Global Fixed-Time Stabilization for Chained Nonholonomic Systems via Output Feedback Control

This paper studies the fixed-time output feedback stabilization control problem for chained nonholonomic systems. By means of switching control and $bi$-limit homogeneous techniques, it is firstly constructed two fixed-time state feedback stabilizing controllers for the considered systems. Then, a new state observer with a formalized switching law is proposed to fixed-time estimate system states, where high-order terms are applied to get uniform convergence regardless of initial conditions and low-order terms are aimed to the exact convergence in finite time. Finally, based on $bi$-limit homogeneous technique and Lyapunov stability theorem, fixed-time output feedback stabilizing controllers, one of which is discontinuous with a specific switching control law and the other is continuous, are constructed and the fixed-time output feedback stabilization of the considered systems is thus guaranteed. An example is presented to show the feasibility of the proposed fixed-time output feedback stabilization control strategy.

Stabilizing Controllers for Landmark Navigation of Planar Robots in an Obstacle-Ridden Workspace

This paper essays a new solution to the landmark navigation problem of planar robots in the presence of randomly fixed obstacles through a new dynamic updating rule involving the orientation and steering angle parameters of a robot. The dynamic updating rule utilizes a first-order nonlinear ordinary differential equation for the changing of landmarks so that whenever a landmark is updated, the path followed by the robot remains continuous and smooth. This waypoints guidance is via specific landmarks selected from a new set of rules governing the robot’s field of view. The governing control laws guarantee asymptotic stability of the 2D point robot system. As an application, the landmark motion planning and control of a car-like mobile robot navigating in the presence of fixed elliptic-shaped obstacles are considered. The proposed control laws take into account the geometrical constraints imposed on steering angle and guarantee eventual uniform stability of the car-like system. Computer simulations, using Matlab software, are presented to illustrate the effectiveness of the proposed technique and its stabilizing algorithm.

Stabilization of Switched Linear Systems with Control Constraints Based on EA

In this paper, we address the problem of stabilization of switched linear systems. The idea is to look for a state feedback control law using evolutionary algorithms (EA) in order to assure the stability of the switched linear systems under control constraints. In some cases when states are not available and only outputs are measurable, the previous method is applied to design an output feedback controller which stabilizes the system. Both stabilizing controllers are developed using deferential evolution and genetic algorithm. Two numerical examples illustrate our proposed theory and point out the effectiveness of our proposed approaches.