The asymptotic output tracking problem is studied for a class of non-minimum phase nonlinear systems without requiring the a priori knowledge, or even the existence, of a finite-dimensional exosystem that generates the prescribed periodic reference signal. The design strategy is illustrated in two steps. First, it is shown that the knowledge of a solution to a certain two-point boundary value problem involving the underlying zero-dynamics of the plant is instrumental and sufficient to construct a state feedback regulator that achieves boundedness of the trajectories and (exact) asymptotic tracking, hence completely circumventing the need for solving partial differential equations. Then, since the computation of the latter solution may be affected by numerical errors that are particularly detrimental in the presence of unstable zero-dynamics, the above architecture is robustified by means of an additional hybrid feedback loop whose trajectories converge to a solution of the two-point boundary value problem. Once the latter scheme has been established and discussed, the extension to the case of output feedback is presented, firstly in the specially structured case in which the input vector field depends only on the measured output and then extended to the generic case. The theory is then corroborated by means of a physically motivated numerical example involving an inverted pendulum on a cart. Interestingly, it is also shown that the solution provided by the hybrid scheme above coincides with the limiting solution of a suitably defined cheap optimal control problem.

无需先验条件，研究了一类非最小相位非线性系统的渐近输出跟踪问题对产生规定的周期性参考信号的有限维系外系统的了解甚至存在。分两个步骤说明了设计策略。首先，表明对涉及植物潜在的零动力学的某些两点边值问题的解决方案的知识是有帮助的，并且足以构建实现轨迹有界和（精确）渐近的状态反馈调节器。跟踪，因此完全避免了求解偏微分方程的需要。然后，由于后者溶液的计算可以由是在不稳定的零动力学的存在特别有害的数值误差的影响，上述结构是抗差通过附加的混合反馈回路，其轨迹收敛到两点边值问题的解。一旦建立并讨论了后一种方案，便会提出对输出反馈情况的扩展，首先是在特殊结构的情况下，其中输入矢量场仅取决于测量的输出，然后扩展到一般情况。然后，通过一个涉及小车上倒立摆的物理数字示例来证实该理论。有趣的是，还显示出上述混合方案提供的解决方案与适当定义的廉价最优控制问题的极限解决方案相吻合。