Finite-time Stabilization For Nonholonomic Systems

This paper mainly discusses the finite-time stabilization and tracking control problems for nonholonomic systems. The problem of finite-time stabilization refers to the states of system can reach the equilibrium point in a finite time under the designed control laws. In this paper, the main contents and conclusions are as follows:1. The finite-time dynamic feedback tracking problem is considered for nonholonomic wheeled mobile robots with uncalibrated visual parameters. Firstly, a tracking error system is given which converts the tracking problem into a finite-time stabilization problem of the tracking error system. Then, the multi-step switching control law are designed by utilizing the finite-time stability theory and backstepping techniques, so that the closed-loop system can track the given reference trajectory in a finite time.2. For the nonholonomic chained systems with communication delays in control inputs, we discuss the finite-time stabilization of two cases respectively, one is to determine the type of chain system, and another is a chained system with uncertain parameters. Firstly, we can transform the systems with the input delays into two general non-delay systems through integral and state transform, and scaling the uncertain parameters, then designing the switching control laws by using a two-step method, to stabilize the systems within a finite time.3. The finite-time dynamic feedback stabilization control problem is considered for a class of nonlinear systems under the input saturation, and a switch control strategy is proposed, and we design multi-step switching discontinuous control laws, which can divide the complex nonlinear systems into different simple subsystems by finite switches in order to ensure that the proposed control laws in every step satisfy the saturation constraints, and at the same time ensure that the system states can converge to a prespecified point or the equilibrium point in a finite time.4. According to these conclusions, some specific numerical examples are given and the simulation experiments verify that the proposed control laws are effective.