Stabilization of polynomial systems in ℝ3 via homogeneous feedback

In this paper, we study the stabilization problem of a class of polynomial systems of odd degree in dimension three. The constructed stabilizing feedback is homogeneous and guarantee the homogeneity of the closed loop system.mynotered In the end of the paper, we show the efficiency of such a study in the local stabilization of nonlinear systems affine in control.

Interpolation-Based Smart Video Stabilization

Video stabilization is the process of eliminating unwanted camera movements and shaking in a recorded video. Recently, learning-based video stabilization methods have become very popular. Supervised learning-based approaches need labeled data. For the video stabilization problem, recording both stable and unstable versions of the same video is quite troublesome and requires special hardware. In order to overcome this situation, learning-based interpolation methods that do not need such data have been proposed. In this paper, we review recent learning-based interpolation methods for video stabilization and discuss the shortcomings and potential improvements of them.

A Mechanical Feedback Classification of Linear Mechanical Control Systems

We give a classification of linear nondissipative mechanical control system under mechanical change of coordinates and feedback. First, we consider a controllable case that is somehow a mechanical counterpart of Brunovský classification, then we extend the result to all linear nondissipative mechanical systems (not necessarily controllable) which leads to a mechanical canonical decomposition. The classification of Lagrangian systems is given afterwards. Next, we show an application of the classification results to the stability and stabilization problem and illustrate them with several examples. All presented results in this paper are expressed in terms of objects on the configuration space Rn only, while the state-space of a mechanical control system is Rn×Rn consisting of configurations and velocities.

Stabilizing the spatial position of a quadrotor by the backstepping procedure

<div>The paper considers the problem of synthesizing a control law that stabilizes the spatial position of an airborne object. The control object is a quadrotor with nonlinear dynamics. To solve the stabilization problem, a mathematical model of the quadrotor has been developed, taking into account its positionin the Cartesian and Euler coordinate systems. The new control law has been synthesized using the backstepping procedure. This control law is based on the Lyapunov-type stabilization criterion. New results analysis of the quadrotor dynamics, where has been showing the dependence of the control accuracy on the parameter of the stabilization criterion also presented. An algorithm for the directed search of the procedure parameter also has been proposed. It ensures the desired quality of the transient process. Simulation results confirming the results of the oretical research have been presented as well.</div>

On the Steady State Motions Control Problem for Mechanical Systems with Relay Controllers

The paper presents the solution to the stabilization problem of steady state motions for a holonomic mechanical system by using relay controllers. This solution is achieved by proving new theorems on the asymptotic stability of the solution to a differential equation with a discontinuous right-hand side. The novelty of the theorems is based on the limiting inclusions construction and the use of semidefinite Lyapunov functions. As an example, the stabilization problem of steady-state motion for a five-link robot manipulator is solved by using relay controller.

Finite-Time Simultaneous Stabilization of a Set of Nonlinear Singular Systems

This study addresses the problems of finite-time simultaneous stabilization for two nonlinear singular systems and more than two nonlinear singular systems. First, we design a suitable output feedback controller and combine the two nonlinear singular systems to generate an augmented system by using an augmented technique. Based on a sufficient condition of the augmented system impulse-free, an important result, that is, the augmented system is finite-time stabilization is presented. Then, the finite-time stabilization problem of more than two singular systems is investigated by dividing the N systems into two sets. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed finite-time stabilization controller for two nonlinear singular systems.