V. M. ALEKSANDROV
Russia, 630090, Novosibirsk,
Ave. of acad. Koptyug, 4,
S.L.Sobolev Institute of Mathematics, Siberian
Branch of the Russian Academy of Sciences,
It is suggested an iterative method of finding time-optimal control for quasi-linear systems. Upon specifying mathematical description of the controlled process the structure of controlling device is specified as well. The device is chosen to belong to the class of relay controllers through their being widespread and easily realizable. As a result instead of folloving a common practice for imposing inequalities on the control vector components we have constraints in the form of equalities. A method is suggested to pass to nonlinear systems with separated linear control. Time-optimal control for nonlinear systems with linealy selected control appears to be relay one, which essentially simplifies the computing. A system of linear algebraic equations is obtained that relates the increments of control switching moments and the increment of completion time to the increments of phase coordinates. It is determined how the increments of the initial conditions for the normalized adjoint system relay to the increments of the control switching moments. As a result a system of linear algebraic equations is obtained that relates the increments of the initial conditions for the normalized adjoint system and the increment of the completion time to the increments of the phase coordinates in the final moment. Ultimately the problem of finding time-optimal control reduces to a sequence of the solutions to Cauchy problems and systems of linear algebraic equations. It is proved that the sequence of controls converges to the optimal control. The computing algorithm and the results of modelling for a number of nonlinear systems are given.