The synthesis problem for optimal control systems in the class of discrete controls is under consideration. The problem is investigated by reducing to a linear programming (LP) problem with consequent use of a dynamic version of the adaptive method of LP. Both perfect and imperfect information on behavior of control system cases are studied. Algorithms for the optimal controller, optimal estimators are described. Results are illustrated by examples.

The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two terms: the first one evaluates the state of the system at a fixed terminal time, and the second one is an integral evaluation of the control on the whole time interval. In order to solve this problem, we propose to reduce it to some auxiliary optimal control problem in a dynamical system described by a first-order ordinary differential equation. The reduction is based on the representation formula for solutions to linear fractional differential equations and is performed by some linear transformation, which is called the informational image of a position of the original system and can be treated as a special prediction of a motion of this system at the terminal time. A connection between the original and auxiliary problems is established for both open-loop and feedback (closed-loop) controls. The results obtained in the paper are illustrated by examples.

The study of the subdivision driving technology of a stepper motor and two types of typical acceleration and deceleration curves aims at optimizing the open-loop control performance of the stepper motor. The simulation model of a two-phase hybrid stepper motor open-loop control system is set up based on the mathematical model of the stepper motor, in order to let the stepper motor have the smaller stepper angle, two types of typical acceleration and a deceleration curve algorithm are designed for the real- time online calculation based on the subdivision driving technology. It respectively carries out the simulation analysis for their control effects. The simulation results show that the parabolic acceleration and deceleration curves have a larger maximum in-step rotation angle and the faster dynamic response ability in the same control period, and at the same time, the position tracking error of an intermediate process is smaller.