Related papers: Control Sets for Bilinear and Affine Systems
In this paper, we investigate the controllability of bilinear control systems of the form $\dot{s} = As + uBs$, where $s \in \mathbb{S}^2$ and $A, B \in gl(3, \mathbb{R})$ are skew-symmetric matrices. First, we prove that the algebraic…
Let H denote the 3-dimensional Heisenberg Lie group. The present paper classify all possible linear control systems on the homogeneous spaces of H through its closed subgroups and expose a detailed study on the control behavior…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
Recent developments in data-driven control have revived interest in the behavioral approach to systems theory, where systems are defined as sets of trajectories rather than being described by a specific model or representation. However,…
This note presents a sufficient condition for partial approximate ensemble controllability of a set of bilinear conservative quantum systems in an infinite dimensional Hilbert space. The proof relies on classical geometric and averaging…
We consider the problem of steering control for the systems of one spin 1/2 particle and two interacting homonuclear spin 1/2 particles in an electro-magnetic field. The describing models are bilinear systems whose state varies on the Lie…
Sufficient and necessary conditions are established for controllability of affine control systems where the control is constrained to a set whose convex hull contains the origin but is not necessarily, in contrast with previously known…
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…
In this paper, we investigate the control sets of linear control systems on the Heisenberg group associated with singular derivations. Under the Lie algebra rank condition, we provide a complete characterization of these sets by analyzing…
The control of bilinear systems has attracted considerable attention in the field of systems and control for decades, owing to their prevalence in diverse applications across science and engineering disciplines. Although much work has been…
The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems on Lie groups. In this context, the equations for critical trajectories of the problem are…
Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for…
This paper presents a coordinate-free formulation of virtual holonomic constraints for underactuated Lagrangian control systems on Riemannian manifolds. It is shown that when a virtual constraint enjoys a regularity property, the…
In finite dimensions, controllability of bilinear quantum control systems can be decided quite easily in terms of the "Lie algebra rank condition" (LARC), such that only the systems Lie algebra has to be determined from a set of generators.…
The paper presents new sufficient conditions for the property of strong bi-metric regularity of the optimality map associated with an optimal control problem which is affine with respect to the control variable ({\em affine problem}). The…
In this article, we give a condition for the global controllability of affine nonlinear control systems with drifts on Euclidean spaces. Under regularity assumptions, the condition is necessary and sufficient in the codimension-1 and…
For a symmetric Lie algebra $\mathfrak g=\mathfrak k\oplus\mathfrak p$ we consider a class of bilinear or more general control-affine systems on $\mathfrak p$ defined by a drift vector field $X$ and control vector fields $\mathrm{ad}_{k_i}$…
This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift…
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…
Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…