控制方向未知的全状态约束非线性系统的鲁棒自适应跟踪控制

针对一类控制方向未知的含有时变不确定参数和未知时变有界扰动的全状态约束非线性系统,本文提出了一种基于障碍Lyapunov函数的反步自适应控制方法.障碍Lyapunov函数保证了系统状态在运行过程中始终保持在约束区间内;Nussbaum型函数的引入解决了系统控制方向未知的问题;光滑投影算法确保了不确定时变参数的有界性.障碍Lyapunov函数、Nussbaum型函数及光滑投影算法与反步自适应方法的有效结合首次解决了控制方向未知的全状态约束非线性系统的跟踪控制问题.所设计的自适应鲁棒控制器能在满足状态约束的前提下确保闭环系统的所有信号有界.通过恰当地选取设计参数,系统的跟踪误差将收敛于0的任意小的邻域内.仿真结果表明了控制方案的可行性.

Robust adaptive tracking control for full state-constrained nonlinear systems with unknown control direction

To consider a class of full state-constrained nonlinear systems with completely unknown control coefficients, uncertain time-varying parameters and disturbances, a Barrier Lyapunov function (BLF) based adaptive robust control design method is proposed. BLFs are to ensure that the full state constraints be not violated, the unknown control direction is resolved effectively by the Nussbaum gain function and the boundedness of uncertain time-varying parameters is guaranteed by using the continuous projection algorithm. It is the first time that the BLF, Nussbaum gain function and continuous projection algorithm effectively combine with backstepping adaptive control to solve the tracking control problem for full state-constrained nonlinear system with unknown control direction. As shown as the control result, all the closed loop signals are bounded and full state constraints are not violated. Moreover the system output tracking error will converge to a bounded compact set of zero through select proper parameters. At last, The effectiveness of the proposed control scheme is further verified with a numerical example.