysis on the case where the extremal Hamiltonian is integrable.Comment: 24 pages, 6 figure
Dynamic programming approach to principal-agent problems
We consider a general formulation of the Principal-Agent problem with a
lump-sum payment on a finite horizon, providing a systematic method for solving
such problems. Our approach is the following: we first find the contract that
is optimal among those for which the agent's value process allows a dynamic
programming representation, for which the agent's optimal effort is
straightforward to find. We then show that the optimization over the restricted
family of contracts represents no loss of generality. As a consequence, we have
reduced this non-zero sum stochastic differential game to a stochastic control
problem which may be addressed by the standard tools of control theory. Our
proofs rely on the backward stochastic differential equations approach to
non-Markovian stochastic control, and more specifically, on the recent
extensions to the second order case
Asymptotic control theory for a system of linear oscillators
We present an asymptotic control theory for a system of an arbitrary number
of linear oscillators under a common bounded control. We suggest a design
method of a feedback control for this system. By using the DiPerna-Lions theory
of singular ODEs, we prove that the suggested control law correctly defines the
motion of the system. The obtained control is asymptotically optimal: the ratio
of the motion time to zero under this control to the minimum one is close to 1
if the initial energy of the system is large. The results are partially based
on a new perturbation theory of observable linear systems.Comment: 34 pages; published versio
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