Lyapunov exponents (LE) are an effective tool for analyzing the qualitative characteristics of dynamic systems. Identifiability, recoverability and detectability problem of Lyapunov exponents not studied. This problem is actual. We propose an approach for verifying identifiability, recoverability and detectability. The approach bases on the analysis of geometric frameworks depending on the structural properties coefficient of the system. The structural properties coefficient reflects the change in Lyapunov exponents, and geometric frameworks are a source for deciding on the type of indicators. We obtain conditions for the complete detectability of Lyapunov exponents. These conditions guarantee the receipt of indicators set. We propose a criterion of σ-detectability with a level of υ-non-recoverability and give a method to evaluate it. We propose the method for verifying the adequacy of the Lyapunov exponents set. The permissible mobility border of the largest Lyapunov exponent obtains.

In this paper, we propose a new method for synthesizing the control of plants with sector-bound nonlinearity with a guarantee of finding the controlled signal in given set at any time under conditions of unknown bounded disturbances. The basis of the method consists of two stages. At the first stage, the coordinate transformation is used to reduce the original constrained problem to the problem of studying the input-to-state stability of a new extended system without constraints. Thus, any known control methods can now be applied to stabilize the system in new coordinates. At the same time, to achieve the goal, it is not required to reduce the value of the control error. It is enough to show its boundedness. At the second stage, a control law is synthesized for the extended system, where the adjustable parameter is selected from the solution of linear matrix inequalities. To illustrate the effectiveness of the proposed method, simulation in the MATLAB Simulink is given. The simulation results show the presence of controlled signals in the given set and the boundness of all signals in the control system. It is shown that an increase the value of the gains in the control law improves the quality of disturbance attenuation that is consistent with theoretical results.

The article deals with topical problems of artificial intelligence related to the development of cognitive tools for visualeffective thinking of autonomous intelligent mobile systems, which provide them with the possibility of organizing expedient behavior in a priori undescribed problematic environments. A self-learning algorithm with an active-passive logic of behavior has been developed that allows intelligent systems to automatically generate conditional programs of expedient behavior that reflect the patterns of transformation of various situations of an a priori undescribed, unstable problem environment. A characteristic feature of the proposed self-learning algorithm is the imitation of testing trial actions in the current operating conditions, which gives the intelligent system the ability to study the patterns of the problem environment without changing the current operating conditions during the self-learning process, which may not be related to the specified goal of expedient behavior. For a formal description of the current situations of the problem environment, as well as conditional signals fixed in the generated conditional programs of expedient behavior, it is proposed to use fuzzy semantic networks. This allows autonomous intelligent mobile systems to accumulate experience of expedient behavior regardless of a specific subject area and transfer it to new conditions of an a priori undescribed problem environment, similar to the previously studied operating conditions. Boundary estimates of the complexity of self-learning algorithms are found that have a polynomial dependence on the number of vertices of fuzzy semantic networks compared with each other in the process of self-learning and the power of the set of trial actions worked out by the intelligent system, represented in its memory in the form of frame-like fuzzy specified structures. A simulation of the expedient behavior of autonomous intelligent systems was carried out, organized on the basis of the proposed self-learning algorithm, which showed its efficiency and effectiveness in adapting intelligent systems to a priori undescribed, unstable problem environments. The practical significance of the results obtained lies in the effectiveness of their use for the development of problem solvers for autonomous intelligent mobile systems for various purposes, which provide the ability to perform complex tasks in a priori undescribed real problem environments.

In this paper, we tackle the handling-comfort conflicting problem of a quarter-car system using Active Disturbance Rejection Control (ADRC). ADRC parameters are tuned using Vyshnegradsky equations which determine the stability criteria of a third order system. To do this, a multi-objective optimization procedure for selection of ADRC observer coefficients is formulated using a genetic algorithm. Suspension deflection and sprung mass acceleration responses are tested to a random road disturbance input. Simulation results show that the compromised solution between handling and comfort can be achieved by introducing the sprung mass acceleration into the feedback loop of ADRC. Using this approach allows for improving the issue of comfort up to 50 percent with just 10 percent worse performance of the issue of handling.

The relevance of the work is due to the widespread introduction of unmanned aerial vehicles, including quadcopters, in various areas of both civil and military applications. A review of various methods of controlling quadcopters, considering their features as nonlinear objects of high dimensionality, is performed. The work is devoted to stabilizing a quadcopter on a complex trajectory defined by functional coordinate relationships in 3D space. A nonlinear dynamic model of the quadcopter in a coupled coordinate system is constructed. The quadcopter control is based on a combination of two control actions. When solving the inverse dynamics problem, program control provides motion along a given trajectory. Stabilization of motion along the desired trajectory is provided by phase coordinate feedback. The stabilizing regulator ratios are found by the modal control method based on the solution of a linear matrix inequality using a linearized model. The found feedback ratios provide the required degree of stability of the closed-loop system, ensuring the quadcopter robustness to parametric perturbations. The legitimacy of this approach to the synthesis of control of a nonlinear system is substantiated by the topological equivalence theorem for the nonlinear system and the linearized model in that the nonlinear system has stable or unstable manifolds, which are analogs of the stable or unstable spaces of the linearized system. The results of computational experiments to estimate the error in reproducing a given quadcopter trajectory are presented. A simulation of the quadcopter behavior was performed, and the trajectory reproduction error was calculated to confirm the effectiveness of the synthesized stabilizing control and the optimal control based on the Pontryagin maximum principle. According to this criterion, the stabilizing control synthesized based on linear matrix inequalities is more effective for the quadcopter. Computational experiments were performed using the MATLAB application software package.

It is noted that it is necessary to obtain reliable information about air signals that determine the spatial movement of aircraft plane (AP), including small-sized, unmanned and manned, to ensure flight safety in the surface disturbed layer of the atmosphere. It is shown that traditional air data systems of AP implementing aerodynamic and wind cock methods for measuring the parameters of incoming air flow using air pressure receivers installed on the right and left side and distributed over the fuselage, braking temperature receiver and wind cock sensors of aerodynamic angles of incidence and gliding have a complex design, considerable weight and cost, which limits their use on small-sized, unmanned and other aircraft classes. It is noted that the developed air data system with one fixed receiver of incoming air flow, built on the basis of the vortex method for measuring the parameters of incoming air flow, can significantly simplify the design and reduce the mass of system, but provides measurement only in the azimuthal or vertical plane in a limited range of measurement of the aerodynamic angle. The air data system being developed, which implements an ion-mark method for measuring the parameters of incoming air flow, allows for panoramic measurement of the aerodynamic angle, but also only in one plane with increasing complexity of the design and increasing requirements for the identity of the channels of the multichannel measuring circuit, which also limits their use on small-sized aircraft. The known capabilities and advantages of the ultrasonic method for measuring the parameters of gas flows and a panoramic sensor of the aerodynamic angle and true airspeed with a fixed receiver of the incoming air flow have determined the possibility of using the ultrasonic method for spatial measurement of air signals. The functional scheme of the electronic system for spatial measuring air signals of aircraft plane with one (integrated) fixed receiver of incoming air flow and ultrasonic instrumentation channels connected to the input of the computer is revealed. To expand the functionality, a static pressure receiver-hole is installed on the external streamlined surface of the system’s receiving board, connected by a pneumatic channel to the input of an absolute pressure sensor with a frequency output, which is also connected to the input of a computer, at the output of which digital output signals of the air data system of aircraft plane are generated. Analytical models of informative signals and algorithms for spatial determination of air signals in instrumentation channels of the electronic system with one fixed receiver of incoming air flow are obtained. The essential advantages of the considered electronic system are revealed, which increase the competitiveness and efficiency of the system application on small-sized and other classes of aircraft planes to improve flight safety and the efficiency of solving flight tasks.