Control of underactuated systems with non-holonomic constraints has been an issue of interest in recent years. These systems are hard to control because their linearization makes them uncontrollable and current approaches generally involve complex calculations. In this manuscript, a controller for trajectory tracking and positioning for a second-order chained form system using a simple approach based on linear algebra is proposed. The control law is formulated by setting two of the six variables trajectories, while the other four are calculated assuming the equations system has an exact solution, and ensuring the error tends to zero. The stability of the proposed control system is demonstrated through the Khalil Lemma, and simulations show the performance of the controller.

中文翻译：

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基于线性代数的控制：在二阶链式系统中的应用


近年来，具有非完整约束的欠驱动系统的控制一直是人们感兴趣的问题。这些系统很难控制，因为它们的线性化使它们无法控制，并且当前的方法通常涉及复杂的计算。在这篇手稿中，提出了一种使用基于线性代数的简单方法来对二阶链式系统进行轨迹跟踪和定位的控制器。通过设置六个变量轨迹中的两个来制定控制律，而其他四个变量则在假设方程组有精确解的情况下进行计算，并确保误差趋于零。通过哈利勒引理证明了所提出的控制系统的稳定性，并且仿真显示了控制器的性能。