Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchro-nization of two different chaotic systems with fully unknown parameters and nonlinear inputs. We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero. We assume that both the master＇s and the slave＇s system parameters are unknown in advance. Proper adaptation laws are derived to tackle the unknown parameters. An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time. We prove that both reaching and sliding mode phases are stable in finite time. An estimation of convergence time is given. Two illustrative examples show the effectiveness and usefulness of the proposed technique. It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.

一类非线性系统鲁棒自适应控制器

反步设计法是针对不确定非线性系统的进行鲁棒自适应控制器设计的主要方法之一,它主要是靠递推来完成,方法简单,但存在过参数化问题。在反步设计法的基础上,通过引入调节函数,选取合适的虚拟控制律,设计一种鲁棒自适应控制器。然后,利用Lyapunov稳定性理论证明了该设计不仅能够克服过参数化的问题,而且能够保证所设计的系统具有鲁棒自适应稳定性。仿真实例证明了该方法的有效性。