A new approach is presented for sensor fault detection reconstruction and state estimation. The system considered is linear polytopic parameter-vary ing (LPV) system. The main idea is the design of a novel robust adaptive observer based on and polyquadratic formulation with a new set of relaxation. Sufficient conditions are given by a set of Linear Matrix Inequalities (LMI) in order to guarantee the stability of the system and the asymptotic convergence of the fault error. A simulation example has been studied to illustrate the proposed methods by detecting constant and variable sensor fault.

The article is devoted to the formulation and solution of the two-criterion pursuit-evasion game on the plane of one pursuer against two targets, one of which is false. A false target is used to distract the pursuer, allowing the true target (in the process of diverting) to maximize the minimum possible distance to the pursuer. The specificity of the pursuer is that it has a circular classification zone of radius R, within which it has the ability to instantly classify the target as false or true. The game is that the pursuer minimizes the time required to approach one of the targets to a distance not exceeding R (R-encounter), and the targets, acting in concert, maximize the minimum distance between the pursuer and the remaining target. The game continues until the R-meeting of the pursuer with the first (false) target, i.e. until the classification of the false target. It is assumed that the first target is false a priori the persecutor is not known. The strategy of using a false target is precisely to release it to distract the pursuer from the true target. In reality, the false target is a mobile drone, which is controlled programmatically by the on-Board computer. In the class of open-loop controls the staging was investigated in 1984 by Ivanov M. N. and Maslov E. P. There is a natural question: what will give an extension of a class of open-loop controls of the false targets to the class of closed-loop controls, i.e. to the class of controls with a feedback? This question is quite appropriate in connection with the great progress in the development of microprocessor technology and improving the performance of on-Board computers, which makes it possible to use more complex algorithms for controlling Autonomous mobile objects. This article gives a negative answer to the above question, namely, it is shown that the extension of the class of open-loop controls by a false target does not improve the quality of control. It is proved that in this game there is a Nash equilibrium in the program strategies of the players.

The solution of the so-called problem of speed of response in one coordinate, which has important theoretical and practical importance, is investigated. It is formulated with reference to linear one-dimensional high-order control objects described by a system of ordinary differential equations in a certain phase space. The transient time tnn of the system designed is understood in a sense of the classical control theory in reference to one (output) coordinate of the object and is determined by using the zone Δ = σ* = 4.321 %, which equals the given (desirable) value of the overshoot of the system synthesized. This overshoot corresponds with the speed of response oscillating second-order element with a damping coefficient ζ= = 2 2 0,7071 / . It is indispensable to mention here that the equation Δ = σ is one of the necessary conditions for the maximum speed of response of the system with the oscillating character of transient processes. In accordance to this the task of the speed of response by one coordinate can be described by the following generalized formulation: one must find the linear algorithm of the feedback signal, which provides a preset order of the astatism na for the closed-loop control system and converts the control object from a zero state into a final state, which is determined by the constant signal of the input, with a minimal time value of the transient processes of the system tnn and the preset value of the overshoot σ m σ* while fulfilling the constraint of the control signal |u(t)| m umax. Nowadays the task mentioned is approximately solved by the algebraic method of the synthesis of linear control systems with the determination of a desirable transfer function of the designed closed-loop system based on model normalized transfer functions (NTF). In the works by Kim D. P. there was carried out the analysis of four types of normalized transfer functions characterized by the increased speed of response. In this work two additional types of normalized transfer functions are suggested, in comparison with mentioned NTF they have the increased speed of response in case of the preset value of the overregulation σ* = 4.321 %. On their basis and using the methodology of the modal control the method of the synthesis of the controller is suggested; this method ensures the transient time of the designed system to be close to the minimum in case of the preset constraint of the overregulation and the value of the control signal. It needs to be emphasized that in contrast to the algebraic method of the synthesis, this method is applied to a wider range of control objects: as to minimal-phased objects as to non-minimum-phased ones; as to the objects containing zeros as to those without them. The method is illustrated by an example of synthesis of control system speed of response of the fourth order, containing the results of its modeling.

The approach to the analysis of Lyapunov systems stability of linear ordinary differential equations based on multiplicative transformations of difference schemes of numerical integration is presented. As a result of transformations, the stability criteria in the form of necessary and sufficient conditions are formed. The criteria are invariant with respect to the right side of the system and do not require its transformation with respect to the difference scheme, the length of the gap and the step of the solution. A distinctive feature of the criteria is that they do not use the methods of the qualitative theory of differential equations. In particular, for the case of systems with a constant matrix of the coefficients it is not necessary to construct a characteristic polynomial and estimate the values of the characteristic numbers. When analyzing the system stability with variable matrix coefficients, it is not necessary to calculate the characteristic indicators. The varieties of criteria in an additive form are obtained, the stability analysis based on them being equivalent to the stability assessment based on the criteria in a multiplicative form. Under the conditions of a linear system stability (asymptotic stability) of differential equations, the criteria of the systems stability (asymptotic stability) of linear differential equations with a nonlinear additive are obtained. For the systems of nonlinear ordinary differential equations the scheme of stability analysis based on linearization is presented, which is directly related to the solution under study. The scheme is constructed under the assumption that the solution stability of the system of a general form is equivalent to the stability of the linearized system in a sufficiently small neighborhood of the perturbation of the initial data. The matrix form of the criteria allows implementing them in the form of a cyclic program. The computer analysis is performed in real time and allows coming to an unambiguous conclusion about the nature of the system stability under study. On the basis of a numerical experiment, the acceptable range of the step variation of the difference method and the interval length of the difference solution within the boundaries of the reliability of the stability analysis is established. The approach based on the computer analysis of the systems stability of linear differential equations is rendered. Computer testing has shown the feasibility of using this approach in practice.

A conceptual approach to the problem of managing spatial configurations of DNA molecules is considered. The work is problematic in nature and is a synthesis of the authors’ research in the field of modeling the behavior and structure of DNA by the methods of the mechanics of a deformable solid. The subject of research in this paper is the question of the applicability of methods of control theory to a living object by the example of a DNA molecule. The paper considers both issues of controllability on examples of the influence of the parameters of a molecule on its configuration, and questions of observability and identification of parameters of a molecule, based on the visible configuration in the natural environment. A brief review of the authors’ results in terms of adaptation to the objects of research of existing and development of new mathematical models of deformable elastic objects with regard to their internal structure is given. The proposed approach is based on the concept of transition using known methods of molecular dynamics from a multi-element discrete medium to a continuum containing momentary stresses. To this end, in previous works, the authors obtained the dependence of the components of the strain tensors, force and moment stresses on various types of interatomic interaction potentials (LennardJones potential, Born-Meyer potential, etc.). The need to choose as the base model of a continuum containing momentary stresses is dictated by the peculiarities of the main object of study - nucleic acid molecules and biopolymers - which have several degrees of freedom of rotational motions. Also, as an example, we consider the case for which the reduction from the three-dimensional problem of the asymmetric theory of elasticity to a one-dimensional one was carried out by splitting the three-dimensional problem into a set of two-dimensional and one-dimensional problems. The kinematic parameters that are necessary to attract in order to obtain a closed system of equations of the one-dimensional moment theory of rods with the system of Kirchhoff’s differential equations are indicated. The remaining geometrical values are found from the relations defining them. The proposed approach is consistent with current trends in the field of molecular modeling in biophysics and physico-chemical biology, and it seems promising in solving the problems of controlling genetic and biochemical processes involving DNA.

The article is devoted to the development of searching and covering task in different areas, for example, for extinguishing fires, during search operations in the air, on the ground, etc. Two probabilistic models were created based on the characteristics of the sensors and the search zone, that is, the probability density of the target position and the conditional probability of detecting the target by the sensor under the conditions that the target is at the point of observation (depending on the distance between the sensor and the point of observation). Based on these models, the parameters and the search procedure were analyzed; more precisely, the relationship and formulas between the target detection probability, the search time and other parameters were found. The main difference of the proposed research lies in the fact that by optimizing the obtained relations and formulas it is possible to obtain an optimal distribution of time in the search process, as a result, to increase the probability of target detection. In the research process, at first, the case where the distribution probability of target position in the search area represents a discrete form (network map) is investigated, then a formula for the probability of target detection in a discrete and continuous probe is obtained. Using the method of Lagrange multipliers and dynamic programming, the optimal distribution of search time in each cell was obtained. Further, according to the result obtained, the study was expanded to a continuous distribution probability of target position in the search area, the functional probability of detecting the target of search time, probability density of target and the search trajectory (velocity) was derivated. As a result of solving this functional, for a given search time and probability density distribution of target, optimal control (trajectory and speed) was obtained. The simulation confirmed the efficiency of the proposed search method. The simulation result shows that the greater the probability density of target and the slower the agent’s movement speed, the greater the probability of target detection, for some values of the search parameters, the difference in probabilities of target detection reaches 75.3 %.

The complex control system of the helicopter-type aircraft is considered, its design is described depending on the requirements for the aircraft and interaction with the interfaced onboard equipment. The main elements of the system are the subsystems of remote and automatic control of the helicopter. In the process of developing such a system, much attention is paid to ensuring a high level of reliability and maintaining the functions necessary for the safe completion of the flight. Therefore, the main requirement for an integrated management system is the probability of its failure in backup management with improved stability of the control object is not higher than 10-9. The authors of the article conducted the analysis of the integrated management system on accutanecost in conditions of failure of the elements included in its composition. In the course of the analysis the assessment of fault safety of subsystems of remote and automatic control is carried out. At the same time, for each system, the influence of obvious and not obvious failures on the change in the controllability of the aircraft and the safety of its flight was considered. Also, the analysis of the system in the conditions of failure of the on-Board equipment of the device. Special attention is paid to the study of the dynamics of the Executive mechanism of the system in the conditions of failure of the onboard hydraulic power supply system. The paper presents the results of studies of changes in the force, speed and quality factor of the electrohydraulic drive at various failures of hydraulic power lines on Board the aircraft. The obtained results can be used in the process of designing complex control systems, studies of electrohydraulic drives and development of methods for parrying the consequences of failures of the helicopter’s onboard equipment with respect to the complex control system, including the creation of algorithms for reconfiguring the system and the logic of controlling the functioning of its elements.