### CONTROL OVER DYNAMIC SYSTEMS

HYBRID ALGORITHM OF OUTPUT CONTROL WITH COMPENSATION FOR UNKNOWN MULTI-SINUSOIDAL PERTURBATION
Bobtsov Alexey Alexeevich, Vedyakov Alexei A, Kolyubin Sergey A, Pyrkin Anton Alexandrovich

7

The problem of output control over linear parametrically indeterminate object with inaccurately defined relative degree under the action of unknown external multi-sinusoidal perturbation is considered. A solution to the problem is found in the class of hybrid adaptation algorithms including channels of stabilization and identification of perturbation action parameters.

GENERALIZED MODAL CONTROL IN THE PROBLEM OF PARAMETRICALLY INVARIANT DISCRETE SYSTEM SYNTHESIS
Slita Olga V., Ushakov Anatoly Vladimirovich

11

Control over discrete object with uncertainty in the state matrix is considered. The problem of invariance assurance is solved with the use of properties of eigenvectors and eigenvalues spectrum of a matrix function on the state matrix and application of generalized modal control capabilities. An example is presented.

STUDY OF POSITIVE SYSTEMS PROCESSES ON THE BASE OF QUALITATIVE EXPONENTIAL STABILITY
Grigoriev Valeriy V., Vladimir Boikov, Bystrov Sergey V., Alexander I. Ryabov, Olga K. Mansurova

15

A concept of qualitative exponential stability is introduced for a class of dynamic positive discrete systems. The concept provides a base for presented analysis of quality of convergent and non-convergent processes.

EXPONENTIAL STABILITY OF LINEAR SYSTEMS WITH DISTRIBUTED PARAMETERS
Grigoriev Valeriy V., Bystrov Sergey V., Ivan M. Pershin, Alla K. Naumova, Alena N. Guryanova

20

Frequency methods of analysis of linear system with distributed parameters are used to formulate a modified Nyquist criterion of exponential stability for such systems.

HEREDITARY MODEL OF INERTIAL TIME DELAY IN OPTIMAL CONTROL PROBLEMS
Dmitry Muzyka, Peshcherov Ruslan O, Tertychny-Dauri Vladimir Yu.

27

Organization of time delay in channel of dynamic object control is considered with the use of the Volterra equation with variable limits of integration (integrated hereditary procedure of delay). An integral formula is obtained which allows for setting a control law depending on the time delay value. The formula is derived by an iterative approximation procedure in the scheme of the Volterra integral equation of the second kind.

CONTROL OVER DYNAMIC OBJECTS AND SYSTEMS DEGENERATION: GRAMIAN APPROACH
Dmitriy Biryukov, Dudarenko Natalya Alexandrovna, Ushakov Anatoly Vladimirovich

34

The problem of control over degeneration of dynamic objects and systems is considered. A gramian-based approach is used based on calculation of singular values of the controllability gramian for input-output relations and subsequent application of the degenerative functional apparatus.

CONTROL SYNTHESIS IN TWO-DIMENSIONAL SYSTEM WITH SMOOTH NONLINEARITIES
Bushuev Alexander B., Olga K. Mansurova

38

The control object — nonlinear compensational homeostasis — is considered as a mathematical model of conflict situation between the two channels. To synthesize a control resolving the conflict, potential functions of canonical catastrophes are applied.

SYNTHESIS OF INTERVAL OBSERVER FOR LINEAR SYSTEM WITH VARIABLE PARAMETERS
Stanislav Chebotarev, Kremlev Artem Sergeevich

42

The conditions which allows for construction of an interval observer are analyzed. The observer is supposed to be able to estimate the range of system variable values which certainly includes the actual value of the state at a given time.

### CONTROL AND INFORMATION PROCESSING IN ROBOTIC SYSTEMS

SYNTHESIS OF CONTROL SYSTEM FOR A QUADROCOPTER WITH THE USE OF A SIMPLIFIED MATHEMATICAL MODEL
Pyrkin Anton Alexandrovich, Tatiana A. Maltseva, Dmitriy V. Labadin, Maxim O. Surov , Bobtsov Alexey Alexeevich

47

An algorithm for synthesis of a control system for a quadrocopter is presented. The algorithm is based on a simplified mathematical model and is easy to realize in contrast to the known algorithms.

MODELING AND IDENTIFICATION OF DYNAMICS OF A HYDRAULIC ACTUATOR WITH A SPOOL VALVE. PART I. MODELING
Aranovskiy Stanislav V., Leonid B. Freidovich, Liliya V. Nikiforova, Losenkov Andrei A

52

Approaches to the problem of modeling of hydraulic actuator are considered. A model for the spool dynamics consisting of a linear block and two static nonlinear subsystems is presented.

MODELING AND IDENTIFICATION OF DYNAMICS OF A HYDRAULIC ACTUATOR WITH A SPOOL VALVE. PART II: IDENTIFICATION
Aranovskiy Stanislav V., Leonid B. Freidovich, Liliya V. Nikiforova, Losenkov Andrei A

57

A method for identification of dynamic model parameters is suggested for the case when only pressures in the hydraulic cylinders but not the valve displacements are measured. The approach is verified by presented results of experiments.

AUTONOMOUS MULTI-AGENT “ROBOT-GUIDE” SYSTEM TO SOLVE AREA MONITORING PROBLEMS
Kremlev Artem Sergeevich, Kolyubin Sergey A, Sergey A. Vrazhevsky

61

The problem of control over a group of robots at the “leader-follower” operation mode retaining positional relationship in unknown environment is considered. To smooth the "follower" robot motion path, an algorithm based on the gradient descent method is applied.

TASK OF CONTROL FOR MULTICHANNEL DYNAMIC SYSTEM OVER PIECEWISE SMOOTH TRAJECTORY
Kapitanyuk Yuri A, Chepinsky Sergey A

65

The problem of control over multichannel object motion along a piecewise smooth trajectory is solved. The control synthesis is based on a differential-geometric approach. Main results are presented as a task-oriented model of motion and a suitable nonlinear control algorithm.

### APPLIED PROBLEMS AND TECHNICAL MEANS OF CONTROL

ALGORITHM OF CONTROL OVER WHEELED MOBILE ROBOT MOVEMENT IN THE PROBLEM OF EXTERNAL SYSTEM MONITORING
Gennady I. Boltunov, Lyamin Andrey Vladimirovich, Alexandra I. Petrik

71

The problem of control over autonomous wheeled mobile robot moving in a complex dynamic environment is considered. A mathematical model of wheeled mobile robot is developed and analyzed. An control algorithm for robot movement along a circle in a medium with mobile external systems is created, the algorithm effectiveness is illustrated by results of mathematical modeling.

ANALYSIS OF THE EFFECT OF WIND DISTURBANCES ON AIRCRAFT COURSE STABILIZATION SYSTEM
Grigoriev Valeriy V., Bushuev Alexander B., Коровьяков А. Н., Yury V. Litvinov

75

A numerical characteristic of operational effectiveness of aircraft stabilization system under the influence of random disturbances is proposed. The characteristic is noted to be convenient in practical applications.

THE DYNAMICS OF THREE-STATE PWM-CONTROLLED PIEZOELECTRIC ACTUATOR
Vladimir Boikov, Bystrov Sergey V., Andrey Yu. Korolev

81

A dynamic model of linear piezoelectric actuator powered by three-state pulse-width modulator is developed. The main difference from the classical consideration of the modulator consists in the presence of a third state - state "disabled". The use of pulse-width modulation is shown to cause nonlinearity of static characteristics and parametric unsteadiness. The mathematical model makes it possible to account for the undesirable effects when applied to the problem of control system synthesis.

MULTIFUNCTIONAL ACTIVE ARTIFICIAL ARM
Borgul Alexander S, Zimenko Konstantin Alexandrovich, Margun Alexei Anatolievich, Kremlev Artem Sergeevich

86

Principle of operation, construction, and control system of active hand prosthesis with 7 DOF are described. Requirements for these devices are always ambivalent. For example, number of control signals decreases with increasing of amputation’s degree. But at the same time operator needs to increase number of active joints. An algorithm for control over the device based on application of EEG control signals, force sensitive sensors, and accelerometer is developed. The control system makes it possible to increase the number of active DOF, improve the system accuracy, and compensate external disturbances and reactive torque caused by the prosthesis movement.

CORRECTION OF PERSPECTIVE PROJECT DISTORTION IN A TECHNICAL VISION SYSTEM
Blinnikov Andrey A., Vladimir Boikov, Vitaly V. Bulatov, Alexander A. Kulchitsky, Anatoly Sporyagin

89

Image distortion caused by perspective projection of object space onto photo detector matrix plane in mobile robot vision system is considered. An algorithm for elimination of the distortion is proposed.