Almost linearizable control systems

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.