In paper developed version of the basic concepts, models and methods for the formulation and solution of problems of control and diagnosing of processes in systems, tasks of constructing models of processes in which the causal relationships of events are transformed into functional dependencies between elements in sequences, problems of formalizing of process control rules, etc. For this extended classical recurrent definition of the sequences, which presents the functional elements depending on the immediately preceding to them m elements to offered Z-recurrent definition, which defines the functional relationship between sets of elements in the sequence. The orders of Z-recurrent forms have the form of a set of numbers and are convenient for accurate and complete characterization of the connections of events in processes. The tasks of control, diagnosing, constructing new models of processes, assessing the complexity of processes and rules for managing processes can be formulated and solved using numerical indicators of Z-recurrent definitions. A classification of Z-recurrent definitions of sequences and a classification of processes are constructed, an algorithm for checking the feasibility of determining a Z-recurrent form for given sequences of form is developed. The Z-recurrent definition of sequence is complemented by the Z-recurrent sequence pattern method, which includes: introducing a linear order on the base set of sequence elements, constructing an image for the sequence in the form of a sequence of executing or non-executing relationships between the elements represented by a linear order, and applying Z-recurrent definitions to the constructed image of the sequence. The problem on which the solution of the considered problems is based is the recognition of two sequences by properties, which are determined by the indicators of Z-recurrent definitions of sequences, which have the form of orders of Z-recurrent forms. Sets of orders in executing or non-executing Z-recurrent forms characterize the sequences and the analyzed sets of sequences, which allows you to set and solve problems related to system management: problems of control and diagnosing of processes in the system, problems of constructing process models, problems of formalizing and complexity estimation of control rules of processes.

The main concern of this paper is the problem of optimal stabilization of a quasilinear stochastic system with controllable parameters. Systems of this type are described by linear stochastic differential equations with multiplicative noises whose matrices, in general case, are nonlinear functions of control. The performance criterion is a modification of the classic quadratic performance cost. The goal is to minimize the criterion on the set of admissible control processes. This formulation of the problem is interesting because it allows us to study a wide range of optimization problems of linear systems with multiplicative perturbations, including: optimization of design parameters of the system, the problem of optimal stabilization under constraints on the gain matrix of the linear regulator in the form of inequalities, the problem of optimal stabilization of linear stochastic systems under information constraints. The main result of this paper is the necessary conditions for the optimal vector in the problem of stabilization of a quasilinear stochastic system with controllable parameters.The numerical gradient-type procedure for synthesis of the optimal stabilizing vector is also proposed. In addition, using obtained results we construct the algorithm for synthesis of a suboptimal time-dependent control. The result of the proposed algorithm is piecewise constant control, which gives the value of the criterion is guaranteed not worse than for the optimal stabilizing vector. This algorithm is relatively simple and one may use it for calculations in real time. The obtained results are applied to the problem of optimal stabilization under information constraints, in which the necessary optimality conditions are also obtained and the gradient-type procedure for the synthesis of the optimal control is proposed. The use of the obtained results is demonstrated by a model example.

The authors develop an adaptive approach to synthesis of intelligent digital models, which have acquitted particular significance during the research of controlled mechanical constructions. Capacity for generation of active reactions to external functional and energy impacts is a distinctive feature, when the object automatically finds rational or optimal states by means of respective adaptation to the aforesaid impacts. The paper presents principles of intelligent model construction, which simulates the processes of controlled transitions between various states of "the controlled construction" in presence of NON-factors. The principle of cyclic adaptive control has been taken as the basis of generation of the "controlled construction" intelligent model, where in every cycle the managerial decision generation technology is implemented, which provides maintenance of the current construction state or its transition to a more preferable state. The identification process for identification of states of the studied construction has been analyzed, and it assumes comparison of the current values of its parameters corresponding to microstates of the informational image along with classification parameters of the preliminary designated multiple taxons of microstates. A taxonomic scheme was offered for this purpose based on the use of five main taxons having the definite system meaning. It has been shown that application of the squared distance metrics to median abscissa of the selected intervals is technologically sufficient as a proximity measure of the parameter value to the taxon of microstates. The management scenario has been considered in the intelligent mechatronic system, which displays transitions between the optimal states of "the controlled construction" under the influence of external factors. An example, of the intelligent model of mechanical construction is shown in the form of a pulse-type regulator for control of the executive mechanism of system reactions. Construction of the pulse-type regulator is based on the use of the virtual signal formation scheme of mismatch between the current value of the input signal and its value defined by the intelligent system setting mechanism. This mismatch is subject to discrete convolution with the tabulated and abridged original of the required pulse characteristic. It is also shown that sufficiently economical recurrent interrelations for calculations according to mismatch values are formed during construction of the model on the basis of proportional integral and differential regulators.

In this paper, we consider the convey-crane system, which can transport loads for industrial purposes. The mathematical model, describing the motion of convey-crane, is presented by a Lagrangian mechanical system of nonlinear equations with two degrees of freedom and one control action. It is supposed that the rope has no mass, its stiffness is not taken into account, and there is no friction in the joints. The stabilization problem of the desired convey-crane position is posed underuncertain mass inertia characteristics, an action of non-smooth bounded disturbances and incomplete measurements. Based on the passivity property, the control law with linear and sigmoidal parts is constructed for the solution of the problem. The only measurement of the convey-crane position is available without a noise in the measurements. We use the low order observer with sigmoidal corrective action to obtain the needed velocity estimates for the control law. It is shown that the using of sigmoidal function as a prelimit realization of sign-function provides disturbances invariance with the given accuracy. With respect to the smoothness and boundness, sigmoidal function helps to avoid overshoot in the transient responses and excessive consumption of control resources. Moreover, unlike the sign-function, a sigmoidal function is realized in the electromechanical systems with actuator dynamics, in which the physical restrictions on the forces and general moments are posed. The constructed control law with linear and sigmoidal parts is simulated for the convey-crane system in MATLAB- Simulink. The classical PD-controller is simulated too for the purpos e of comparison. The results of modeling are proved the effectiveness of the proposed approach.

The article is devoted to the development of an algorithm for modeling the characteristics of steels in accordance with customer requirements. A mathematical model is presented that takes into account the optimal levels of the main factors and their interaction, providing the required values of the characteristics. The next step in the study of the mathematical model was modeling by means of functional modeling methodology IDEF0. Input and output data, as well as normative documents of model management and mechanisms of this management for building a functional model are defined. The control mechanism was the software product OptimalSostav, developed using the object-oriented programming language Delphi. The software product is designed to simulate the characteristics of steels using the specified limits of permissible minimum and maximum values of mechanical properties. The algorithm of realization of the control mechanism, which is based on the fractional factor analysis, is described. The presented algorithm allows to identify the influence of chemical composition on the mechanical properties of steels in the form of mathematical and graphical dependencies and to determine the specified mechanical properties that meet the requirements of the customer. The main possibilities and the scope of the software product, which allows to solve the problem of predicting the optimal chemical composition, providing the required mechanical characteristics, as well as to adjust the process of steel melting within a given chemical composition to achieve the desired set of properties. The application of the software product on the example of the analysis of the influence of chemical elements on the mechanical properties of 75HMF roll steel is shown. The results of modeling in the form of mathematical and graphic dependences are given and the estimation of efficiency of application of the software product is given. The results of solving the problem of approximation of the obtained graphic dependences of the influence of chemical elements on the mechanical properties of the studied steel grade by means of Microsoft Excel are presented. It is established that the developed mathematical and algorithmic software of the software product allows to study the percentage of chemical elements in relation to the total composition of the alloy, based on the obtained pie charts and dependency graphs. The adequacy of the model is confirmed by experimental results.

The analytical solution of an approximate (truncated) equation for the vector of a rigid body finite rotation has made it possible to solve the problem of determining the quaternion of orientation of a rigid body for an arbitrary angular velocity and small angle of rotation of a rigid body with the help of quadratures. Proceeding from this solution, the following approach to the construction of the new analytical algorithm for computation of a rigid body orientation with the use of strapdown INS is proposed: 1) By the set components of the angular velocity of a rigid body on the basis of mutually — unambiguous changes of the variables at each time point, a new angular velocity of a rigid body is calculated; 2) Using the new angular velocity and the initial position of a rigid body, with the help of the quadratures we find the exact solution of an approximate linear equation for the vector of a rigid body finite rotation with a zero initial condition; 3) The value of the quaternion orientation of a rigid body (strapdown INS) is determined by the vector of finite rotation. During construction of the algorithm for strapdown INS orientation at each subsequent step the change of the variables takes into account the previous step of the algorithm in such a way that each time the initial value of the vector of finite rotation of a rigid body will be equal to zero. Since the proposed algorithm for the analytical solution of the approximate linear equation for the vector of finite rotation is exact, it has a regular character for all angular motions of a rigid body).

We design the navigation and control system for unmanned aerial vehicle (UAV) with four tilting rotors. The considered UAV implements the so-called X-sceme, which implies the main body and four symmetrical beams, upon which rotors with propellers are mounted. It is different from the classical quadrotor by having four additional servomotors that may change the orientation of the rotors with respect t the main body, thus increasing the control parameters number. Greater number of the actuators in the system, on the one hand, opens new venues for UAVs’ applications but, on the other hand, makes the mathematical model of the UAV’s dynamics quite complicated. The latter calls for new control algorithms to be developed. We start by forming the mathematical models of the UAV’s dynamics. It is shown that the introduction of the tilting motors allows implementing independent control of the quadrotor’s position and attitude. The control loop is designed on the base on the analytical dynamics inversion. The expressions for the control parameters thus obtained are subjected to the numerical analysis, which allows taking into account technical constraints for maximal motor speed and tilt angles. Feedback in the control loop is implemented by simulation of the on-board sensors’ signals, whose characteristics correspond to those of the sensors used in the UAV’s experimental prototype design. The signals are processed with the aid of the unscented Kalman filter algorithm. The results of numerical experiments corroborate the efficiency of the developed control and navigation algorithms. The mission simulated in the numeric experiments is tracking of a pre-defined trajectory and pointing with a body-fixed camera at a mobile object, which, in turn, moves along a programmed trajectory.The results of the numeric experiments show that the UAV is capable of performing complex maneuvers with independent position and attitude control.