Related papers: Existence and uniqueness of control sets with a no…
For each vector $x\in \ell^{\infty}$, we can define the non-empty compact set $L_x$ of accumulation points of $x$. Given an infinite subset $A$ of $\mathbb{N}\backslash\{1\}$, we can therefore investigate under which conditions on $A$, the…
This paper addresses the fundamental question of determining the minimum number of distinct control laws required for global controllability of nonlinear systems that exhibit singularities in their feedback linearising controllers. We…
This paper establishes a unified framework connecting local controllability, necessary conditions for optimality, and attainability in free-time optimal control problems. The central object of our investigation is the $\Lambda$-set, which…
We prove the convergence of solutions of nonlocal conservation laws to their local entropic counterpart for a fundamentally extended class of nonlocal kernels when these kernels approach a Dirac distribution. The nonlocal kernels are…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
We address a linear control system under geometric constraints on control and study its reachable sets starting at zero time from the origin. The main result is the existence of a limit shape of the reachable sets as the terminal time tends…
We treat the periodic trajectory tracking problem: given a periodic trajectory of a control-affine, left-invariant driftless system in a compact and connected Lie group $G$ and an initial condition in $G$, find another trajectory of the…
A closed quantum system is defined as completely controllable if an arbitrary unitary transformation can be executed using the available controls. In practice, control fields are a source of unavoidable noise. Can one design control fields…
Non-singular horizonless ultracompact objects provide a simple resolution to the black holes singularity problem. It has been shown that, if these objects are compact enough to exhibit the presence of the light-ring required to mimic the…
In the paper, we introduce and address the problem of structural averaged controllability for linear ensemble systems. We provide examples highlighting the differences between this problem and others. In particular, we show that structural…
In this paper we will generalize the Kalman rank condition for the null controllability to $n$-coupled linear degenerate parabolic systems with constant coefficients, diagonalizable diffusion matrix, and $m$-controls. For that we prove a…
We prove a converse Lyapunov theorem for boundedness of reachability sets for a general class of control systems whose flow is Lipschitz continuous on compact intervals with respect to trajectory-dominated inputs. We show that this…
Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…
Control theory concerns with the question if and how it is possible to drive the behavior of a complex dynamical system. A system is said to be controllable if we can drive it from any initial state to any desired final state in finite…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
A covering of a group is a finite set of proper subgroups whose union is the whole group. A covering is minimal if there is no covering of smaller cardinality, and it is nilpotent if all its members are nilpotent subgroups. We complete a…
We study a class of non-autonomous boundary control and observation linear systems that are governed by non-autonomous multiplicative perturbations. This class is motivated by different fundamental partial differential equations, such as…
The reachable set for a finite dimensional quantum system is shown to be the orbit of the group corresponding to the internal and control Hamiltonians, even if this group is not compact.
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…
We show that a linear group without unipotent elements of infinite order possesses properties akin to those held by groups of non positive curvature. Moreover in positive characteristic any finitely generated linear group acts properly and…