Controlled Synchronization of One Class of Nonlinear Systems under Information Constraints

Output feedback controlled synchronization problems for a class of nonlinear unstable systems under information constraints imposed by limited capacity of the communication channel are analyzed. A binary time-varying coder-decoder scheme is described and a theoretical analysis for multi-dimensional master-slave systems represented in Lurie form (linear part plus nonlinearity depending only on measurable outputs) is provided. An output feedback control law is proposed based on the Passification Theorem. It is shown that the synchronization error exponentially tends to zero for sufficiantly high transmission rate (channel capacity). The results obtained for synchronization problem can be extended to tracking problems in a straightforward manner, if the reference signal is described by an {external} ({exogenious}) state space model. The results are applied to controlled synchronization of two chaotic Chua systems via a communication channel with limited capacity.Comment: 8 pages, 2 figure

Chaotic Observer-based Synchronization Under Information Constraints

Limit possibilities of observer-based synchronization systems under information constraints (limited information capacity of the coupling channel) are evaluated. We give theoretical analysis for multi-dimensional drive-response systems represented in the Lurie form (linear part plus nonlinearity depending only on measurable outputs). It is shown that the upper bound of the limit synchronization error (LSE) is proportional to the upper bound of the transmission error. As a consequence, the upper and lower bounds of LSE are proportional to the maximum rate of the coupling signal and inversely proportional to the information transmission rate (channel capacity). Optimality of the binary coding for coders with one-step memory is established. The results are applied to synchronization of two chaotic Chua systems coupled via a channel with limited capacity.Comment: 7 pages, 6 figures, 27 reference

Controlled Synchronization Under Information Constraints

The class of controlled synchronization systems under information constraints imposed by limited information capacity of the coupling channel is analyzed. It is shown that the framework proposed in A. L. Fradkov, B. Andrievsky, R. J. Evans, Physical Review E 73, 066209 (2006) is suitable not only for observer-based synchronization but also for controlled master-slave synchronization via communication channel with limited information capacity. A simple first order coder-decoder scheme is proposed and a theoretical analysis for multi-dimensional master-slave systems represented in the Lurie form (linear part plus nonlinearity depending only on measurable outputs) is provided. An output feedback control law is proposed based on the Passification theorem. It is shown that the upper bound of the limit synchronization error is proportional to the upper bound of the transmission error. As a consequence, both upper and lower bounds of limit synchronization error are proportional to the maximum rate of the coupling signal and inversely proportional to the information transmission rate (channel capacity). The results are applied to controlled synchronization of two chaotic Chua systems coupled via a controller and a channel with limited capacity.Comment: 7 pages, 8 figure

Passification-Based Robust Phase-Shift Control for Two-Rotor Vibration Machine

In this paper, the solution to the problem of robust control of the phase shift during rotation at a given speed of the unbalanced rotors for a two-rotor vibratory machine is presented. The solution to this problem is relevant for the development of vibration technologies (for example, a vibro-transportation of bulk materials). The proposed controller includes two proportional-integral (PI) rotor speed controllers with a cross-coupling, which receive signals with opposite signs from the phase shift controller. Unlike previous works, where a PI controller for phase shift control was also taken, including the adaptive controller with an implicit reference model (IRM), in the present paper, a relay-type signal controller with an integral component without a parametric adaptation is used. This approach allows, while maintaining robustness, to increase the operation speed and accuracy of the control process, avoiding at the same time the possible divergence of the tunable parameters due to the influence of noises and disturbances caused, among other things, by vibrations of the setup’s structural elements and measurement errors. For the control law design, the speed-gradient method was employed. For various types of reference phase-shift signals (constant, harmonic, chaotic), the results of extensive experimental studies performed on the mechatronic vibration setup and the simulations accomplished based on the results of identifying the parameters of the stand drive model are presented in the paper. The obtained results confirm the efficiency and robustness of the proposed algorithm and allow one to reveal the system performance properties

Control of Two Satellites Relative Motion over the Packet Erasure Communication Channel with Limited Transmission Rate Based on Adaptive Coder

The paper deals with the navigation data exchange between two satellites moving in a swarm. It is focused on the reduction of the inter-satellite demanded communication channel capacity taking into account the dynamics of the satellites relative motion and possible erasures in the channel navigation data. The feedback control law is designed ensuring the regulation of the relative satellites motion. The adaptive binary coding/decoding procedure for the satellites navigation data transmission over the limited capacity communication channel is proposed and studied for the cases of ideal and erasure channels. Results of the numerical study of the closed-loop system performance and accuracy of the data transmission algorithm on the communication channel bitrate and erasure probability are obtained by extensive simulations. It is shown that both data transmission error and regulation time depend approximately inversely proportionally on the communication rate. In addition the erasure of data in the channel with probability up to 0.3 does not influence the regulation time for sufficiently high data transmission rate

Symmetrical Control Law for Chaotization of Platform Vibrations

The paper proposes an experimentally validated method of chaotization of the platform movement process based on the principle of feedback control using a symmetrical (bidirectional) controller. The significance is shown and the prospect of chaotization of platform oscillations for vibration technologies, in particular, mixing of bulk materials, is disclosed. The proposed algorithm was comprehensively experimentally studied with a laboratory vibratory setup, and the results of experiments demonstrating its efficacy are presented

Methods of Intelligent Control in Mechatronics and Robotic Engineering: A Survey

Artificial intelligence is becoming an increasingly popular tool in more and more areas of technology. New challenges in control systems design and application are related to increased productivity, control flexibility, and processing of big data. Some kinds of systems require autonomy in real-time decision-making, while the other ones may serve as an essential factor in human-robot interaction and human influences on system performance. Naturally, the complex tasks of controlling technical systems require new modern solutions, but there remains an inextricable link between control theory and artificial intelligence. The first part of the present survey is devoted to the main intelligent control methods in technical systems. Among them, modern methods of adaptive and optimal control, fuzzy logic, and machine learning are considered. In its second part, the crucial achievements in intelligent control applications in robotic and mechatronic systems over the past decade are considered. The references are structured according to the type of such common control problems as stabilization, controller tuning, identification, parametric optimization, iterative learning, and prediction. In the conclusion, the main problems and tendencies toward intelligent control methods improvement are outlined

Symmetrical Control Law for Chaotization of Platform Vibrations

The paper proposes an experimentally validated method of chaotization of the platform movement process based on the principle of feedback control using a symmetrical (bidirectional) controller. The significance is shown and the prospect of chaotization of platform oscillations for vibration technologies, in particular, mixing of bulk materials, is disclosed. The proposed algorithm was comprehensively experimentally studied with a laboratory vibratory setup, and the results of experiments demonstrating its efficacy are presented

Historical Overview of the Speed-gradient Method Applications for Nonlinear Control Problems

The present surveyed paper provides a historical overview of the Speed-gradient method and its applications to nonlinear control problems since mid-1970-th, when the method was originated, till the present days. It is demonstrated that it is widely used an efficient and a useful tool for solving various problems in the field of the nonlinear control