This paper addresses the tracking control problem of a class of high-order uncertain nonlinear systems under time-varying asymmetric output constraints. Most relevant results in the literature have two main restrictions: R1) some constraints need to be imposed on powers and growth conditions have to be established for the nonlinear functions of the system; R2) nonlinear bounding functions must be derived based on repeated derivations of virtual control variables during the design process. By integrating an improved technique of adding a power integrator with a dynamic surface control (DSC) method, we develop a systematic tracking control scheme that eliminates both of the above restrictions. Moreover, with an improved time-varying nonlinear transformed function introduced for high-order systems, the proposed scheme can be regarded as a unified tool in the sense that it works no matter whether the constraint is symmetric, asymmetric, or even without a constraint. The above results are also extended to systems with uncertain gain functions, and the proposed scheme estimates only one adaptive parameter. The simulation results of two deterministic practical applications show that the proposed control scheme is effective not only for high-order systems, but also for high-order-free systems.

本文研究了时变非对称输出约束下一类高阶不确定非线性系统的跟踪控制问题。文献中最相关的结果有两个主要限制：R1）需要对功率施加一些限制，并且必须为系统的非线性功能建立增长条件；R2）非线性边界函数必须在设计过程中基于虚拟控制变量的重复推导得出。通过将添加功率积分器的改进技术与动态表面控制（DSC）方法集成在一起，我们开发了一种系统的跟踪控制方案，该方案消除了上述两个限制。此外，针对高阶系统引入了改进的时变非线性变换函数，从约束是否对称，不对称甚至没有约束的意义上讲，该方案都可以视为统一工具。上述结果还扩展到具有不确定增益函数的系统，并且所提出的方案仅估计一个自适应参数。两个确定性实际应用的仿真结果表明，所提出的控制方案不仅对高阶系统有效，而且对高阶自由系统也有效。