Optimal Terminal Control Problem for Discrete-Time Dynamical System

Andrey Shorikov

In this report we consider the dynamical system
that consist of one controlled object. The motion of this object is described by linear discrete-time recurrent vector equation. It is assumed that the set constraining control action is known and is convex, closed and bounded polyhedron (with a finite number of vertices) in the corresponding Euclidean vector space. Under these
assumptions, we formulate and solve the optimal terminal control problem with a convex functional for such linear discrete-time dynamical system. In order to solve of
optimal terminal control problem we suggest a recurrent numerical algorithm which reduce the initial multistep problem to solving a sequence of direct and inverse one-step linear and convex programming problems.

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