Solving terminal problems for multidimensional affine systems based on transformation to a quasicanonical form

The paper considers a terminal problem for multidimensional affine systems, which are not linearizable by a feedback. The affine system is transformed to a regular quasicanonical form using a smooth nondegenerate change of variables within the range ofstates. In addition, the terminal problem for the initial system is transformed to the equivalent terminal problem for the system of a quasicanonical form. A method of solving the terminal problems is proposed for the quasicanonical systems, which is based on a concept of dynamics inverse problems generalization. The sufficient condition for applying the proposed method is proved. The numerical procedure of solving the terminal problems for the systems of a quasicanonical form is proposed. There is an example ofsolution development of a terminal problem for a sixth-order system using the above-mentioned method. The obtained results may be used for solving problems of terminal control over technical systems.

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