Transformation of Affine Systems and Solving of Terminal Control Problems

A terminal problem for multidimensional affine systems that are not feedback linearizable is considered. It is assumed that the control time interval is not specified and to be determined too. By the smooth non-degenerate variable substitution in the state space, the system is transformed to a regular quasicanonical form with two-dimensional canonical subsystems. A method for solving a terminal problem of the obtained class is offered on assumption that the right-hand side of one of the equations is positive in the whole state space. A sufficient condition for existence of the terminal problem solution is proved for the indicated class of systems. A numerical procedure for constructing the terminal problem solution is proposed and an example illustrating the proposed numerical procedure is given. The obtained results may be used in solving terminal control problems for technical systems.

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