Time-varying parameters estimation with adaptive neural network EKF for missile-dual control system

In this paper, a filtering method is presented to estimate time-varying parameters of a missile dual control system with tail fins and reaction jets as control variables. In this method, the long-short-term memory(LSTM) neural network is nested into the extended Kalman filter(EKF) to modify the Kalman gain such that the filtering performance is improved in the presence of large model uncertainties. To avoid the unstable network output caused by the abrupt changes of system states,an adaptive correction factor is introduced to correct the network output online. In the process of training the network, a multi-gradient descent learning mode is proposed to better fit the internal state of the system, and a rolling training is used to implement an online prediction logic. Based on the Lyapunov second method, we discuss the stability of the system, the result shows that when the training error of neural network is sufficiently small, the system is asymptotically stable. With its application to the estimation of time-varying parameters of a missile dual control system, the LSTM-EKF shows better filtering performance than the EKF and adaptive EKF(AEKF) when there exist large uncertainties in the system model.

IDENTIFICATION OF TIME-VARYING MODAL PARAMETERS USING LINEAR TIME-FREQUENCY REPRESENTATION

A new method of parameter identification based on linear time-frequencyrepresentation and Hubert transform is proposed to identity modal parameters of linear time-varyingsystems from measured vibration responses. Using Gabor expansion and synthesis theory, measuredresponses are represented in the time-frequency domain and modal components are reconstructed bytime-frequency filtering. The Hilbert transform is applied to obtain time histories of the amplitudeand phase angle of each modal component, from which time-varying frequencies and damping ratios areidentified. The proposed method has been demonstrated with a numerical example in which a lineartime-varying system of two degrees of freedom is used to validate the identification scheme based ontime-frequency representation. Simulation results have indicated that time-frequency representationpresents an effective tool for modal parameter identification of time-varying systems.

Adaptive Containment Control for Fractional-Order Nonlinear Multi-Agent Systems With Time-Varying Parameters

This paper investigates adaptive containment control for a class of fractional-order multi-agent systems(FOMASs)with time-varying parameters and disturbances.By using the bounded estimation method,the difficulty generated by the timevarying parameters and disturbances is overcome.The command filter is introduced to solve the complexity problem inherent in adaptive backstepping control.Meanwhile,in order to eliminate the effect of filter errors,a novel distributed error compensating scheme is constructed,in which only the local information from the neighbor agents is utilized.Then,a distributed adaptive containment control scheme for FOMASs is developed based on backstepping to guarantee that the outputs of all the followers are steered to the convex hull spanned by the leaders.Based on the extension of Barbalat's lemma to fractional-order integrals,it can be proven that the containment errors and the compensating signals have asymptotic convergence.Finally,three simulation examples are given to show the feasibility and effectiveness of the proposed control method.

TECHNICAL STABILITY OF NONLINEAR TIME-VARYING SYSTEMS WITH SMALL PARAMETERS

Technical stability:allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condition, technical stability relative to certain prescribed state constraint sets of a class of nonlinear time-varying systems with small parameters was analyzed by means of vector Liapunov function method. Explicit criteria of technical stability are established in terms of coefficients of the system under consideration. Conditions under which the technical stability of the system can be derived from its reduced linear time-varying (LTV) system were further examined, as well as a condition for linearization approach to technical stability of general nonlinear systems. Also, a simple algebraic condition of exponential asymptotic stability of LTV systems is presented. Two illustrative examples are given to demonstrate the availability of the presently proposed method.

Linear numerical calculation method for obtaining critical point,pore fluid,and framework parameters of gas-bearing media

Up to now, the primary method for studying critical porosity and porous media are experimental measurements and data analysis. There are few references on how to numerically calculate porosity at the critical point, pore fluid-related parameters, or framework-related parameters. So in this article, we provide a method for calculating these elastic parameters and use this method to analyze gas-bearing samples. We first derive three linear equations for numerical calculations. They are the equation of density p versus porosity Ф, density times the square of compressional wave velocity p Vp^2 versus porosity, and density times the square of shear wave velocity pVs^2 versus porosity. Here porosity is viewed as an independent variable and the other parameters are dependent variables. We elaborate on the calculation steps and provide some notes. Then we use our method to analyze gas-bearing sandstone samples. In the calculations, density and P- and S-velocities are input data and we calculate eleven relative parameters for porous fluid, framework, and critical point. In the end, by comparing our results with experiment measurements, we prove the viability of the method.

Prediction method of physical parameters based on linearized rock physics inversion

A linearized rock physics inversion method is proposed to deal with two important issues, rock physical model and inversion algorithm, which restrict the accuracy of rock physics inversion. In this method, first, the complex rock physics model is expanded into Taylor series to get the first-order approximate expression of the inverse problem of rock physics;then the damped least square method is used to solve the linearized rock physics inverse problem directly to get the analytical solution of the rock physics inverse problem. This method does not need global optimization or random sampling, but directly calculates the inverse operation, with high computational efficiency. The theoretical model analysis shows that the linearized rock physical model can be used to approximate the complex rock physics model. The application of actual logging data and seismic data shows that the linearized rock physics inversion method can obtain accurate physical parameters. This method is suitable for linear or slightly non-linear rock physics model, but may not be suitable for highly non-linear rock physics model.

Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

Complete synchronization could be reached between some chaotic and/or hyperchaotic systems under linear coupling. More generally, the conditional Lyapunov exponents are often calculated to confirm the stability of synchronization and reliability of linear controllers. In this paper, detailed proof and measurement of the reliability of linear controllers are given by constructing a Lyapunov function in the exponential form. It is confirmed that two hyperchaotic systems can reach complete synchronization when two linear controllers are imposed on the driven system unidirectionally and the unknown parameters in the driving systems are estimated completely. Finally, it gives the general guidance to reach complete synchronization under linear coupling for other chaotic and hyperchaotic systems with unknown parameters.

Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays

In this paper, the problem of exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and Mode-dependent probabilistic time-varying coupling delays is investigated. The sam- pling period is assumed to be time-varying and bounded. The information of probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred complex dynamical network model. Based on the condition, the design method of the desired sampled data controller is proposed. By constructing a new Lyapunov functional with triple integral terms, delay-distribution-dependent exponential synchronization criteria are derived in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

Identification of Modal Parameters with Linear Structure under Non-stationary Ambient Excitation

Empirical mode decomposition (EMD) is proposed to identify linear structure under non-stationary excitation,and non-white noise coefficient is introduced under the assumption of random signals consisting of white noise and non-white noise signals. The cross-correlation function of response signal is decomposed into mode functions and residue by EMD method. The identification technique of the modal parameters of single freedom degree is applied to each mode function to obtain natural frequencies, damping ratios and mode shapes. The results of identification of the five-degree freedom linear system demonstrate that the proposed method is effective in identifying the parameters of linear structures under non-stationary ambient excitation.

Identification of Time-Varying Modal Parameters for Thermo-Elastic Structure Subject to Unsteady Heating

A time-varying modal parameter identification method combined with Bayesian information criterion(BIC)and grey correlation analysis(GCA)is presented for a kind of thermo-elastic structures with sparse natural frequencies and subject to an unsteady temperature field.To demonstrate the method,the thermo-elastic structure to be identified is taken as a simply-supported beam with an axially movable boundary and subject to both random excitation and an unsteady temperature field,and the dynamic outputs of the beam are first simulated as the measured data for the identification.Then,an improved time-varying autoregressive(TVAR)model is generated from the simulated input and output of the system.The time-varying coefficients of the TVAR model are expanded as a finite set of time basis functions that facilitate the time-varying coefficients to be time-invariant.According to the BIC for preliminarily determining the scope of the order number,the grey system theory is introduced to determine the order of TVAR and the dimension of the basis functions simultaneously via the absolute grey correlation degree(AGCD).Finally,the time-varying instantaneous frequencies of the system are estimated by using the recursive least squares method.The identified results are capable of tracking the slow time-varying natural frequencies with high accuracy no matter for noise-free or noisy estimation.

Mean-square exponential stability for stochastic time-varying delay systems with Markovian jumping parameters:a delay decomposition approach

The mean-square exponential stability problem is investigated for a class of stochastic time-varying delay systems with Markovian jumping parameters. By decomposing the delay interval into multiple equidistant subintervals, a new delay-dependent and decay-rate-dependent criterion is presented based on constructing a novel Lyapunov functional and employing stochastic analysis technique. Besides, the decay rate has no conventional constraint and can be selected according to different practical conditions. Finally, two numerical examples are provided to show that the obtained result has less conservatism than some existing ones in the literature.

Determination of the parameters of a linear-viscoelastic thin layer using the normally-incident ultrasonic waves

This paper proposes a method of simultaneous determination of the four layer parameters （mass density, longitudinal velocity, the thickness and attenuation） of an immersed linear-viscoelastic thin layer by using the normally-incident reflected and transmitted ultrasonic waves. The analytical formula of the layer thickness related to the measured trans- mitted transfer functions is derived. The two determination steps of the four layer parameters are developed, in which acoustic impedance, time-of-flight and attenuation are first determined by the reflected transfer functions. Using the derived formula, it successively calculates and determines the layer thickness, longitudinal velocity and mass density by the measured transmitted transfer functions. According to the two determination steps, a more feasible and simplified measurement setups is described. It is found that only three signals （the reference waves, the reflected and transmitted waves） need to be recorded in the whole measurement for the determination of the four layer parameters. A study of the stability of the determination method against the experimental noises and the error analysis of the four layer parameters are made. This study lays the theoretical foundation of the practical measurement of a linear-viscoelastic thin layer.

H_∞ Output Feedback Control for Stochastic Systems with Mode-dependent Time-varying Delays and Markovian Jump Parameters

This paper deals with the H∞ control problems of Markovian jump systems with mode-dependent time delays. First, considering the mode-dependent time delays, a different delay-dependent H∞ performance condition for Markovian jump systems is proposed by constructing an improved Lyapunov-Krasovskii function. Based on this new H∞ disturbance attenuation criterion, a full-order dynamic output feedback controller that ensures the exponential mean-square stability and a prescribed H∞ performance level for the resulting closed-loop system is designed. Illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Stability analysis of time-varying systems via parameter-dependent homogeneous Lyapunov functions

This paper considers the stability analysis of linear continuous-time systems, and that the dynamic matrices are affected by uncertain time-varying parameters, which are assumed to be bounded, continuously differentiable, with bounded rates of variation. First, sufficient conditions of stability for time-varying systems are given by the commonly used parameter-dependent quadratic Lyapunov function. Moreover, the use of homogeneous polynomial Lyapunov functions for the stability analysis of the linear system subject to the time-varying parametric uncertainty is introduced. Sufficient conditions to determine the sought after Lyapunov function is derived via a suitable paramenterization of polynomial homogeneous forms. A numerical example is given to illustrate that the stability conditions are less conservative than similar tests in the literature.

Selection of the Linear Regression Model According to the Parameter Estimation

In this paper, based on the theory of parameter estimation, we give a selection method and, in a sense of a good character of the parameter estimation, we think that it is very reasonable. Moreover, we offer a calculation method of selection statistic and an applied example.

Assessment on Evaluating Parameters of Rice Core Collections Constructed by Genotypic Values and Molecular Marker Information

Eleven evaluating parameters for rice core collection were assessed based on genotypic values and molecular marke＇ information. Monte Carlo simulation combined with mixed linear model was used to eliminate the interference from environment in order to draw more reliable results. The coincidence rate of range （CR） was the optimal parameter. Mean Simpson index （MD）, mean Shannon-Weaver index of genetic diversity （M1） and mean polymorphism information content （MPIC） were important evaluating parameters. The variable rate of coefficient of variation （VR） could act as an important reference parameter for evaluating the variation degree of core collection. Percentage of polymorphic loci （p） could be used as a determination parameter for the size of core collection. Mean difference percentage （MD） was a determination parameter for the reliability judgment of core collection. The effective evaluating parameters for core collection selected in the research could be used as criteria for sampling percentage in different plant germplasm populations.

Assessment of active tectonics from geomorphic indices and morphometric parameters in part of Ganga basin

Ganga river basins exposed to active erosional and deformational processes. The recurrence of landslides, floods, and seismic activities makes it more susceptible to deformational activities. The tectonic analysis using geomorphic indices and morphometric parameters will help in determining the hazard-prone area of the river basin. Geomorphic indices and morphometric parameters are calculated to investigate the role of neotectonic activities, as it acts as a controlling factor in the development of landforms in the tectonically active terrains. Neotectonic activities influence the terrain topography, which significantly affects the drainage system and geomorphological setup of the area. In this study, the assessment of active tectonics of study area was determined using Advanced Spaceborne Thermal Emission and Reflection Radiometer(ASTER) Global Digital Elevation Model(GDEM) based on Geomorphic Indices(Stream Length Gradient index, Hypsometric integral, Asymmetry factor, Basin shape, Valley floor width to Valley height ratio, Mountain front sinuosity index) cumulatively with Linear, Areal and Relief morphometric parameters on 27 delineated basins of the study area. The combined classification of Relative Tectonic Activity Index(Iat) and morphometric parameters of 27 basins categorized all the zones into four different classes:Class 1 – Very High(<1.97;410 km^2);Class 2 – High(1.97 – 2.05;275 km^2);Class 3 – Moderate(2.05 – 2.21;273 km^2),and Class 4 – Low(>2.21;299 km^2). The basins with tectonic activities have a consistent relationship with structural disturbances, basin geometry, and field studies. The tectonically active zonation of a part of Ganga basin using geomorphic indices and morphometric parameters suggest that it has significant influence of neotectonic activities in a part of Ganga basin.

Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Global stabilizing controller design for linear time-varying systems and its application on BTT missiles

A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved by the invariant eigenvalues and the gradually varying eigenvectors. A sufficient stability criterion is given by constructing a series of Lyapunov functions based on the selected discrete characteristic points. An important contribution is that it provides a simple and feasible approach for the design of gain-scheduled controllers for linear time-varying systems, which can guarantee both the global stability and the desired closed-loop performance of the resulted system. The method is applied to the design of a BTT missile autopilot and the simulation results show that the method is superior to the traditional one in sense of either global stability or system performance.