Related papers: Necessary conditions for local controllability of …
We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
For a symmetric system, we want to study the problem of crossing an hypersurface in the neighborhood of a given point, when we suppose that all of the available vector fields are tangent to the hypersurface at the point. Classically one…
We present a necessary condition for the small-time local controllability of multi-input control-affine systems on $R^d$ . This condition is formulated on the vectors of $R^d$ resulting from the evaluation at zero of the Lie brackets of the…
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…
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain…
In this article we study control problems with systems that are governed by ordinary differential equations whose vector fields depend linearly in the time derivatives of some components of the control. The remaining components are…
The local controllability of a rich class of affine nonlinear control systems with nonhomogeneous quadratic drift and constant control vector fields is analyzed. The interest in this particular class of systems stems from the ubiquity in…
In this paper, we study small-time local controllability of real analytic control-affine systems under small perturbations of their vector fields. Consider a real analytic control system $\mathcal{X}$ which is small-time locally…
This note deals with the local exact controllability to a particular class of trajectories for the Boussinesq system with nonlinear Navier-slip boundary conditions and internal controls having vanishing components. Briefly speaking, in two…
In this paper we explicitly calculate the control sets associated with a linear control system on the two dimensional solvable Lie group. We show that a linear control system of such kind admits exactly one control set or infinite control…
Sufficient conditions for the controllability of a conservative reduced system are given. Several examples illustrating the theory are also presented.
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
Controllability properties are studied for control-affine systems depending on a parameter and with constrained control values. The uncontrolled systems in dimension two and three are subject to a homoclinic bifurcation. This generates two…
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…
We will study the controllability problem of a bilinear control system on $\mathbb{R}^2:$ the main result is the characterization of the Lie algebra rank condition for the system. On the other hand, using elementary techniques, we recover…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
The objective of this paper is to study the controllability of discrete-time linear control systems in solvable Lie groups. In the special case of nilpotent Lie groups, a necessary and sufficient condition for controllability is…
We study a control problem governed by a semilinear parabolic equation with pointwise control and state constraints imposed at every point of the space-time cylinder. We obtain second order sufficient optimality conditions for local…
In this paper we give a necessary and sufficient condition for local controllability around closed orbits for general smooth control systems. We also prove that any such system on a compact manifold has a closed orbit.