Boris Andrievsky

Adaptive synchronization methods for signal transmission on chaotic carriers

The problem of synchronization of chaotic systems in the presence of additive bounded noise is considered. Two kinds of adaptive synchronization algorithms are evaluated by simulation: (i) an algorithm of adaptive observers made robust by parametric feedback or dead zone; (ii) an algorithm of parameter identification with implicit adjustable model and augmented signals.The results are illustrated by numerical examples of synchronization of Chua systems. Application of the proposed adaptive synchronization algorithms to the problem of signal transmission is discussed.

Control of chaos: methods and applications in mechanics

A survey of the field related to control of chaotic systems is presented. Several major branches of research that are discussed are feed-forward (‘non-feedback’) control (based on periodic excitation of the system), the ‘Ott–Grebogi–Yorke method’ (based on the linearization of the Poincaré map), the ‘Pyragas method’ (based on a time-delayed feedback), traditional for control-engineering methods including linear, nonlinear and adaptive control. Other areas of research such as control of distributed (spatio-temporal and delayed) systems, chaotic mixing are outlined. Applications to control of chaotic mechanical systems are discussed.

Adaptive Observer-Based Synchronization of Chaotic Systems With First-Order Coder in the Presence of Information Constraints

We analyze the performance of an adaptive chaotic synchronization system under information constraints assuming that some system parameters are unknown and only the system output is measured. Such a problem was studied previously in the absence of information constraints based on an adaptive observer scheme, allowing for its use in message transmission systems. We provide analytical bounds for the closed-loop system performance (asymptotic synchronization error) and conduct a numerical case study for a typical chaotic system, namely the Chua circuit, in the presence of information constraints. It is shown that the time-varying quantizer with one-step memory provides a reasonable approximation of the minimum transmission rate for adaptive state estimation.

Combined Adaptive Controller for UAV Guidance

Combined adaptive control law for an autopilot of the unmanned aerial vehicle (UAV) homing guidance system is proposed. The adaptation algorithm provides prescribed attitude motion dynamics for different flight conditions. Simulation results verify efficiency of the combined adaptive controller in the case of significant uncertainty of the UAV parameters and time dependence of the guidance loop.

Synchronization of Passifiable Lurie Systems Via Limited-Capacity Communication Channel

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 multidimensional 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 sufficiently high transmission rate (channel capacity). The results obtained for the synchronization problem can be extended to tracking problems in a straightforward manner if the reference signal is described by an external (exogenous) state space model. The results are illustrated by the controlled synchronization of two chaotic Chua systems via a communication channel with limited capacity.

Control and estimation under information constraints: Toward a unified theory of control, computation and communications

An attempt is made to overview an emerging area of research devoted to analysis and design of control systems under constraints caused by limited information capacity of communication channels. The problem’s prehistory dating back to the 1960s–1970s, as well as the new approaches that appeared during the last decade were analyzed. Much attention was paid to various versions of the celebrated data rate theorem. Consideration was given to the problems of control through the communication networks and some results obtained for the nonlinear systems. The basic application areas were listed in brief.

Hidden oscillations in aircraft flight control system with input saturation

Abstract The presence of actuator saturation can dramatically degrade the system performance. Since the feedback loop is broken when the actuator saturates the unstable modes of the regulator may then drift to undesirable values. The consequences are that undesired nonlinear oscillations appear and that the settling time may unacceptably increase. Rigorous analysis of nonlinear aircraft models is a very difficult task, that is why a numerical simulation is often used as an analysis and design tool. In this paper difficulties of numerical analysis related to the existence of hidden oscillations in the aircraft control system are demonstrated.

Feedback Kalman-Yakubovich lemma and its applications to adaptive control

In this paper we give a survey of results related to the feedback Kalman-Yakubovich lemma (FKYL) giving necessary and sufficient solvability conditions for some class of bilinear matrix inequalities or conditions of feedback passivity of linear systems. Applications to adaptive and variable structure control systems are also discussed.

Estimation and Control Under Information Constraints for LAAS Helicopter Benchmark

A scheme for state estimation and control under information constraints is implemented for “LAAS Helicopter benchmark”. Parameter estimates of the “Helicopter” pitch dynamics model are obtained by means of the real-time identification algorithm. The hybrid continuous-discrete observation procedure for transmission of the measured data over the limited-band communication channel with adaptive tuning of the coder range parameter is proposed and used in the experiments for pitch motion control of the “Helicopter”. Experimental results for pitch motion control of the “Helicopter” are presented, showing efficiency of the proposed method.

Combined adaptive autopilot for an UAV flight control

The combined adaptive control (CAC) law for an autopilot of the unmanned aerial vehicle (UAV) attitude control is considered. The adaptive algorithm includes the variable-structure controller with forced sliding motion, parametric identification algorithm and the parallel feedforward compensator. The adaptation algorithm provides the prescribed dynamic properties of the attitude control system for various flight conditions of the UAV. The simulation results for nonlinear UAV dynamics model are presented.