具有输入饱和的不确定非线性系统自适应渐近跟踪控制

将一类具有输入饱和的严格反馈单输入单输出非线性系统作为研究对象,解决其自适应渐近跟踪控制问题.与已有结果不同,所考虑的虚拟控制参数可以是未知且增益函数的上界信息也是未知的,这给控制器的设计带来了挑战.通过结合光滑函数及有界估计方法,设计一种新颖的自适应渐近跟踪控制策略;其次,通过引入Nassbaum函数解决由输入饱和不确定参数以及未知虚拟控制参数带来的影响;此外,通过利用未知增益的下界信息巧妙地构造一个特殊的李雅普诺夫函数并结合不等式技巧,可以消除对控制增益函数上界信息的需要,并保证系统的全局稳定性和跟踪性能;最后,通过实例仿真及对比仿真表明所提出自适应渐近跟踪控制算法的有效性.

Adaptive asymptotic tracking of uncertain nonlinear systems with input saturation

The adaptive control problem of a class of strict feedback single-input single-output (SISO) nonlinear systems with input saturation is investigated in this paper. Different from the existing results, the considered virtual control coefficients can be unknown and the upper bound information is also unknown. A novel adaptive asymptotic tracking control scheme is developed by introducing some well-defined smooth functions and the bounded estimation approach. A Nussbaum function is introduced to compensate for the influence caused by input saturation and unknown virtual control parameters. By using the lower bound information of the unknown gain and delicately constructing a specific composite Lyapunov function for the closed-loop system as well as several useful inequalities, the need for upper bound information is eliminated and the global stability and tracking performance in the presence of input saturation can be guaranteed. Finally, the effectiveness of the proposed adaptive algorithm is illustrated with a practical simulation example and a comparative simulation.