We extend the approach based on the linearization of triangular systems to new classes of non-linearizable control systems that are almost linearizable. This means that there exists a change of variables and control mapping all but one equations of the initial nonlinear system to a linear system. We show how this property can be used for solving the problem of constructive controllability, i.e., finding trajectories connecting two given points. Namely, we explicitly find a change of variables and control that maps \(n-1\) equations of the initial system to a linear system. For the remaining first-order nonlinear differential equation, which contains one unknown scalar parameter, the boundary value problem is considered. Once this one-dimensional problem is solved, a trajectory connecting two given points for the initial system is explicitly found. Moreover, we solve the stabilization problem for systems from the proposed classes under additional natural conditions. We give several examples to illustrate a constructive character of our approach.

我们将基于三角系统线性化的方法扩展到几乎可线性化的新型非线性控制系统。这意味着存在变量的变化，并且控制将初始非线性系统中除一个方程式之外的所有方程式映射到线性系统。我们展示了如何将此属性用于解决构造可控制性的问题，即找到连接两个给定点的轨迹。即，我们明确找到变量的变化并控制\（n-1 \）的映射初始系统到线性系统的方程。对于包含一个未知标量参数的其余一阶非线性微分方程，考虑了边值问题。一旦解决了该一维问题，就可以明确找到连接初始系统的两个给定点的轨迹。此外，我们在额外的自然条件下解决了拟议类别系统的稳定性问题。我们举几个例子来说明我们方法的建设性特征。