Scientific results:
We have obtained a solution of the problem of ensuring multiple-synchronization modes for a two-rotor vibratory machines. We have developed, researched and experimentally confirmed, using the SV-2M testing rig of the Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, algorithms of adaptive and non-adaptive control for the multiple synchronization of the vibration exciters of two-rotor vibration units that ensures the reduced phase synchronization of rotors in the operational region at a specified rotation frequency.
We have proposed new decentralization algorithms ensuring both uniform and specified non-uniform placement of mobile agents on a stretch in the conditions of communication delays and network technology switching.
Our researchers have developed a technology for the strictly mathematically substantiated synthesis of reactive (reflex-like) of resource-efficient algorithms for autonomous navigation and motion control in ensembles of airborne, underwater and space drones in three dimensions ensuring the detection, localization, and subsequent dense sweeping of the isosurface (the level set) of an unknown and unpredictably changing field. We reviewed a typical situation for applications when only the value of the field at the current location of a robot is available for measurement; among the examples of such fields is the concentration of a pollutant, level of radiation, salinity, temperature or the hydrogen index of a medium, the cumulative strength of signal emitted by an object or a group of objects etc. The result accounts for the limitations of the kinematics of drones that are characteristic of the applications — the non-holonomicity, the absence of all-wheel drive and the limitations of velocity — and proposes a resource-efficient architectures of a group that is robust to disturbing factors and equipment failures - the non-use of communication systems and the complete algorithmic homogeneity of the ensemble (all the drones adhere to a common rule and are identical in terms of performed roles). The results provide mathematically strict guarantees o global convergence to the target isosurface, the optimal self-allocation of drones for its most efficient sweeping and the absence of collisions between drones. The corresponding algorithms do not utilize means of communication and consume minimum computation capacity, which allows, on one side, use cheap equipment for conducting complex missions and, on the other side, in the case of the use of advanced equipment, to reserve its capacity for conducting associated main tasks.
Regarding networks of mobile agents with a nonlinear dynamics, we have obtained and mathematically substantiated algorithmic solutions of the problem of preserving the consensus in the context of the limitations for the bit rate of data transmission between agents as well as (possibly) sensor and actuator equipment of an individual agent. Such limitations can be caused by the properties of the environment (for instance, underwater wireless communications), the requirements for power consumption (space communications), the use of resources of communication channels for solving related problems etc. For three widespread architecture of agent group organization we uncovered strictly substantiated design requirements for the data transmission rate that allow to preserve the consensus, and algorithms have been developed for controlling agents, which ensure such preservation. The interest in distributed algorithms of achieving and preserving the consensus with regard to a specific dynamic variable is explained by their fundamental nature. In particular, they form the basis of the standard technology of solving the more general problem of forming and sustaining the required spatial configuration of a group of mobile robots.
Our researchers have compared the local, modal methods and the method of controlling shape in application to controlling oscillations of distributed elastic systems. A metal beam acted as the control object, the control system includes a finite set of piezoelectric plates (sensors and actuators) glued to the beam on specific regions. We compared the specified method for the problems of canceling forced oscillations of the beam on the first and second resonances, determined that the modal approach is preferred (when using two sensor-actuator pairs, the decrease of the amplitude of oscillations of the beam at both resonances amounted to more than 30 dB).
The Laboratory has researched a non-linear model of a metamaterial to determine the influence of nonlinearity on dynamic processes of deformation, finding the physical factors allowing to control the processes of nonlinear localization of deformation waves. The Laboratory has conducted an analytical and numerical research of controlling nonlinear deformation waves in a metamaterial.
We have solved the problem of controlling rotational motion of a solid body in the case when, in addition to the controlling moment, the body is subjected to disturbing forces, which are oscillations with zero mean values. Our researchers have studied the cases of linear and significantly nonlinear moments. We obtained conditions under which disturbances do not disrupt the stability of programmed motion.
The Laboratory has solved the problem of the three-axis electrodynamic stabilization of a satellite in an orbital coordinate system with the use of control containing a delay distribution. We have found the conditions for the parameters of control and the value of delay under which the exponential stability of programmed motion is guaranteed.
We have proven the possibility of building a control system similar to a PID regulator with distributed delay for the electrodynamic stabilization of the programmed rotation of a satellite under which the dynamic symmetry axis of the satellite is stabilized along the local vertical, while the satellite itself slowly rotates around this axis in the conditions of a disturbing gravitation moment. We found conditions for the parameters of control and the value of delay under which the exponential stability of programmed motion is guaranteed.
The Laboratory has studied the stability of a discrete-continuous linear mechanical systems with delay and switching in positional forces. On the basis of the Razumikhin’s theorem and the use of Lyapunov-Krasovskiy functionals we have found the conditions of the exponential stability of the system. The developed approaches allow to compute the limit value of delay in data transmission channels under which stability is preserved.
We have developed mechanical systems that are under the influence of dissipative, nonconserfative and potential forces described by homogeneous functions. It is suggested that there is a delay in the potential forces. Using a special structure of the Lyapunov–Krasovskiy functionals of the complete type, we found the conditions of asymptotic stability for the trivial equilibrium position for any constant non-negative delay.
The Laboratory has researched a mechanical system that is under the influence of strongly nonlinear potential and dissipative forces, with nonlinear nonstationary disturbances having zero mean values. Using a special structure of the Lyapunov function, we have found conditions under which disturbances do not affect the asymptotic stability of the location of the equilibrium of the system. The developed approach was applied to the problem of single-axis stabilization of a solid body.
A new method has been developed for the digital control of multi-dimensional systems in the context of perturbations acting on the dynamics of the object and measurement. The developed algorithm ensures the hyperexponential stability of a closed system when nonlinear control algorithms are used. Nonlinear algorithms can be discretized in the spatial and the temporal variable by finite differences for the assessment of derivatives of the output variable. We have found the conditions of stability for a closed system in the form of the solvability of linear matrix inequalities allowing to compute the limit value of discretization and delay in data transmission channels under which a closed system maintains its stability.
Education and retraining of personnel:
At the 15th Multi-conference on the Problems of Control (4-6 October 2022, Saint Petersburg) we conducted the local conference «Observers and filters» that was devoted to the problems of creating modern methods of control and their applications in practice under circumstances of disturbances, measurement noise, uncertainty and the use of digital communication channels.
Collaboration:
Tel Aviv University (Israel), Center for Scientific Research and Higher Education at Ensenada (Mexico).
