Robust Adaptive Synchronization Control Research Articles

Synchronization of chaotic satellite systems with an unknown parameter

Spacecraft (satellite) formation has several applications in space exploration. Synchronization controllers are essential in satellite formation systems. This article proposes a novel robust adaptive synchronization control (RASC) technique for two identical three-dimensional chaotic satellite systems attitude synchronization with an unknown system parameter, unknown bounded model uncertainties, unknown external disturbances, and nonlinear terms. This controller achieves smooth error vector convergence to zero. The closed-loop has a robust performance as the controller avoids plant nonlinear terms cancellation. This controller has two parts. (i) A nonlinear controller for keeping the closed-loop stable; it flourishes robust and faster error vector convergence to zero with reduced fluctuations. (ii) An adaptive nonlinear controller that compensates exogenous disturbances and model uncertainties using online estimations of model uncertainties and bounds. The Lyapunov stability theory assures the closed-loop's global asymptotic robust stability. Computer simulation results-based analysis verifies the theoretical findings. The article includes a comparative study and discusses the control effort saturation effects.

Function Projective Synchronization of Two Complex Networks with Unknown Sector Nonlinear Input and Multiple Time-Varying Delay Couplings

This paper deals with the function projective synchronization of two complex dynamic networks with unknown sector nonlinear input, multiple time-varying delay couplings, model uncertainty, and external interferences. Based on Lyapunov stability theory and inequality transformation method, the robust adaptive synchronization controller is designed, by which the drive and response systems can achieve synchronization according to the function scaling factor. Different from some existing studies on nonlinear system with sector nonlinear input, this paper studies the synchronization of two complex dynamic networks when the boundary of sector nonlinear input is unknown. The controller does not include the boundary value of the sector nonlinear input and the time delay term, so it is more practical and relatively easy to implement. The corresponding simulation examples demonstrate the effectiveness of the proposed scheme.

Oscillation free robust adaptive synchronization of chaotic systems with parametric uncertainties

The complexity of the closed-loop system, short transient response time, and fast synchronization error convergence rates are the three basic parameters that limit hacking in the data encryption and secure the communication systems. This paper addresses the following two challenges: The full-order synchronization (FOS) of two parametrically excited second-order nonlinear pendulum (PENP) chaotic systems with uncertain parameters. The reduced-order synchronization (ROS) between the canonical projection part of an uncertain third-order chaotic Rossler and the uncertain PENP systems. This article designs a new robust adaptive synchronization control (RASC) algorithm to address the above two challenges. The proposed controller achieves the FOS and ROS in a shorter transient time, and the synchronization error signals converge to the origin with faster rates in the presence of bounded unknown state-dependent and time-dependent disturbances. The Lyapunov direct method verifies this convergence behavior. The paper provides parameters updated laws that confirm the convergence of the uncertain parameters to some fixed values. The controller does not cancel the nonlinear terms of the plant; this property of the controller keeps the nonlinear terms in the closed-loop that results in the enhanced complexity of the dynamical system. The proposed RASC strategy is successful in synthesizing oscillation free convergence of the synchronization error signals to the origin for reducing the transient time and guarantees the asymptotic stability at the origin. The simulation results endorse the theoretical findings.

Delay-range-dependent local adaptive and robust adaptive synchronization approaches for time-delay chaotic systems

This paper studies the local adaptive and robust adaptive control methodologies for the synchronization of the chaotic drive and the response systems with finite time lags, bounded delay rates, unknown parameters, and perturbations. A local adaptive coherence control condition under bounded initial condition is developed to synthesize a feedback controller capable of executing successful synchronization of the drive and the response systems with uncertain parameters and delay belonging to a range (with either zero or nonzero lower bound). A sufficiency condition for the adaptive control approach is inculcated through an amendment in the conventional Lyapunov–Krasovskii functional, which enables to develop the adaptation laws for the unknown parameters associated with the nonlinearity in the dynamical behavior of the drive and the response systems. Further, a robust adaptive synchronization control condition for asymptotic convergent behavior of the synchronization error to a bounded region under perturbations as well as disturbances is provided. Indifferent to the existing works, delay-range-dependent adaptive synchronization methodologies are derived in this paper, and the rendered controller design conditions are valid for both the slow and the fast variations in time delays. Numerical simulations for the chaotic delayed Hopfield neural networks are presented to elaborate the efficacy of the proposed delay-range-dependent adaptive and robust adaptive synchronization control methodologies.

Adaptive mechanism for synchronization of chaotic oscillators with interval time-delays

This paper addresses the adaptive feedback controller design for the synchronization of chaotic systems with interval time-delays in their state vectors by exploiting a lower and an upper bound on time-delays. Simple control and adaptation laws are developed for chaos synchronization, and linear matrix inequalities (LMIs) are derived to ensure asymptotic convergence of the synchronization error between the master–slave systems, using the proposed feedback control strategy, by employing a novel treatment of Lyapunov–Krasovskii functional. Further, the proposed strategy is strengthened by exploiting \(L_2 \) stability against disturbances and perturbations and corresponding LMIs for robust adaptive controller synthesis are derived. Furthermore, a novel delay-range-dependent robust adaptive synchronization control approach for dealing with locally Lipschitz non-delayed and delayed nonlinearities in the dynamics of chaotic oscillators is provided by employing an additional adaptation law for the nonlinearities. A numerical simulation example is provided to illustrate effectiveness of the proposed synchronization approach.

Nonlinear Dynamics of Controlled Synchronizations of Manipulator System

The nonlinear dynamics of the manipulator system which is controlled to achieve the synchronization motions is investigated in the paper. Firstly, the control strategies and modeling approaches of the manipulator system are given, in which the synchronization goal is defined by both synchronization errors and its derivatives. The synchronization controllers applied on the manipulator system include neuron synchronization controller, improved OPCL synchronization controller, and MRAC-PD synchronization controller. Then, an improved adaptive synchronized control strategy is proposed in order to estimate online the unknown structure parameters and state variables of the manipulator system and to realize the needed synchronous compensation. Furthermore, a robust adaptive synchronization controller is also researched to guarantee the dynamic stability of the system. Finally, the stability of motion synchronizations of the manipulator system possessing nonlinear component is discussed, together with the effect of control parameters and joint friction and others. Some typical motions such as motion bifurcations and the loss of synchronization of it are obtained and illustrated as periodic, multiperiodic, and/or chaotic motion patterns.

Robust Adaptive Synchronization Control for a Class of Perturbed and Delayed Neural Networks

This paper is concerned with the asymptotic synchronization problem of a general neural network using the robust adaptive control technique. It is considered a class of modified Cohen---Grossberg neural networks which is supposed to undergo unknown perturbations caused by state-independent nonlinearities and bounded mixed time-varying delays on neuron amplification and activation functions. An adaptive compensation control strategy is proposed to ensure the elimination of the perturbed and delayed effects by means of adaptive estimations of unknown controller parameters. Through Lyapunov stability theory, it is shown that the proposed adaptive compensation controllers can guarantee the asymptotic synchronization of neural networks without knowing the knowledge of bounds of nonlinearities and delays. A numerical example is provided to illustrate the effectiveness of the developed techniques.

Synchronization of Uncertain Chaotic Systems with Unknown Response Systems

Considering the situation with the same dimension but different structure in driven system and response system, a new kind of robust adaptive synchronization controller is designed based on the Lyapunov stability theorem . Both the unknown parameters and uncertain functions are considered and an adaptive turning law is constructed to handle the unknown parameters and a robust control law is adopted to deal with the uncertain functions in the system. At last, a four dimension chaotic system is taken as an example to testify the rightness of the proposed method. And numerical simulation result shows that the proposed method can realize the synchronization between driven chaotic system and response system with unknown parameters and uncertain nonlinear functions

Distributed adaptive control for synchronization of unknown nonlinear networked systems

This paper is concerned with synchronization of distributed node dynamics to a prescribed target or control node dynamics. A design method is presented for adaptive synchronization controllers for distributed systems having non-identical unknown nonlinear dynamics, and for a target dynamics to be tracked that is also nonlinear and unknown. The development is for strongly connected digraph communication structures. A Lyapunov technique is presented for designing a robust adaptive synchronization control protocol. The proper selection of the Lyapunov function is the key to ensuring that the resulting control laws thus found are implementable in a distributed fashion. Lyapunov functions are defined in terms of a local neighborhood tracking synchronization error and the Frobenius norm. The resulting protocol consists of a linear protocol and a nonlinear control term with adaptive update law at each node. Singular value analysis is used. It is shown that the singular values of certain key matrices are intimately related to structural properties of the graph.

Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems

In this paper, a robust adaptive neural network synchronization controller is proposed for two chaotic systems with input time delay and uncertainty. The studied chaotic system may possess a wide class of nonlinear time-delayed input uncertainty. The radial basis function (RBF) neural network is used to approximate the unknown continuous bounded function item of the time delay uncertainty via appropriate weight value updated law. With the output of RBF neural network, a robust adaptive synchronization control scheme is presented for the time delay uncertain chaotic system. Finally, a simulation example is used to illustrate the effectiveness of the proposed synchronization control scheme.