基于非线性映射的约束系统自适应反推控制

针对基于障碍Lyapunov函数的非线性约束系统反推控制中, 控制器结构复杂、约束量初值选取区间小、会引入额外参数等问题, 提出了一种新的基于非线性映射的自适应反推控制方案. 该方法扩大约束量的初值选取区间为整个约束区间, 增加了系统初值选取和控制器设计的便易性. 约束量被映射至实数空间中, 因此映射后的新系统可以直接应用反推法设计控制器, 简化了控制器结构且不会引入额外参数. 证明了映射前后系统具有一致的收敛性, 保证闭环系统所有信号一致有界, 并且跟踪误差渐近收敛于零. 仿真结果进一步验证了本文方法的有效性.

Adaptive Backstepping Control for Constrained Systems Using Nonlinear Mapping

In this paper, a novel nonlinear mapping based adaptive backstepping control is presented for nonlinear systems with output constraint to overcome the problems faced by barrier Lyapunov function based backstepping control, such as complex controller structure, small set for initial value of constrained output and extra parameters employment. The constrained output can take any initial value within the output constrained space, so added flexibility is achieved in the control design. By mapping the constrained output into the real number set, the backstepping control design can be directly used for the transformed system, while simultaneously prevent the constraints from being violated. A similar convergence feature is proved between the system and its mapping, so that the stability of the closed-loop system is guaranteed in the sense that all closed-loop signals are uniformly bounded and the tracking error converges to zero asymptotically. Simulation results demonstrate the effectiveness of the proposed control.