Related papers: The collision avoidance and the controllability fo…

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…

Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity…

We study a time minimization problem on the group of motions of a plane with admissible control in a half-disk. The considered control system describes a model of a car that can move forward on a plane and turn in place. Optimal…

Given a control system on a manifold that is embedded in Euclidean space, it is sometimes convenient to use a single global coordinate system in the ambient Euclidean space for controller design rather than to use multiple local charts on…

The paper is devoted to the controllability problem for 3D compressible Euler system. The control is a finite-dimensional external force acting only on the velocity equation. We show that the velocity and density of the fluid are…

This paper applies the recently developed framework for integral control on nonlinear spaces to two non-standard cases. First, we show that the property of perfect target stabilization in presence of actuation bias holds also if this bias…

In this article, we study the control aspects of the one-dimensional compressible Navier-Stokes equations with Maxwell's law linearized around a constant steady state with zero velocity. We consider the linearized system with Dirichlet…

In this paper, we study the tracking controllability of a 1D parabolic type equation. Notably, with controls acting on the boundary, we seek to approximately control the solution of the equation on specific points of the domain. We prove…

The problem of tracking an arbitrary curve in the state space is considered for underactuated driftless control-affine systems. This problem is formulated as the stabilization of a time-varying family of sets associated with a neighborhood…

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…

The paper addresses the problem of controller synthesis for control-affine nonlinear systems to meet reach-avoid-stay specifications. Specifically, the goal of the research is to obtain a closed-form control law ensuring that the…

This paper presents a novel approach for collision avoidance in optimal and model predictive control, in which the environment is represented by a large number of points and the robot as a union of padded polygons. The conditions that none…

This paper deals with the controllability of linear one-dimensional hyperbolic systems. Reformulating the problem in terms of linear difference equations and making use of infinite-dimensional realization theory, we obtain both necessary…

Trajectory planning in dense, interactive traffic scenarios presents significant challenges for autonomous vehicles, primarily due to the uncertainty of human driver behavior and the non-convex nature of collision avoidance constraints.…

We study control systems on the tangent bundle of a smooth manifold induced by vertical lifts of vector fields. The Vertical dynamics acts exclusively along the fibers, leaving the base point unchanged and reducing the system to a linear…

This paper presents a novel control protocol for distance and orientation formation control of rigid bodies, whose sensing graph is a static and undirected tree, in the special Euclidean group SE(3). The proposed control laws are…

In this paper we study the controllability of an artificial advection-diffusion system through the boundary. Suitable Carleman estimates give us the observability on the adjoint system in the one dimensional case. We also study some basic…

We consider a one dimensional transport equation with varying vector field and a small viscosity coefficient, controlled by one endpoint of the interval. We give upper and lower bounds on the minimal time needed to control to zero,…

This work investigates both local null controllability and large time null controllability for a class of complete Ladyzhenskaya Boussinesq systems, where the controls are distributed and supported on small subsets of the domain. The proof…

This paper presents an approach to mutual collision avoidance based on Nonlinear Model Predictive Control (NMPC) with time-dependent Reciprocal Velocity Constraints (RVCs). Unlike most existing methods, the proposed approach relies solely…