Related papers: High order sufficient conditions for tracking
In this paper, we propose new conditions guaranteeing that the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control…
Trajectory tracking of nonlinear dynamical systems with affine open-loop controls is investigated. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. We introduce exactly…
This thesis investigates optimal trajectory tracking of nonlinear dynamical systems with affine controls. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. The concept of…
In this paper we address the problem of tracking control of nonlinear systems via contraction analysis. The necessary conditions of the systems which can achieve universal asymptotic tracking are studied under several different cases. We…
This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it…
We investigate optimal control of dynamical systems which are affine, i.e., linear in control, but nonlinear in state. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible, a task…
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…
Accurate tracking of planned trajectories in the presence of perturbations is an important problem in control and robotics. Symmetry is a fundamental mathematical feature of many dynamical systems and exploiting this property offers the…
We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following…
We consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite-dimensional systems which are bounded-input, bounded-output stable. We describe under which conditions…
In this paper, we solve the problem of finding a certified control policy that drives a robot from any given initial state and under any bounded disturbance to the desired reference trajectory, with guarantees on the convergence or bounds…
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…
An analysis of necessary conditions for the existence of controlled dynamics with an attractor of a specified topological type is given. It uses the Hopf classification by degree for Gauss maps of manifolds to spheres of the same dimension,…
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.
We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present…
Just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so it is too with an explicit parameterisation of system dynamics by control. However, such…
This paper addresses the trajectory-tracking problem for a class of electromechanical systems. To this end, the dynamics of the plants are modeled in the so-called port-Hamiltonian framework. Then, the notion of contraction is exploited to…
We obtain higher order necessary conditions for a minimum of a Mayer optimal control problem connected with a nonlinear, control-affine system, where the controls range on an m-dimensional Euclidean space. Since the allowed velocities are…
A major challenge in autonomous driving is designing control architectures that guarantee safety in all relevant driving scenarios. Given a safe desired reference trajectory for the vehicle, a trajectory following controller has to ensure…