Adaptive Parameter Update Laws Research Articles

Adaptive hybrid complex projective synchronization of chaotic complex system

In this paper defines an adaptive hybrid complex projective synchronization method to synchronize two chaotic complex systems. Base on Lyapunov stability theory, the adaptive control law and parameter update law are derived to make the state of two chaotic complex systems, which are adaptive hybrid complex projective synchronized. This paper extends projective synchronization from the field of real numbers to the field of complex numbers for a chaotic complex system. Different components of the complex system synchronized to different scale complex numbers. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.

Projective synchronization of time‒delayed chaotic systems with unknown parameters using adaptive control method

The present article aims to study the projective synchronization between two identical and non‒identical time‒delayed chaotic systems with fully unknown parameters. Here the asymptotical and global synchronization are achieved by means of adaptive control approach based on Lyapunov–Krasovskii functional theory. The proposed technique is successfully applied to investigate the projective synchronization for the pairs of time‒delayed chaotic systems amongst advanced Lorenz system as drive system with multiple delay Rössler system and time‒delayed Chua's oscillator as response system. An adaptive controller and parameter update laws for unknown parameters are designed so that the drive system is controlled to be the response system. Numerical simulation results, depicted graphically, are carried out using Runge–Kutta Method for delay‒differential equations, showing that the design of controller and the adaptive parameter laws are very effective and reliable and can be applied for synchronization of time‒delayed chaotic systems. Copyright © 2014 John Wiley & Sons, Ltd.

Invariant Manifold Approach for Time-Varying Extremum-Seeking Control Problem

In this paper, the minimization of an unknown but measurable cost function using extremum-seeking control is considered. The main contribution of the paper is to formulate the extremum-seeking problem as a time-varying estimation problem. The concepts of invariant manifold and adaptive parameter update law are used for adaptive estimation of the time-varying gradient of the unknown cost function. The proposed approach is shown to avoid the need for averaging analysis which minimizes the sensitivity of the closed-loop performance to the choice of dither signal.

Robust Synchronization of Hyperchaotic Systems with Uncertainties and External Disturbances

The robust synchronization of hyperchaotic systems with uncertainties and external disturbances is investigated. Based on the Lyapunov stability theory, the appropriate adaptive controllers and parameter update laws are designed to achieve the synchronization of uncertain hyperchaotic systems. The robust synchronization of two hyperchaotic Chen systems is taken as an example to verify the feasibility of the presented schemes. The size of the subcontroller gain’s influences on the convergence speed is discussed. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed synchronization schemes.

Generalized function projective lag synchronization of a class of hyperchaotic systems with fully uncertain parameters

Chaos synchronization is the essential theoretical basis of chaotic secure communication.Since time delay of function projective synchronization had rarely been considered,the adaptive controllers and parameter update laws were designed based on Lyapunov stability theory and adaptive control method,and generalized function projective lag synchronization of a class of hyperchaotic system was achieved.Then,taking hyperchaotic Lorenz-Stenflo(LS) system and hyperchaotic Lu system with fully uncertain parameters as an example the correctness and effectiveness of the method was varified,and the influence of external disturbance and time delay on the effect of the synchronization control were studied.The numerical simulations show the effectiveness,feasibility and robustness of the proposed method.

Adaptive synchronization for stochastic T–S fuzzy neural networks with time-delay and Markovian jumping parameters

This paper concerned with the adaptive synchronization for Takagi–Sugeno (T–S) fuzzy neural networks with stochastic noises and Markovian jumping parameters. By using a new nonnegative function and an M-matrix method, several sufficient conditions are derived to ensure the adaptive synchronization for stochastic T–S fuzzy neural networks. Moreover, the adaptive controller and parameter update laws are designed via adaptive feedback control methods. Finally, a numerical example is given to illustrate the effectiveness of proposed theories.

Coexistence of anti-synchronization and complete synchronization of delay hyperchaotic Lü systems via partial variables

This work is devoted to investigating the coexistence of anti-synchronization (AS) and complete synchronization (CS) of two identical delay hyperchaotic Lü systems via partial variables. Based on the Lyapunov stability theory, a simple synchronization scheme only with linear inputs is considered. The sufficient conditions of synchronization are also obtained for both linear feedback and adaptive control approaches. The coexistence of AS and CS between two nearly identical delay chaotic systems with unknown parameters is explored. A single input controller is proposed and the adaptive parameter update laws are developed. Numerical simulation results are presented to demonstrate the effectiveness of the proposed chaos synchronization scheme.

Complete synchronization of delay hyperchaotic Lü system via a single linear input

This work is devoted to investigating the complete synchronization of two identical delay hyperchaotic Lu systems with different initial conditions, and a simple complete synchronization scheme only with a single linear input is proposed. Based on the Lyapunov stability theory, sufficient conditions of synchronization are obtained for both linear feedback and adaptive control approaches. The problem of adaptive synchronization between two nearly identical delay hyperchaotic Lu systems with unknown parameters is also studied. A single input adaptive synchronization controller is proposed, and the adaptive parameter update laws are developed. Numerical simulation results are presented to demonstrate the effectiveness of the proposed chaos synchronization scheme.

Hybrid synchronization phenomenon in two coupled delay hyperchaotic Lorenz systems with unknown parameters via a single linear controller

This work is devoted to investigating the hybrid synchronization phenomenon of two identical hyperchaotic Lorenz time-delay systems with different initial conditions, and a simple coexistence of anti-phase and complete synchronization scheme only with a single variable controller is proposed. Based on the Lyapunov stability theory, sufficient conditions of synchronization are obtained for both linear feedback and adaptive control approaches. The problem of adaptive synchronization between two nearly identical chaotic systems with unknown parameters is also studied. A single input adaptive synchronization controller is proposed and the adaptive parameter update laws are developed. Numerical simulation results are presented to demonstrate the effectiveness of the proposed chaos synchronization scheme.

Chaos control and hybrid projective synchronization of several new chaotic systems

The problems on purposefully creating and controlling chaos are investigated. First, several new 4D chaotic systems are presented based on a 3D chaotic system and three dynamical characteristics are verified. Second, it is demonstrated that they can be stabilized to their equilibrium points by a same single scalar adaptive feedback control law. Third, two of the chaotic systems with constant parameters are in hybrid projective synchronization (HPS) by presented adaptive feedback control strategies, which can be simplified into a scalar form for identical drive–response systems to achieve complete synchronization. Furthermore, HPS between two of the chaotic systems with response system parameters unknown is also considered and adaptive parameter update laws are developed. Numerical simulations show their characteristics and verify the effectiveness of the strategies.

Modified function projective lag synchronization for multi-scroll chaotic system with unknown disturbances

In this paper, we treat the modified function projective lag synchronization between two non-identical multi-scroll chaotic systems with unknown disturbances. By utilizing the lyapunov stability theory, the fuzzy adaptive controller and parameter update law are derived to make the state of chaotic system achieve modified function projective lag synchronization. The controller can keep the systems stable even when the disturbance changes. Finally numerical simulations are performed to show the effectiveness of the proposed method.

Chaos control and hybrid projective synchronization for a class of new chaotic systems

The problems on chaos control and hybrid projective synchronization for a class of new chaotic systems are considered. First, new 4D chaotic systems are proposed by introducing an additional state into a 3D quadratic chaotic system and the states of the systems corresponding to the different ranges of parameter b are exhibited. Second, a single scalar adaptive feedback controller for chaos control of the systems is presented. Third, hybrid projective synchronization (HPS) of two of the chaotic systems with parameters in different conditions are investigated by presenting adaptive feedback control strategies with adaptive parameter update laws and considering controller simplification to achieve complete synchronization. Finally, numerical simulations are demonstrated to verify the effectiveness of the strategies.

Chaos Control and Hybrid Projective Synchronization of a Novel Chaotic System

Adaptive feedback controllers based on Lyapunov′s direct method for chaos control and hybrid projective synchronization (HPS) of a novel 3D chaotic system are proposed. Especially, the controller can be simplified ulteriorly into a single scalar one to achieve complete synchronization. The HPS between two nearly identical chaotic systems with unknown parameters is also studied, and adaptive parameter update laws are developed. Numerical simulations are demonstrated to verify the effectiveness of the control strategies.

Adaptive Vision-based Missile Guidance in the Presence of Evasive Target Maneuvers

AbstractA nonlinear adaptive visual servo guidance law is presented for a bank-to-turn (BTT) missile airframe that achieves near zero miss distance interception of a target undergoing unknown evasive maneuvers. The controller is developed assuming unknown missile linear velocity and target depth measurements; hence can be regarded as a pure vision-based guidance law. By approximating the unknown, scaled relative velocity via power series expansion, a continuous adaptive parameter update law is developed to compensate for the unknown missile-target relative velocity and the depth measurements. In addition, robust elements are included in the guidance law to compensate for external disturbances and parameter identification errors. A rigorous Lyapunov-based stability analysis is utilized to prove uniformly ultimately bounded (UUB) stability of the system states, and high-fidelity numerical simulation results are provided to verify the performance of the proposed missile guidance law.

Review article on adaptive synchronization of chaotic systems with unknown parameters

This review article studies some adaptive chaos synchronization methods that were already presented in the literature for a general class of chaotic systems. In this regard, the proposed adaptive controllers and parameter update laws in several papers are inspected, and it is shown that many works suffer from novelty and they can be categorized in a union set.

Adaptive control and synchronization of identical new chaotic flows with unknown parameters via single input

The single input linear feedback control for synchronizing two identical new 3D chaotic flows reported by Li et al. [X.F. Li, K.E. Chlouverakis, D.L. Xu, Nonlinear dynamics and circuit realization of a new chaotic flow: a variant of Lorenz, Chen and Lu, Nonlinear Analysis RWA 10 (4) (2009) 2357-2368] is proposed in this paper. Sufficient conditions of synchronization are obtained for both linear feedback and adaptive control approaches. The problem of adaptive synchronization between two nearly identical chaotic systems with unknown parameters is also studied. Based on the Lyapunov stability theory, two kinds of single input adaptive synchronization controllers are designed and the adaptive parameter update laws are developed.

Adaptive modified function projective synchronization of different hyperchaotic systems

This article treats the modified function projective synchronization between the hyperchaotic Lorenz-Stenflo(LS) system and a novel hyperchaotic CYQY system, and also that between the LS system and hyperchaotic Chen system, which have completely unknown parameters. By utilizing Lyapunov stability theory and active control method, the adaptive controllers and parameter update laws are derived to make the states of different hyperchaotic systems to attain adaptive modified function projective synchronization. The systems unknown parameters can be identified simultaneously. Numerical simulations are presented to demonstrate the effectiveness of the proposed methods.

Adaptive actuator failure compensation for redundant manipulators

SUMMARYThis paper presents an adaptive actuator failure compensation method, which compensates for uncertainties due to unknown actuator failures for redundant manipulator systems. The method is first developed for manipulators whose joints are concurrently actuated. While physical realization of concurrently actuated manipulators and the advantages of their use have been understood before, in this paper failure modeling, controller structure, and adaptive update rules for handling uncertainties from the actuator failures are studied. The adaptive actuator failure compensation method is then expanded for a cooperating multiple manipulator system with uncertain actuator failures. Dynamic equations of such a multiple manipulator system in the task space are derived and the adaptive actuator failure compensation problem is formulated in the task space, for which a compensation controller structure is proposed with stable adaptive parameter update laws. The adaptive control scheme is able to compensate for the uncertainties of system parameters and actuator failures in a more general sense. For both cases, closed-loop system stability and asymptotic tracking are proved, despite uncertain system failures.

Adaptive control of nonlinear smart base-isolated buildings using Gaussian kernel functions

In this paper, a direct adaptive control scheme using Gaussian kernel functions is presented for the active control of nonlinear base-isolated buildings. The control scheme is based on direct adaptive control where the system response is made to follow a desired trajectory. The number of kernel functions is adaptively estimated using a growing and pruning strategy which results in the reduction of the computational overhead. Stable adaptive parameter update laws for Gaussian kernels are derived using Lyapunov approach. Performance of the proposed control scheme is evaluated on the recently developed nonlinear three-dimensional base-isolated benchmark structure. The analytical model of the benchmark structure is highly complex due its three-dimensional nature incorporating lateral and torsional responses, the biaxial interaction of the nonlinear bearings at the isolation layer, and strong coupling between the isolation level forces and the superstructure responses. Control action is provided by eight actuators distributed at the isolation level in each principal direction of the structure, and utilizing the state information corresponding to the base of the structure only. Results are presented using a comprehensive set of the performance indices to realistically quantify the trade-offs associated with the control of nonlinear base-isolated buildings. The main advantages of the adaptive controller presented in this paper are: (i) the control algorithm does not require estimating the system parameters, specifically, mass, stiffness and damping, (ii) the exact nature of the nonlinear dynamics need not be known, and (iii) the control synthesis is noniterative, and on-line. Copyright © 2007 John Wiley & Sons, Ltd.

Adaptive control and synchronization of a four-dimensional energy resources system with unknown parameters

This paper is involved with control and synchronization of a new four-dimensional energy resources system with unknown parameters. Based on the Lyapunov stability theorem, by designed adaptive controllers and parameter update laws, this system is stabilized to unstable equilibrium and synchronizations between two systems with different unknown system parameters are realized Numerical simulations are given for the purpose of illustration and verification.