Program packages method for solving closed-loop guidance problem with incomplete information for linear systems

The method of program packages [1] is a tool for identyfying the solvability conditions of guaranteed positional control problems when information on observed states is incomplete. In this talk a version of the method applicable to the problem of guaranteed positional guidance of a linear control system to a convex target set at a specified ti me is presented. The observed signal on the system’s states is assumed to be linear and the set of its admissible initial states is assumed to be finite. The method is based on clusterisation of the set of initial states according to the corresponding homogeneous signals and the moments of their separation from each other. A program package is a set of programs which are parametrized by the initial states and satisfying the ”non-anticipatory” condition. It is proved that the problem of guaranteed positional guidance is equivalent to the problem on the program package guidance which itself is equivalent to the program guidance of an extended linear control system to an extended convex target set [2]. For the latter problem a solvability criterion which reduces the task to the solution of a finite- dimensional optimization problem is produced using the separation theorem for convex sets. A procedure of construction the guiding program package and the corresponding guiding positional strategy which solves the given problem is described