The identification problem of Lyapunov exponents is considered for dynamic systems with periodic coefficients under uncertainty. Indexes identification is based on the analysis of a special class of frameworks describing dynamics of indexes change. The method of frameworks obtaining is described. The adequacy concept of obtained estimations Lyapunov exponents is introduced. The adequacy criterion is based on the analysis of the structure definition domain. The domain which belongs to the set of Lyapunov exponents estimates is determined. The method proposed for the order estimation of the system. The method is based on the properties analysis of almost periodic to Bohr functions and proposed frameworks. The case when lineals for Lyapunov exponents are crossed is considered. WE obtain to an infinite spectrum of Lyapunov exponents. Upper bound for the smallest index and mobility limit for the large index are obtained and the index set of the system is determined. The graphics criteria based on the analysis of framework properties are proposed for the adequacy estimation of obtained indexes. The histogram method is applied to check of estimations set. It is shown that a dynamic system with periodic coefficients can have a set of Lyapunov exponents. The extension of almost periodic functions on Bohr is proposed to the problem solve of Lyapunov exponents evaluation. The system order estimation is obtained on the basis of the framework property analysis.

In the paper a linear control system described by its characteristic polynomial with interval coefficients including parameters of controller linearly is considered. Problem of the research is finding parameters of a controller guaranteeing dynamic characteristics of a system despite interval parametric uncertainty of its object. It is proposed to base a controller synthesis on root quality indices: minimal stability degree and maximal oscillability degree. Desired values of these indices will be provided with the help of dominant poles method. Applying this method consists in placing a pair of complex-conjugate dominant poles; all other poles — unrestricted poles — will be placed by defining a right border of their allocation area on a complex plane. To apply dominant poles method, a feature of stability degree and oscillability degree to be determined by images of certain vertices of a parametric polytope was used. To synthesize a controller, it is proposed to divide its parameters in two groups: dependent ones and unrestricted ones. The first group of controller parameters is to provide desired allocation of dominant poles in one of vertices of parametric polytope (a dominant vertex). Unrestricted parameters of a controller are to provide desired distance between dominant poles and allocation area of unrestricted poles. To find coordinates of a dominant vertex and verifying vertices providing unrestricted poles allocation, an interval extension of basic phase equation of a root locus theory was developed. This resulted in interval phase inequalities, whose solution allows finding coordinates of desired vertices of characteristic polynomials coeffi cients polytope. Knowing a dominant vertex polynomial and dominant poles allows expressing dependent parameters of a controller from unrestricted ones. Obtained expressions allow placing unrestricted poles in a desired area of a complex plane. To do this, a D-partition by unrestricted parameters of a controller is performed in all verifying vertices of parametric polytope of a system. After choosing values of unrestricted parameters from intersection of all stability domains obtain during D-partition, dependent parameters of a controller can be calculated. An example of synthesizing a PID-controller guaranteeing desired values of dynamics characteristics for an interval control system of the fourth order is provided.

Solution of the problem of fault accommodation in nonlinear dynamic systems is related to constructing the control law which provides full decoupling with respect to fault effects. The possibility of this solution is strictly limited by the demand on the system state vector availability (this vector is immediately included into control law description). As a rule, not all components of the state vector are immediately measurable at practice. Also, it is impossible to estimate full state vector for the system with unknown (affected by the faults) dynamics. The purpose of this article is to solve the problem of full decoupling by constructing a compensator that is independent of the fault effects a nd is based on a new control law. A solution is based on so-called logic-dynamic approach using only linear methods to solve the problem for nonlinear systems. The implementation of this method does not require a preliminary estimation of the parameters. It is assumed that fault detection and isolation procedure is performed by known methods. Assume the fault occurred and detected, then a solution of the control problem is performed on the basis of additional system that corresponding in a definite sense to the initial model. To solve the problem of accommodation, an efficient algorithm based on a logical-dynamic approach is presented, as a result of which a compensator is constructed. Additional system does not contain unknown vector that describes defects. As a result, fault accommodation effect is achieved. Theoretical results are demonstrated by illustrative and illustrative example.

In emergency situation robot control system stops the manipulator by shutdowning drivers and activating brakes. This mode is used in all cases of equipment failure detection or while alarm bottom is pressed on control panel. Emergency braking is uncontrolled motion. As result manipulator movement deviates from program trajectory as the relations between velocities in joints differ significantly. This creates danger of collisions with objects in robot work space. The paper describes device that can be connected to control system. Connection needs insignificant changing in hardware architecture of robot control system. Device consists of controller and individual electronic schemes that are able to activate brakes of each degree of freedom regardless from other one. This feature allows to design braking trajectory by activating brakes in specific sequence and calculated delays. Mathematical solution for deviation minimization problem of braking trajectory from program one is presented. The solution is reduced to mathematical formulas which depend of the temporary velocities and values of braking decelerations in manipulator joints. The considered way of control differs from similar one described earlier by that in emergency situation drivers turn off immediately. On the first stage manipulator brakes by friction forces in gear boxes. Theoretical evaluations show that in all cases this reduces deviations from program trajectory. Additionally the new way can be used even if fault takes place at least one of drivers.

A dynamic model of motion in the sagittal plane of the passive exoskeleton of the lower extremities, integrated with a similar model of a human operator that determines the movement of the whole structure, is considered. The exoskeleton is designed to help the operator to move additional point load, placed in the "backpack" on the back. The design of the exoskeleton does not have active propulsive elements in the joints; it is endowed with only a semi-automatic system for locking or releasing the knee joints at certain stages of movement, which, however, affect the overall gait pattern. The energy costs and peak values of the control torques that the human operator applies in the process of moving the exoskeleton on certain types of regular, flat, single-support walkings are studied. The results obtained allow us to estimate the effectiveness of the mode of locking-releasing the knee joint used by such devices. Both cases of impact-free transitions to the locked knee mode and transitions accompanied by the occurrence of shock effects in a dynamic system were investigated. In mathematical modeling, the mass inertial characteristics of the human body were taken into account in accordance with the data adopted in anthropology.

The article proposes a control method for autonomous unmanned aerial vehicles (UAVs) group of a fixed-wing type intended to both implement and support flight information with predetermined relative distances between the vehicles. The suggested approach provides any selected geometric formation shape construction and further preservation when UAVs enter a straight-line trajectory described by a given course with arbitrary initial positions of UAVs in the horizontal plane. The proposed method feature is "autopilot—UAV" system’s nonlinear structure consideration, manifesting itself in both the autopilot input commands restrictions existence as well as nonholonomic UAV dynamics. In addition, there is an unlimited multi-UAV system scalability available due to decentralization. We take into account the need to maintain a minimum flight speed of not less than the stall speed and the final speed of the formation equal to the cruising speed of this type of UAV. The nonlinear group control laws synthesized using Lyapunov’s direct method are based on the decentralized consensus interaction topology, initially developed for linear agents, which implies each vehicle to interact with its neighboring vehicles only. Global asymptotic stability for the current control laws has been proved. As a result, proposed control laws determine a non-uniform path-following vector field for each vehicle in the whole UAV group flight space (currently two-dimensional space). The suggested field vector norm at a certain space point is the airspeed command for the vehicle at that point while the vector direction is the course angle command. The proposed approach effectiveness has been successfully tested in the MATLAB/Simulink while using realistic nonlinear six degree-of-freedom (DOF) 12-states fixed-wing UAV models. High fidelity simulation results confirm the suggested approach effectiveness.

The process of deployment elements of constructions and adjustment of the radio-reflecting network of large-sized transformable space-based reflector with the use of a cable-stayed form maintenance system is considered. The deployment process can be broken down into separate phases. At each stage, the movement is due to the impact on the design of the actuator — the element of the control system. Energy for the deployment of the reflector elements is produced by drives, in particular an electric machine. The use of this type of actuator allows you to control the process of disclosure. Due to the fact that currently achieved a huge process in computer technology that allows you to perform three-dimensional computing operations in a short time, it is particularly important to use optimal control algorithms. When deployment the reflector for two types of motion — rotational and translational — mathematical models based on Lagrange equations of the II-kind are obtained. These mathematical models take into account such parameters as dissipation, the presence of longitudinal and transverse deformation. The models provide for the presence of a stop and a lock, as an Executive element in the deployment selected brushless DC motor. All the observations made allow us to formulate a smooth statement disclose items on the stop with minimum oscillation of the structure. The developed models allow to analyze the n-th number of natural oscillation frequencies. Modeling with different parameters of the model is carried out. The parameters of the transition process of the spoke at the opening of the first link with the other links embedded in it and at the fully covered spoke are analyzed. It is shown that depending on the mass-dimensional parameters there is a significant change in the dynamics. For the spoke extension stage, the weight and size characteristics have little effect on the opening dynamics. The smaller the Young’s modulus and density of the material, the greater the damped longitudinal oscillations.. The simulation of this stage with a spoke made of different materials is carried out. Various methods are proposed to reduce the opening time at all stages and minimize transverse and longitudinal oscillations. The possibility of application of the developed mathematical models for a wide range of tasks is shown.