Related papers: Quadratic obstructions to controllability: from OD…
We show that a bilinear control system is approximately controllable if and only if it is controllable in $\mathbb{R}^{n}\setminus\{0\}$. We approach this problem by looking at the foliation made by the orbits of the system, and by showing…
We describe algorithms, and experimental strategies, for the Pareto optimal control problem of simultaneously driving an arbitrary number of quantum observable expectation values to their respective extrema. Conventional quantum optimal…
In this paper, we study the relative controllability of linear difference equations with multiple delays in the state by using a suitable formula for the solutions of such systems in terms of their initial conditions, their control inputs,…
We consider a linear Schr\"odinger equation, on a bounded interval, with bilinear control. Beauchard and Laurent proved that, under an appropriate non degeneracy assumption, this system is controllable, locally around the ground state, in…
This paper is devoted to study exact controllability of two one-dimensional coupled wave equations with first-order coupling terms with coefficients depending on space and time. We give a necessary and sufficient condition for both exact…
We consider systems of parabolic equations coupled in zero order terms in a star-like or a tree-like shape, with an internal control acting in only one of the equations. We obtain local exact controllability to the stationary solutions of…
While the optimization landscape of policy gradient methods has been recently investigated for partially observed linear systems in terms of both static output feedback and dynamical controllers, they only provide convergence guarantees to…
This paper is devoted to the controllability analysis of a class of linear control systems in a Hilbert space. It is proposed to use the minimum energy controls of a reduced lumped parameter system for solving the infinite dimensional…
We present a unified approach for determining and proving obstructions to small-time local controllability of scalar-input control systems. Our approach views obstructions to controllability as resulting from interpolation inequalities…
In quantum control theory, the fundamental issue of controllability covers the questions whether and under which conditions a system can be steered from one pure state into another by suitably tuned time evolution operators. Even though Lie…
We study a classical multiparticle system (such as Toda lattice) whose dynamics we intend to control by forces applied to few particles of the system. Various problem settings, typical for control theory are posed for this model; among…
The optimal time for the controllability of linear hyperbolic systems in one dimensional space with one-side controls has been obtained recently for time-independent coefficients in our previous works. In this paper, we consider linear…
This paper studies the partially observed stochastic optimal control problem for systems with state dynamics governed by Partial Differential Equations (PDEs) that leads to an extremely large problem. First, an open-loop deterministic…
Approximate controllability of the Euler equations is investigated by means of a finite set of actuators. It is proven that approximate controllability holds if we can find a saturating subset of actuators. The notion of saturating set is…
This paper is concerned with a linear quadratic (LQ, for short) optimal control problem with fixed terminal states and integral quadratic constraints. A Riccati equation with infinite terminal value is introduced, which is uniquely solvable…
This paper concerns some time optimal control problems of three different ordinary differential equations in $\mathbb{R}^2$. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to…
We derive existence results and first order necessary optimality conditions for optimal control problems governed by quasilinear parabolic PDEs with a class of first order nonlinearities that include for instance quadratic gradient terms.…
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…
The paper introduces and solves a structural controllability problem for continuum ensembles of linear time-invariant systems. All the individual linear systems of an ensemble are sparse, governed by the same sparsity pattern.…
Consider a finite ground set $E$, a set of feasible solutions $X \subseteq \mathbb{R}^{E}$, and a class of objective functions $\mathcal{C}$ defined on $X$. We are interested in subsets $S$ of $E$ that control $X$ in the sense that we can…