The tracking control problem for a class of partial state constrained nonlinear system is studied in this article. The system is divided into two semistrict feedback nonlinear subsystems, one is state constrained and the other is state free. By means of state transformation, the state constraint problem is transformed into the bounded problem of the transformed function. Compared with the barrier Lyapunov function (BLF) method, it not only solves the state constraint problem but also circumvents the feasibility check on virtual controllers. Based on the cross backstepping control, the constrained controller and unconstrained controller are designed simultaneously. It solves the coupling problem effectively in the design of cross processing control. On the other hand, dynamic surface control is used which effectively avoids “computation explosion” caused by backstepping control. The designed controllers can ensure the error signals converge to a small neighbourhood of zero and keep the asymmetric time-varying constraints on system partial states are satisfied for all the time. Finally, simulation experiments are carried out on a hyperchaotic Rössler system to verify the efficacy of the control scheme.

中文翻译：

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一类具有部分状态约束的非严格反馈非线性系统的自适应交叉反步控制

本文研究了一类局部状态约束非线性系统的跟踪控制问题。该系统分为两个半严格反馈非线性子系统，一个是状态约束的，另一个是无状态的。通过状态变换，将状态约束问题转化为变换函数的有界问题。与障碍李雅普诺夫函数（BLF）方法相比，它不仅解决了状态约束问题，还绕过了对虚拟控制器的可行性检查。在交叉反步控制的基础上，同时设计了约束控制器和无约束控制器。有效解决了交叉处理控制设计中的耦合问题。另一方面，采用动态曲面控制，有效避免反步控制带来的“计算爆炸”。所设计的控制器可以保证误差信号收敛到零的一个小邻域，并始终满足系统局部状态的非对称时变约束。最后，在超混沌 Rössler 系统上进行了仿真实验，以验证控制方案的有效性。