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We study the set of intrinsic singularities of flat affine systems with $n-1$ controls and $n$ states using the notion of Lie-B\"acklund atlas, previously introduced by the authors. For this purpose, we prove two easily computable…
This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side. Under precise and generic assumptions on the boundary conditions on the other side, we previously…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
This note considers the finite linear independence of coherent systems associated to discrete subgroups. We show by simple arguments that such coherent systems of amenable groups are linearly independent whenever the associated twisted…
In this paper, we present a geometric approach for computing the controlled invariant set of a continuous-time control system. While the problem is well studied for in the ellipsoidal case, this family is quite conservative for constrained…
This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems,…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
Left-invariant optimal control problems on Lie groups form an important class of problems with big symmetry group. They are interesting from the theoretical point of view since they often can be completely studied, and general features can…
We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs (K,Q). If the stable subgroup of the uncontrolled system is closed and K has positive…
We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of…
Let us consider a linear control system \Sigma on a connected Lie group G. It is known that the accessibility set A from the identity e is in general not a semigroup. In this article we associate a new algebraic object S to \Sigma which…
In this paper, we study the controllability properties and the Lie algebra structure of networks of particles with spin immersed in an electro-magnetic field. We relate the Lie algebra structure to the properties of a graph whose nodes…
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…
The purpose of this paper is to present explicitly the solution curve for affine control systems on Lie groups under the assumption that automorphisms associated to the linear vector fields commutes. If we assume that the derivations…
In this article, we study linear control systems on a 4-dimensional solvable Lie group. Our motivation stems from the model introduced in \cite{baspinar}, which presents a precise geometric framework in which the primary visual cortex $V1$…
We prove that each $3$-dimensional connected topological loop $L$ having a solvable Lie group of dimension $\le 5$ as the multiplication group of $L$ is centrally nilpotent of class $2$. Moreover, we classify the solvable non-nilpotent Lie…
In this paper, we study the conditions to be satisfied by a discrete-time linear system to ensure output controllability using sparse control inputs. A set of necessary and sufficient conditions can be directly obtained by extending the…
In mathematics and engineering, control theory is concerned with the analysis of dynamical systems through the application of suitable control inputs. One of the prominent problems in control theory is controllability which concerns the…
This paper is devoted to study boundary controllability of the Korteweg-de Vries equation posed on a finite interval, in which, because of the third-order character of the equation, three boundary conditions are required to secure the…
Statistical linearization has recently seen a particular surge of interest as a numerically cheap method for robust control of stochastic differential equations. Although it has already been successfully applied to control complex…