Vol 58, No 1 (2019)

This paper considers some classes of linear time-varying systems with control and output vectors that can be reduced to time-invarint systems using a constructive transformation with state-space extension. As an illustrative example, the calibration problem of a gimballess inertial navigation system on a single degree-of-freedom turn table is solved.

The article considers the practical application of the analysis and estimation of the controlled Markov jump process states by continuous, discrete, and counting observations in the development of state monitoring algorithms for network connections operating under the Transmission Control Protocol (TCP). A specific feature of the applied problem is the physical heterogeneity of the channel providing the TCP connection under study: along with the wired section, there is a wireless “last mile” of the channel. The current state of the entire connection cannot be directly observed, and there is just indirect statistical information in the form of a flow of acknowledgements of successful packet transmission, as well as packet loss counting processes and timeouts. In this part of the work, not only the controlled stochastic dynamic observation system was used for the mathematical description of the TCP New Reno connection but also the developed high-precision algorithm for tracking this connection state according to the available statistical information. The numerical examples make it possible to define causes of channel losses, such as congestion in the wired section or signal attenuation in the wireless section, and as a result modify the TCP algorithm so as to significantly increase the bandwidth.

This paper considers a system consisting of a carrier body and two linear dissipative oscillators attached to it. The body moves in a straight horizontal line under the action of a bounded control force and a small unknown perturbation. It is assumed that the coordinate and velocity of the body are known at all times and the phase states of the oscillators cannot be measured. A control law which stops the carrier body at the origin of coordinates in finite time is proposed. The effectiveness of the proposed control law is illustrated by numerical modeling.

Methods of controlling electroplating processes are considered, and the shortcomings in the use of basic engineering and structural configurations for this purpose are revealed. An original approach consisting of controlling current regimes in a multianode bath is proposed. In implementing this approach, the problem of the optimal control over electroplating processes in compliance with the criteria of the coating’s nonuniformity and process duration is formulated. The electroplating process in a bath with multi anodes is considered as an object of control, for which the input and output vectors of the process are specified, together with the external disturbances and the control vector. The control vector is related with the optimality criterion by composing a mathematical model with the distributed coordinates based on an elliptic partial differential equation with different ways of correcting the corresponding current in every anodic section. A series of experiments with a complicatedly shaped article are performed to prove the adequacy of this mathematical model and the efficiency of the proposed approach and demonstrate a “ravine” character of the target criterion function. A three-level architecture is selected for the control system to implement the optimal control. The procedure of the preliminary search for the optimal control with the formation of a corresponding matrix is proposed due to the very time-consuming character of the solution of the formulated problem. The actions to be performed in the cases when the control matrix contains or does not contain the found solution for an incoming lot of articles are considered.

An algorithm for constructing the time optimal control of a nonlinear fourth-order system that must visit two fixed points in the prescribed order is proposed. This system describes the motion of a car or an aircraft in the horizontal plane with a variable controllable speed and controllable steering angle.

The boundary controllability of oscillations of a plane membrane is studied. The magnitude of the control is bounded. The controllability problem of driving the membrane to rest is considered. The method of proof proposed in this paper can be applied to any dimension but only the two-dimensional case is considered for simplicity.

An iterative method for solving routing problems subject to constraints and possible dependence of the cost functions on the list of tasks that have not been accomplished is considered. Such statements occur in some problems of nuclear power engineering and in developing optimizing programs for sheet cutting on programmable numerically controlled machines (in the first case, the dependence on the list of tasks can occur due to sequential dismantling of radiation sources, and in the second case it can be due to taking into account technological constraints using penalties). It is assumed that the problems under examination are large, which calls for the use of heuristic methods. The approach proposed in the paper makes it possible to design an iterative procedure based on optimizing insertions that use widely interpreted dynamic programming. The proposed algorithm is implemented on a multicore personal computer.

A dynamic problem of a spacecraft (SC) turning from an arbitrary initial position to the required terminal angular position with restricted control is considered and solved. The termination time of the maneuver is known. The control program is optimized using the quadratic criterion of quality; the minimized functional characterizes the energy consumed in the turn. The construction of the optimal control of the turn is based on quaternion variables and Pontryagin’s maximum principle. It is shown that during the optimal turn, the moment of force is parallel to the straight line fixed in the inertial space, and the direction of the angular momentum in the process of the SC’s rotation is constant relative to the inertial coordinate system. The formalized equations and computational expressions for determining the optimal turning program are obtained. A special mode of control is studied in detail, and the conditions of the impossibility of occurrence of this mode are formulated. The control algorithms allow performing turns over a fixed time period with the minimum angular kinetic energy. A comprehensive solution to the control problem is given for a dynamically symmetric SC: the dependences as explicit functions of time for the control variables and relations for calculating the key parameters of the turn maneuver’s control law are obtained. A numerical example and the results of the mathematical modeling of the SC’s motion with the optimal control are given, which demonstrate the practical feasibility of the method for controlling the attitude of the SC.