Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems

This paper introduces a novel hybrid optimization algorithm by taking advantage of the stochastic properties of chaotic search and the invasive weed optimization (IWO) method. In order to deal with the weaknesses associated with the conventional method, the proposed chaotic invasive weed optimization (CIWO) algorithm is presented which incorporates the capabilities of chaotic search methods. The functionality of the proposed optimization algorithm is investigated through several benchmark multi-dimensional functions. Furthermore, an identification technique for chaotic systems based on the CIWO algorithm is outlined and validated by several examples. The results established upon the proposed scheme are also supplemented which demonstrate superior performance with respect to other conventional methods.     

State and parameter estimation for nonlinear systems

State and parameter estimators are obtained for systems described by nonlinear evolution equations. Linear infinite dimensional observability theory together with a variety of fixed point theorems can be employed to obtain a finite time observer. Moreover, a nonlinear asymptotic observer is produced using stability results. The problem of joint state and parameter estimation is converted to the state estimation case, via an augmented state, so that these observer results can be utilised. Examples and remarks on the generality of the results are given.     

Synchronization of chaotic systems with parameter driven by a chaotic signal

Chaos control with driving parameter scheme in uncoupled identical chaotic oscillators is presented. By driving the parameter of chaotic systems using external chaotic signal, synchronization and anti-synchronization can be implemented. Numerical simulations show that either synchronization or anti-synchronization can appear depending significantly on initial condition and on driving strength. The proposed method is particularly suited for a variety of chaotic systems, which cannot couple with each other in engineering.     

Synchronization of chaotic systems with parameter driven by a chaotic signal

Chaos control with driving parameter scheme in uncoupled identical chaotic oscillators is presented. By driving the parameter of chaotic systems using external chaotic signal, synchronization and anti-synchronization can be implemented. Numerical simulations show that either synchronization or anti-synchronization can appear depending significantly on initial condition and on driving strength. The proposed method is particularly suited for a variety of chaotic systems, which cannot couple with each other in engineering.     

Lag synchronization of chaotic systems with parameter mismatches

The paper studies the effect of parameter mismatch on lag synchronization of chaotic systems. It shall be shown that lag synchronization of coupled systems may weakly achieve, when parameter mismatch is small. The error bound of lag synchronization arising from the parameter mismatch is also estimated by rigorously theoretical analysis. Numerical simulations on Chua oscillator are presented to verify the theoretical results.     

Lyapunov function,parameter estimation,synchronization and chaotic cryptography

In this paper we have investigated a new method of synchronization between two non linear systems based upon lyapunov function and parameter estimation through modulational equations. The driving and response systems, both are different and their parameters are unknown.We have constructed the parameter modulation equations and control laws to achieve the synchronization. This method is well applied to two different three dimensional systems and the transverse lyapunov exponents show the effectiveness of the method. Further more we have investigated the cryptographical applications with the help of the above two systems.     

Unified impulsive fuzzy-model-based controllers for chaotic systems with parameter uncertainties via LMI

In this paper, a novel technique based on impulsive fuzzy T–S model is proposed for controlling chaotic systems with parameter uncertainties. According to this new model, a unified methodology for establishing robust stability, asymptotic stability and exponential stability of impulsive controllers is developed. Various robust stability conditions are presented in the form of linear matrix inequalities (LMI). A simple iterative algorithm is also provided for calculating design parameters based on LMI techniques. Finally, a typical design procedure is developed by using well-known chaotic systems for illustration, accompanied by several numerical simulations to demonstrate the validity of the proposed methodology.     

Performance analysis of the AM-SG parameter estimation for multivariable systems

The auxiliary model based stochastic gradient (AM-SG) parameter estimation method is an important identification one. This paper analyzes the performances of the AM-SG estimation algorithm for multiple-input single-output systems (i.e., multivariable systems) under the strong persistent excitation condition. The analysis and simulation results indicate that the parameter estimation errors converge to zero.     

Combined state and least squares parameter estimation algorithms for dynamic systems

The control theory and automation technology cast the glory of our era. Highly integrated computer chip and automation products are changing our lives. Mathematical models and parameter estimation are basic for automatic control. This paper discusses the parameter estimation algorithm of establishing the mathematical models for dynamic systems and presents an estimated states based recursive least squares algorithm, and the states of the system are computed through the Kalman filter using the estimated parameters. A numerical example is provided to confirm the effectiveness of the proposed algorithm.     

Design for estimation of the drift parameter in fractional diffusion systems

We consider a controlled linear differential equation which is partially observed with an additive fractional noise. In this setting, we study the asymptotic (for large observation time) design problem of the input and give an efficient estimator of the unknown signal drift parameter. The optimal estimation input is deduced. The consistency, asymptotic normality and convergence of the moments of the MLE are established.     

Three-stage recursive least squares parameter estimation for controlled autoregressive autoregressive systems

A three-stage recursive least squares parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) systems. The basic idea is to decompose a CARAR system into three subsystems, one of which contains one parameter vector, and to identify the parameters of each subsystem one by one. Compared with the recursive generalized least squares algorithm, the dimensions of the involved covariance matrices in each subsystem become small and thus the proposed algorithm has a high computational efficiency. Finally, we verify the proposed algorithm with a simulation example.     

A parameter estimation scheme for a class of sequential hybrid systems

It may happen that the equations governing the response of dynamical systems have some parameters whose values may not be known a priori and have to be obtained using parameter estimation schemes. In this article, we present a parameter estimation scheme for a class of sequential hybrid systems. By hybrid systems, we refer to those systems whose response is described by different governing equations corresponding to various regimes/modes of operation along with some criteria to switch between the same. In a sequential hybrid system, the different modes are arranged in a specific sequence and the system can switch from a given mode to either the previous mode or the following mode in this sequence. Here, we consider those systems whose governing equations consist of ordinary differential equations and algebraic equations. The conditions for switching between the various modes (referred to as transition conditions) are in the form of linear inequalities involving the system output. We shall first consider the case where the transition conditions are known completely. We present a parameter update scheme along with sufficient conditions that will guarantee bounded parameter estimation errors. Then, we shall consider the case where the transition conditions are not known in the sense that some parameters in these conditions are not known. We present a parameter estimation scheme for this case. We illustrate the performance of the parameter estimation scheme in both cases with some examples.     

Secure communication via parameter modulation in a class of chaotic systems

The problem of secure communication via parameter modulation in a class of chaotic systems is studied. Information signal is used to modulate one parameter of a chaotic system. The resulting chaotic signal is later demodulated and the information signal is recovered using an adaptive demodulator. The convergence of the demodulator is established. We show that the proposed scheme is robust with respect to noise and parameter mismatch. Computer simulation on the Chua circuit is given to validate the theoretical prediction.     

Effect of random parameter switching on commensurate fractional order chaotic systems

The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The disappearance of chaos in such systems which rapidly switch from one family to the other has been investigated here for the commensurate FO scenario. Our simulation study show that a noise-like random variation in the key parameter of the unified chaotic system along with a gradual decrease in the commensurate FO is capable of suppressing the chaotic fluctuations much earlier than that with the fixed parameter one. The chaotic time series produced by such random parameter switching in nonlinear dynamical systems have been characterized using the largest Lyapunov exponent (LLE) and Shannon entropy. The effect of choosing different simulation techniques for random parameter FO switched chaotic systems have also been explored through two frequency domain and three time domain methods. Such a noise-like random switching mechanism could be useful for stabilization and control of chaotic oscillation in many real-world applications.     

D-optimal design of a monitoring network for parameter estimation of distributed systems

This paper addresses the design of a network of observation locations in a spatial domain that will be used to estimate unknown parameters of a distributed parameter system. We consider a setting where we are given a finite number of possible sites at which to locate a sensor, but cost constraints allow only some proper subset of them to be selected. We formulate this problem as the selection of the gauged sites so as to maximize the log-determinant of the Fisher information matrix associated with the estimated parameters. The search for the optimal solution is performed using the branch-and-bound method in which an extremely simple and efficient technique is employed to produce an upper bound to the maximum objective function. Its idea consists in solving a relaxed problem through the application of a simplicial decomposition algorithm in which the restricted master problem is solved using a multiplicative algorithm for optimal design. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional convective diffusion process.     

Parameter estimation of chaotic system with time-delay: A differential evolution approach

It is an important issue to estimate parameters of chaotic system in nonlinear science. In this paper, parameter estimation problem of chaotic system with time-delay is considered. Parameters and time-delay are estimated together by treating time-delay as an additional parameter. The parameter estimation problem is converted to an multi-dimensional optimization problem. A differential evolution (DE) algorithm, which possess a powerful searching capability for finding the solutions for a given optimization problem, is applied to solve this optimization problem. Two illustrative examples are given to verify the effectiveness of the proposed method.     

Parameters estimation,mixed synchronization,and antisynchronization in chaotic systems

Mixed synchronization between two Hindmarsh–Rose neuron models is realized by optimizing the scheme of Lyapunov function with two selectable gain coefficients. Based on the Lyapunov stability theory, the distribution of synchronization region and the nonsynchronization region in the two‐parameter phase space is calculated, respectively. And then the optimized parameter observers and controllers are approached analytically. All unknown parameters with different orders of magnitude are identified accurately, and the error function for corresponding variables decreases to stable value when the two gain coefficients are given values in the synchronization region. Otherwise, only the four larger unknown parameters are estimated exactly and the error function of corresponding variables decreases stably to certain minimal value with an order about 1 × 10^?6, whereas the smallest unknown parameter is approached greatly although the error of corresponding variables are stabilized within certain transient period. © 2014 Wiley Periodicals, Inc. Complexity 20: 64–73, 2014     

Parameter estimation for noisy chaotic systems based on an improved particle swarm optimization algorithm

It is of great importance to estimate the unknown parameters and time delays of chaotic systems in control and synchronization. This paper is concerned with the uncertain parameters and time delays of chaotic systems corrupted with random noise. Parameters and time delays of such chaotic systems are estimated based on the improved particle swarm optimization algorithm for its global searching ability. Numerical simulations are given to show satisfactory results.     

Robust synchronization of a class of chaotic systems with disturbance estimation

This paper investigates the robust synchronization problem for a class of chaotic systems with external disturbances. By using disturbance-observer-based control (DOBC) and LMI approach, the disturbance observers are developed to ensure the boundedness of the disturbance error dynamical. Then, by employing the sliding mode control technique, an adaptive control law is established to eliminate the effect of disturbance error to realize synchronization between the master and slave systems. Finally, the corresponding numerical simulations are demonstrated to verify the effectiveness of proposed method.