Related papers: Periodic control laws for bilinear quantum systems…
The problem of quantum state preparation is one of the main challenges in achieving the quantum advantage. Furthermore, classically, for multi-level problems, our ability to solve the corresponding quantum optimal control problems is rather…
In this paper, we consider the application of optimal periodic control sequences to switched dynamical systems. The control sequence is obtained using a finite-horizon optimal method based on dynamic programming. We then consider Euler…
In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We…
Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…
These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…
In this paper we investigate when linearly independent eigenfunctions of the Schr\''odinger operator may have the same modulus. General properties are established and the one-dimensional case is treated in full generality. The study is…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
In this paper we propose an end-to-end algorithm for indirect data-driven control for bilinear systems with stability guarantees. We consider the case where the collected i.i.d. data is affected by probabilistic noise with possibly…
In this work, we consider the bilinear Schr\"odinger equation $i\partial_t\psi=-\Delta\psi+u(t)B\psi$ in the Hilbert space $L^2(\mathcal{G},\mathbb{C})$ with $\mathcal{G}$ an infinite graph. The Laplacian $-\Delta$ is equipped with…
We prove global internal controllability in large time for the nonlinear Schr\"odinger equation on some compact manifolds of dimension 3. The result is proved under some geometrical assumptions : geometric control and unique continuation.…
In this work we are concerned with solutions to the linear Schr\"odinger type system with mixed dispersion, the so-called biharmonic Schr\"odinger equation. Precisely, we are able to prove an exact control property for these solutions with…
This paper provides a framework for the control of quantum mechanical systems with scattering states, i.e., systems with continuous spectra. We present the concept and prove a criterion of the approximate strong smooth controllability. Our…
We analyze a fully discrete scheme based on the discontinuous (in time) Galerkin approach, which is combined with conforming finite element subspaces in space, for the distributed optimal control problem of the three-dimensional…
We derive conditional a priori error estimates of a wide class of finite volume and Runge-Kutta discontinuous Galerkin methods with abstract limiting for hyperbolic systems of conservation laws in 1D via the verification of weak consistency…
This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr\"odinger equation with coherent control. The open system's dynamics is governed by the…
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential…
Using techniques from the theory of von Neumann algebras, we propose a framework for addressing questions of controllability of bilinear systems on infinite dimensional Hilbert spaces. In the setup, we assume only that the drift and control…
We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an…
We develop and study a time-space discrete discontinuous Galerkin finite elements method to approximate the solution of one-dimensional nonlinear wave equations. We show that the numerical scheme is stable if a nonuniform time mesh is…
This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…