Exponential State Estimation Research Articles

Exponential State Estimation and Passivity of Fuzzy Quaternion-Valued Memristive Neural Networks: Norm Approach

Exponential State Estimation and Passivity of Fuzzy Quaternion-Valued Memristive Neural Networks: Norm Approach

Distributed Exponential State Estimation for Discrete-Time Linear Systems Over Jointly Connected Switching Networks

The existing results on distributed state estimation problems for discrete-time linear systems were obtained over connected static networks, or every-time connected switching networks by a two-time-scale design. This paper further studies the same problem over jointly connected switching networks which can be disconnected at every time instant by a single-time-scale distributed design. Since the existing distributed designs critically rely on the connectedness assumption on the networks and thus may not apply to jointly connected switching networks, we have to modify the local observers and develop a novel approach which makes use of the uniform complete observability property for a discrete-time time-varying system. Additionally, we establish two exponential stability results for two classes of discrete-time switched systems, which may be of independent interest.

Distributed exponential state estimation of linear systems over jointly connected switching networks

Recently, the distributed state estimation problem for continuous-time linear systems over jointly connected switching networks was solved. Due to the use of the generalized Barbalat’s Lemma, it can only show that the estimation errors asymptotically converge to the origin. By a completely different approach, this paper further studies the distributed state estimation problem with two new features. First, the asymptotic convergence is strengthened to the exponential convergence. This strengthened result not only offers a guaranteed convergence rate, but also renders the error system total stability and thus the capability to withstand small disturbances. Second, the coupling gains of our local observers can be different from each other and thus offers greater design flexibility, while the coupling gains in the existing result were required to be identical. These two new features are achieved by establishing exponential stability for two classes of linear time-varying systems, which may have other applications.

New Criteria of Event-triggered Exponential State Estimation for Delayed semi-Markovian Memristor-based Neural Networks

New Criteria of Event-triggered Exponential State Estimation for Delayed semi-Markovian Memristor-based Neural Networks

A New Free-matrix Inequality with application to Exponential State Estimation for Markov Jump Neural Networks

This paper is concerned with an exponential state estimation problem for a class of Markov Jump Neural Networks (MJNNs) with Time-varying Delay (TVD). Firstly, to derive a tighter bound of Exponential-type Integral Quadratic Terms (EIQTs), a new Free-matrix Exponential-type Inequality (FMEI) is provided, which includes some existing ones as its special cases. Secondly, by fully considering the information of attenuation exponent and TVD, a novel Lyapunov-Krasovskii Functional (LKF) is constructed. Then, by employing the new FMEI and other analytical techniques, a less conservative criterion guaranteeing the stochastic stability of the error system is obtained in form of Linear Matrix Inequalities (LMIs). In the end, a numerical example is given to show the effectiveness of the obtained result.

Exponential state estimation for reaction-diffusion inertial neural networks via incomplete measurement scheme

ABSTRACT In this paper, the problem of exponential state estimation for inertial neural networks with reaction-diffusion term (RDINNs) via incomplete measurement scheme is investigated. Unlike the full measurement method, this method estimates the system by measuring the state of partially available neurons. First, by constructing an appropriate variable substitution, the second-order system is transformed into a first-order one. Then, a suitable Lyapunov-krasovskii function (LKF) is constructed, and sufficient conditions for the stability of the system are obtained . Finally, the practicality and effectiveness of the proposed method is further verified by two numerical examples.

Exponential state estimation for competitive neural network via stochastic sampled-data control with packet losses

This paper investigates the exponential state estimation problem for competitive neural networks via stochastic sampled-data control with packet losses. Based on this strategy, a switched system model is used to describe packet dropouts for the error system. In addition, transmittal delays between neurons are also considered. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator with probabilistic sampling in two sampling periods is proposed. Then the estimator is designed in terms of the solution to a set of linear matrix inequalities (LMIs), which can be solved by using available software. When the missing of control packet occurs, some sufficient conditions are obtained to guarantee that the exponentially stable of the error system by means of constructing an appropriate Lyapunov function and using the average dwell-time technique. Finally, a numerical example is given to show the effectiveness of the proposed method.

Exponential synchronization and state estimation of inertial quaternion‐valued Cohen‐Grossberg neural networks: Lexicographical order method

SummaryThis paper addresses the problems of synchronization and state estimation for a class of inertial quaternion‐valued Cohen‐Grossberg neural networks. By means of proper control strategy, sufficient conditions are derived for ascertaining exponential synchronization of quaternion‐valued Cohen‐Grossberg neural networks. Subsequently, the state estimation problem has also been augmented to achieve robust stable performance of the estimation error system. What should be mentioned is that, the system states considered in this paper are taking values in an interval, which implies that the states are varying between two different quaternions, thus, an optimal algorithm (lexicographical order method) is employed, which can be used to determine the “magnitude" of two different quaternions. In this case, the interval proposed by the quaternion‐valued is meaningful. Finally, numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.

Optimal Linear Exponential Quadratic Gaussian Estimation With Intermittent Observations

This letter is concerned with the problem of optimal linear exponential quadratic state estimation for discrete-time Gauss–Markov systems with intermittent observations. The optimal estimator and optimal cost are derived via an information state approach. The necessary and sufficient condition for the existence of the estimator is provided. For a special case when a scalar parameter in the exponential cost goes to zero, the derived estimator reduces to the corresponding Kalman filter. It is also interesting to note that the resulting estimator has the same form as that obtained from the $H_{\infty }$ setting.

Dissipativity and exponential state estimation for quaternion-valued memristive neural networks

In this paper, the global dissipativity and exponential state estimation for quaternion-valued memristive neural networks are investigated. By starting from basic quaternion properties, several algebraic conditions ensuring the global dissipativity and state estimation problems are derived. It is noteworthy that, based on the vector ordering approach, one can compare the “magnitude” of two different quaternion-valued, and thus the closed convex hull derived by two different quaternion-valued connections can be derived. Simulation results are given to show the validate of the mathematical model and the derived conclusions of the memristive system.

Exponential State Estimation for Memristor-Based Discrete-Time BAM Neural Networks With Additive Delay Components.

This paper focuses on the dynamical behavior for a class of memristor-based bidirectional associative memory neural networks (BAMNNs) with additive time-varying delays in discrete-time case. The necessity of the proposed problem is to design a proper state estimator such that the dynamics of the corresponding estimation error is exponentially stable with a prescribed decay rate. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) and utilizing Cauchy-Schwartz-based summation inequality, the delay-dependent sufficient conditions for the existence of the desired estimator are derived in the absence of uncertainties which are further extended to available uncertain parameters of the prescribed memristor-based BAMNNs in terms of linear matrix inequalities (LMIs). By solving the proposed LMI conditions the estimation gain matrices are obtained. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed results.

Adaptive Exponential State Estimation for Markovian Jumping Neural Networks with Multi-delays and Lévy Noises

This paper discusses the adaptive exponential state estimation problem of neutral-type neural networks with multi-delays and Levy noises. The M-matrix method being different from other methods, such as the LMIs method, has been applied to deal with the problem. According to the M-matrix method, some state estimation criteria for neural networks concerning neutral-type delays and no neutral-type delays are acquired to ensure the adaptive exponential estimation. Finally, a simulation example is offered to show the advantages of the theoretical results.

Exponential state estimation, entropy and Lyapunov exponents

In this paper we study the notion of estimation entropy established by Liberzon and Mitra. This quantity measures the smallest rate of information about the state of a system above which an exponential state estimation with a given exponent is possible. We show that this concept is closely related to the α-entropy introduced by Thieullen and we give a lower estimate in terms of Lyapunov exponents, assuming that the system preserves a volume measure, which includes all Hamiltonian and symplectic systems. Although in its current form mainly interesting from a theoretical point of view, our result could be a first step towards a more practical analysis of state estimation under communication constraints.

Non-fragile exponential state estimation for continuous-time fuzzy stochastic neural networks with time-varying delays1

Non-fragile exponential state estimation for continuous-time fuzzy stochastic neural networks with time-varying delays1

Sampled-data synchronization and state estimation for nonlinear singularly perturbed complex networks with time-delays

This study deals with the problem of exponential synchronization and state estimation for singularly perturbed complex networks (SPCNs) with coupling delay under sampled-data control technique. Every node of the SPCNs involve both ‘fast’ and ‘slow’ dynamics that reveals the singular perturbation behavior. By constructing novel Lyapunov functional and by using Kronecker product, some adequate conditions which assure the exponential synchronization are attained in the form of linear matrix inequalities. Moreover, the exponential state estimation problem for the SPCNs are also considered and the state estimator is designed. Lastly, numerical simulations are presented to validate the advantage of the propound theoretical results.

Exponential state estimation for Markovian jumping neural networks with mixed time-varying delays and discontinuous activation functions

This paper is concerned with the exponential state estimation issue for Markovian jumping neural networks with mixed time-varying delays and discontinuous activation functions. By introducing triple-integral terms and quadruple integrals term in Lyapunov–Krasovskii functional, the obtained Lyapunov matrices are distinct for different system modes. Based on the nonsmooth analysis theory and by applying stochastic analysis techniques, the full-order state estimator is designed to ensure that the corresponding error system is exponentially stable in mean square. The desired mode-dependent and delay-dependent estimator can be achieved by solving a set of linear matrix inequalities. Finally, two simulation examples are given to illustrate the validity of the theoretical results.

An Integrated Approach to Global Synchronization and State Estimation for Nonlinear Singularly Perturbed Complex Networks.

This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both "slow" and "fast" dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both slow and fast) of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the slow subsystems within the network are unstable.

Exponential state estimation for discrete-time switched genetic regulatory networks with random delays

This paper is concerned with the problem of state estimator design for a class of discrete-time switched genetic regulatory networks (GRNs) with random time delays. The involved time delays are assumed to be randomly time-varying and are modeled by introducing Bernoulli distributed sequences. By using a piecewise Lyapunov–Krasovskii functional together with the linear matrix inequality (LMI) approach, we design a delay-distributed dependent state estimator such that the estimation error system is globally exponentially stable. Further, a class of switching signals specified by the average dwell time is identified to guarantee the exponential state estimation. All the conditions are established in the framework of LMIs, which can easily be solved by using standard numerical software. If a set of LMIs are feasible, then the desired state estimator can be obtained. Finally, a numerical example with simulation result is provided for the GRN model to illustrate the applicability and usefulness of the obtained theory.

Exponential state estimation for stochastic complex dynamical networks with multi-delayed base on adaptive control

This paper discusses the exponential state estimation problem for stochastic complex dynamical networks involving multi-delayed and adaptive control. A new approach, very different to the linear matrix inequality (LMI) method, has been developed to solve the above problem. Meanwhile, some sufficient conditions are derived to ensure the exponential stability in pth moment for the dynamics of state estimator error. The feedback gain update law is found by the adaptive control technique. An illustrative example is provided to show the usefulness and effectiveness of the proposed design method.

Exponential State Estimation for Neural Networks with Leakage, Discrete and Distributed Delays

In this paper, the design problem of state estimator for neural networks with the mixed time-varying delays are investigated by constructing appropriate Lyapunov-Krasovskii functionals and using some effective mathematical techniques. In order to derive several conditions to guarantee the estimation error systems to be globally exponential stable, we transform the considered systems into the neural-type time-delay systems. Then with a set of linear inequalities(LMIs), we can obtain the stable criteria. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed criterion. Keywords—State estimator, Neural networks, Globally exponential