Department of Control Processes Theory
Institute of Mathematics
National Academy of Sciences of Belarus
220072 Minsk, Belarus
The first procedure includes a piecewise linear approximation of a nonlinear element of the system. Although after such approximation the optimal control problem remains nonlinear, it allows to develop an effective method based on fast algorithms of optimization of linear control systems. The second procedure of the algorithm consists in asymptotic correction of the solution obtained by the first procedure. The suggested method of correction is based on asymptotic expansions of switching points of control and accompanying elements. This is the main difference of the method from known asymptotic methods which are based on asymptotic expansions of primal and dual variables.
The idea of closed-loop solution to the problem is based on constructing a realization of optimal feedback in any concrete control process under unknown but bounded disturbances. The realization of the algorithm of open-loop solution is oriented on fast corrections of optimal open-loop control subject to small variations of initial state. This is possible due to storage a small amount of additional information allowing to avoid the complete integration of primal or adjoint system. Such a realization is a basis of an algorithm of operating an asymptotically optimal controller which generated signals of optimal feedback in actual control processes in real time.
An application of this approach to constructive solution of nonextremal control problems is discussed.
This talk is based on joint work with Professors Rafail Gabasov, Faina Kirillova and Anatolii Kalinin.