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.

QUADRATIC OPTIMIZATION METHOD AND ITS APPLICATION ON OPTIMIZING MECHANISM PARAMETER

In order that the mechanism designed meets the requirements of kinematics with optimal dynamics behaviors, a quadratic optimization method is proposed based on the different characteristics of kinematic and dynamic optimization. This method includes two steps of optimization, that is, kinematic and dynamic optimization. Meanwhile, it uses the results of the kinematic optimization as the constraint equations of dynamic optimization. This method is used in the parameters optimization of transplanting mechanism with elliptic planetary gears of high-speed rice seedling transplanter with remarkable significance. The parameters spectrum, which meets to the kinematic requirements, is obtained through visualized human-computer interactions in the kinematics optimization, and the optimal parameters are obtained based on improved genetic algorithm in dynamic optimization. In the dynamic optimization, the objective function is chosen as the optimal＇ dynamic behavior and the constraint equations are from the results of the kinematic optimization, This method is suitable for multi-objective optimization when both the kinematic and dynamic performances act as objective functions.

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.

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.

Robust Parameter Identification Method of Adhesion Model for Heavy Haul Trains

A robust parameter identification method based on Kiencke model was proposed to solve the problem of the parameter identification accuracy being affected by the rail environment change and noise interference for heavy-duty trains. Firstly, a Kiencke stick-creep identification model was constructed, and the parameter identification task was transformed into a quadratic programming problem. Secondly, an iterative algorithm was constructed to solve the problem, into which a time-varying forgetting factor was added to track the change of the rail environment, and to solve the uncertainty problem of the wheel-rail environment. The Granger causality test was adopted to detect the interference, and then the weights of the current data were redistributed to solve the problem of noise interference in parameter identification. Finally, simulations were carried out and the results showed that the proposed method could track the change of the track environment in time, reduce the noise interference in the identification process, and effectively identify the adhesion performance parameters.

Numerical solutions of linear quadratic control for time-varying systems via symplectic conservative perturbation

Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed 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.

An Optimal Policy with Quadratic Demand, Three-Parameter Weibull Distribution Deterioration Rate, Shortages and Salvage Value

The present paper focuses an optimal policy of an inventory model for deteriorating items with generalized demand rate and deterioration rate. Shortages are allowed and partially backlogged. The salvage value is included into deteriorated units. The main objective of the model is to minimize the total cost by optimizing the value of the shortage point, cycle length and order quantity. A numerical example is carried out to illustrate the model and sensitivity analyses of major parameters are discussed.

Precision motion control for electro-hydraulic axis systems under unknown time-variant parameters and disturbances

This article focuses on asymptotic precision motion control for electro-hydraulic axis systems under unknown time-variant parameters,mismatched and matched disturbances.Different from the traditional adaptive results that are applied to dispose of unknown constant parameters only,the unique feature is that an adaptive-gain nonlinear term is introduced into the control design to handle unknown time-variant parameters.Concurrently both mismatched and matched disturbances existing in electro-hydraulic axis systems can also be addressed in this way.With skillful integration of the backstepping technique and the adaptive control,a synthesized controller framework is successfully developed for electro-hydraulic axis systems,in which the coupled interaction between parameter estimation and disturbance estimation is avoided.Accordingly,this designed controller has the capacity of low-computation costs and simpler parameter tuning when compared to the other ones that integrate the adaptive control and observer/estimator-based technique to dividually handle parameter uncertainties and disturbances.Also,a nonlinear filter is designed to eliminate the“explosion of complexity”issue existing in the classical back-stepping technique.The stability analysis uncovers that all the closed-loop signals are bounded and the asymptotic tracking performance is also assured.Finally,contrastive experiment results validate the superiority of the developed method as well.

A Bayesian model calibration framework for stochastic compartmental models with both time-varying and timeinvariant parameters

We consider state and parameter estimation for compartmental models having both timevarying and time-invariant parameters.In this manuscript,we first detail a general Bayesian computational framework as a continuation of our previous work.Subsequently,this framework is specifically tailored to the susceptible-infectious-removed(SIR)model which describes a basic mechanism for the spread of infectious diseases through a system of coupled nonlinear differential equations.The SIR model consists of three states,namely,the susceptible,infectious,and removed compartments.The coupling among these states is controlled by two parameters,the infection rate and the recovery rate.The simplicity of the SIR model and similar compartmental models make them applicable to many classes of infectious diseases.However,the combined assumption of a deterministic model and time-invariance among the model parameters are two significant impediments which critically limit their use for long-term predictions.The tendency of certain model parameters to vary in time due to seasonal trends,non-pharmaceutical interventions,and other random effects necessitates a model that structurally permits the incorporation of such time-varying effects.Complementary to this,is the need for a robust mechanism for the estimation of the parameters of the resulting model from data.To this end,we consider an augmented state vector,which appends the time-varying parameters to the original system states whereby the time evolution of the time-varying parameters are driven by an artificial noise process in a standard manner.Distinguishing between time-varying and time-invariant parameters in this fashion limits the introduction of artificial dynamics into the system,and provides a robust,fully Bayesian approach for estimating the timeinvariant system parameters as well as the elements of the process noise covariance matrix.This computational framework is implemented by leveraging the robustness of the Markov chain Monte Carlo algorithm permits the estimation of time-invariant parameters while nested nonlinear filters concurrently perform the joint estimation of the system states and time-varying parameters.We demonstrate performance of the framework by first considering a series of examples using synthetic data,followed by an exposition on public health data collected in the province of Ontario.

Identifi cation of model structure parameters via combination of AFMM and ARX from seismic response data

To identify the model structure parameters in shaking table tests from seismic response, especially from time- varying response records, this paper presents a new methodology by combining the online recursive Adaptive Forgetting through Multiple Models （AFMM） and offtine Auto-Regression with eXogenous variables （ARX） model. First, the AFMM is employed to detect whether the response of model structure is time-invariant or time-varying when subjected to strong motions. Second, if the response is time-invariant, the modal parameters are identified from the entire response record, such as the acceleration time-history using the ARX model. If the response is time-varying, the acceleration record is divided into three segments according to the accurate time-varying points detected by AFMM, and parameters are identified by only using the tail segment data, which is time-invariant and suited for analysis by the ARX model. Finally, the changes in dynamic properties due to various strong motions are obtained using the presented methodology. The feasibility and advantages of the method are demonstrated by identifying the modal parameters of a 12-story reinforced concrete （RC） frame structure in a shaking table test.

Optimization design of resistance spot welding parameters of magnesium alloy

By means of the quadratic regression combination design process, the regression equations of nugget diameter and tensile shear load of spot welded joint were established. Effects of welding parameters on the nugget diameter and the tensile shear load were investigated. The results show that effect of welding current on nugget diameter is the most evident. And higher welding current will result in bigger nugget diameter. Besides, interaction effect of electrode force and welding current on tensile shear load is the most evident compared with others. The optimum welding parameters corresponding to the maximum of tensile shear load have been obtained by programming using Matlab software, which is 4, 7 kN electrode force, 28 kA welding current and 4 cycle welding time. Under the condition of the optimum welding parameters, the joint having no visible defects can be obtained, nugget diameter and tensile shear load being 6. 8 mm and 3 256 N, respectively.

Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.

Optimal Parameter Estimation of Transmission Line Using Chaotic Initialized Time-Varying PSO Algorithm

Transmission line is a vital part of the power system that connects two major points,the generation,and the distribution.For an efficient design,stable control,and steady operation of the power system,adequate knowledge of the transmission line parameters resistance,inductance,capacitance,and conductance is of great importance.These parameters are essential for transmission network expansion planning in which a new parallel line is needed to be installed due to increased load demand or the overhead line is replaced with an underground cable.This paper presents a method to optimally estimate the parameters using the input-output quantities i.e.,voltages,currents,and power factor of the transmission line.The equivalentπ-network model is used and the terminal data i.e.,sending-end and receiving-end quantities are assumed as available measured data.The parameter estimation problem is converted to an optimization problem by formulating an error-minimizing objective function.An improved particle swarm optimization(PSO)in terms of time-varying control parameters and chaos-based initialization is used to optimally estimate the line parameters.Two cases are considered for parameter estimation,the first case is when the line conductance is neglected and in the second case,the conductance is considered into account.The results obtained by the improved algorithm are compared with the standard version of the algorithm,firefly algorithm and artificial bee colony algorithm for 30 number of trials.It is concluded that the improved algorithm is tremendously sufficient in estimating the line parameters in both cases validated by low error values and statistical analysis,comparatively.

Improved delay-dependent globally asymptotic stability of delayed uncertain recurrent neural networks with Markovian jumping parameters

In this paper, we have improved delay-dependent stability criteria for recurrent neural networks with a delay varying over a range and Markovian jumping parameters. The criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism. In addition, a numerical example is provided to illustrate the applicability of the result using the linear matrix inequality toolbox in MATLAB.

LMI conditions for quadratic and robust D-stability of interval systems

Sufficient conditions for the quadratic D-stability and further robust D-stability of interval systems are presented in this paper. This robust D-stability condition is based on a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities （LMIs） defined at a series of partial-vertex-based interval matrices other than the total vertex matrices as in previous results. The results contain the usual quadratic and robust stability of continuous-time and discrete-time interval systems as particular cases. The illustrative example shows that this method is effective and less conservative for checking the quadratic and robust D-stability of interval systems.

基于二次型迭代逼近法的电力系统电压鞍结分岔点识别

为实现负荷增长过程中电力系统鞍结分岔点(SNB)的快速准确识别,提出一种直接计算电力系统电压崩溃点的二次型迭代逼近方法,基于系统中PQ节点输出的PV曲线为近似二次型的特点,在节点功率平衡方程中引入负荷增长参数,运用复合函数求导法则就功率方程进行两次求导,理论推导节点电压对负荷参数的一阶、二阶导数表达式,由此确定PV曲线二项式,依靠顶点坐标确定电力系统鞍结分岔点的初始位置,经多次迭代收敛逼近电压崩溃点。所提方法避免了连续潮流法的多次潮流计算,可显著降低计算量。以IEEE 14,IEEE 118节点系统进行仿真验证,证明了该方法的有效性,相较增补P’Q节点法及戴维南等值法,二次型迭代逼近法具有较高的计算效率和鲁棒性。

带参数敏感度的最优权衡投资组合问题的半定规划松弛

考虑带参数敏感度的最优权衡投资组合问题,其模型是一个非凸非可微优化问题,其中目标函数含有极大和极小函数。将该优化问题变换为一个等价的非凸二次约束二次规划问题,提出了等价变换问题的一个紧的半定规划松弛,并估计了其与原问题之间的间隙。数值结果表明,该半定规划松弛可以有效找到大多数测试问题的全局最优解,且计算时间优于求解器GUROBI,从而为寻求问题的一个好的近似解提供方法。

Research on Anti-Fluctuation Control of Winding Tension System Based on Feedforward Compensation

In the fiber winding process,strong disturbance,uncertainty,strong coupling,and fiber friction complicate the winding constant tension control.In order to effectively reduce the influence of these problems on the tension output,this paper proposed a tension fluctuation rejection strategy based on feedforward compensation.In addition to the bias harmonic curve of the unknown state,the tension fluctuation also contains the influence of bounded noise.A tension fluctuation observer(TFO)is designed to cancel the uncertain periodic signal,in which the frequency generator is used to estimate the critical parameter information.Then,the fluctuation signal is reconstructed by a third-order auxiliary filter.The estimated signal feedforward compensates for the actual tension fluctuation.Furthermore,a time-varying parameters fractional-order PID controller(TPFOPID)is realized to attenuate the bounded noise in the fluctuation.Finally,TPFOPID is enhanced by TFO and applied to control a tension control system considering multi-source disturbances.The stability of the method is analyzed by using the Lyapunov theorem.Finally,numerical simulations verify that the proposed scheme improves the tracking ability and robustness of the system in response to tension fluctuations.