Identification of time-varying system and energy-based optimization of adaptive control in seismically excited structure

The combination of structural health monitoring and vibration control is of great importance to provide components of smart structures.While synthetic algorithms have been proposed,adaptive control that is compatible with changing conditions still needs to be used,and time-varying systems are required to be simultaneously estimated with the application of adaptive control.In this research,the identification of structural time-varying dynamic characteristics and optimized simple adaptive control are integrated.First,reduced variations of physical parameters are estimated online using the multiple forgetting factor recursive least squares(MFRLS)method.Then,the energy from the structural vibration is simultaneously specified to optimize the control force with the identified parameters to be operational.Optimization is also performed based on the probability density function of the energy under the seismic excitation at any time.Finally,the optimal control force is obtained by the simple adaptive control(SAC)algorithm and energy coefficient.A numerical example and benchmark structure are employed to investigate the efficiency of the proposed approach.The simulation results revealed the effectiveness of the integrated online identification and optimal adaptive control in systems.

DAMAGE CLASSIFICATION BY PROBABILISTIC NEURAL NETWORKS BASED ON LATENT COMPONENTS FOR TIME-VARYING SYSTEM

A new approach to damage classification for health monitoring of a time-varylng system is presented. The functional-series time-dependent auto regressive moving average （FS-TARMA） time series model is applied to the vibration signal observed in the time-varying system for estimating the TAR/TMA parameters and the innovation variance. These parameters are the functions of the time, represented by a group of projection coefficients on the certain functional subspace with specific basis functions. The estimated TAR/TMA parameters and the innovation variance are further used to calculate the latent components （LCs） as the more informative data for health monitoring evaluation, based on an eigenvalue decomposition technique. LCs are then combined and reduced to numerical values （NVs） as feature sets, which are input to a probabilistic neural network （PNN） for the damage classification. For the evaluation of the proposed method, numerical simulations of the damage classification for a tlme-varylng system are used, in which different classes of damage are modeled by the mass or stiffness reductions. It is demonstrated that the method can identify the damages in the course of operation and the change of parameters on the time-varying background of the system.

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.

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.

Feedforward and feedback optimal control for linear time-varying systems with persistent disturbances

The optimal control problem for linear time-varying systems affected by external persistent disturbances with known dynamic characteristics but unknown initial conditions is consider and a design procedure of a feedforward and feedbaek optimal controller is presented. The condition of existence and uniqueness of the control law is given. The disturbanee observer is proposed to make the feedforward control law realizable physically. Simulation results demonstrate that the feedforward and feedbaek optimal control law is more effective and robust than the elassical state feedbaek control law with respect to external disturbanees.

Scheme of optimal fault detection for linear discrete time-varying systems with delayed state

This paper deals with the problem of the optimal fault detection (FD) for linear discrete time-varying (LDTV) systems with delayed state and l(2)-norm bounded unknown input. The novelty lies in the designing of an evaluation function for the robust FD. The basic idea is to directly construct an evaluation function by using a weighted l(2)-norm of the measurement output, which achieves an optimal trade-off between the sensitivity to fault and the robustness to l(2)-norm bounded unknown input. To avoid complex computation, a feasible solution is obtained via the recursive computation by applying the orthogonal projection. It is shown that such an evaluation function provides a unified scheme for both the cases of unknown input being l(2)-norm bounded and jointly normal distribution, while a threshold may be chosen based on a priori knowledge of unknown input. A numerical example is given to demonstrate the effectiveness of the proposed method.

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.

Feedforward and feedback optimal control for linear time-varying systems with persistent disturbances

The optimal control problem was studied for linear time-varying systems,which was affected by external persistent disturbances with known dynamic characteristics but unknown initial conditions. To damp the effect of disturbances in an optimal fashion,we obtained a new feedforward and feedback optimal control law and gave the control algorithm by solving a Riccati differential equation and a matrix differential equation. Simulation results showed that the achieved optimal control law was realizable,efficient and robust to reject the external disturbances.

Real-Valued Discrete Gabor Transform of Linear Time-Varying Systems: Exact Representation and Approximation

An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more easily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.

Modal Identification of Linear Time-varying Systems Using Continuous Wavelet Transform

A wavelet based identification method for linear time-varying systems is presented,and the ridge and skeleton of the continuous wavelet transform of free response is used to extract time-varying parameters. The stiffness and damping coefficients of single-degree-of—freedom systems,frequencies and damping ratios of multi-degree-of-freedom systems are estimated without any prior information of systems. The proposed method is applied to linear time-varying systems with both abrupt and smooth variation parameters. Gaussian white noise is added to the response to test the anti-noise performance of the algorithm. The simulation results show that the proposed method is capable of accurately tracking the variation of the systems.

Fault detection filter design for linear discrete time-varying systems with multiplicative noise

The problem of fault detection for linear discrete timevarying systems with multiplicative noise is dealt with.By using an observer-based robust fault detection filter（FDF） as a residual generator,the design of the FDF is formulated in the framework of H ∞ filtering for a class of stochastic time-varying systems.A sufficient condition for the existence of the FDF is derived in terms of a Riccati equation.The determination of the parameter matrices of the filter is converted into a quadratic optimization problem,and an analytical solution of the parameter matrices is obtained by solving the Riccati equation.Numerical examples are given to illustrate the effectiveness of the proposed method.

Stabilization of linear time-varying systems with state and input constraints using convex optimization

The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.

New algorithm applied to vibration equations of time-varying system

Vibration equations of time-varying system are transformed to the form which is suitable to precise integration algorithm.Precision analysis and computation efficiency of new algorithm are implemented.The following conclusions can be got.Choosing matrixes M,G and K is certainly flexible.We can place left side of nonlinear terms of vibration equations of time-varying system into right side of equations in precise integration algorithms.The key of transformation from vibration equations of time-varying system to first order differential equations is to form matrix H,which should be assured to be nonsingular.With suitable disposal,precision and computation efficiency of precise integration algorithms are greatly larger than those of general methods.

Commutant Lifting for Optimal Control of Time-varying Systems

This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem. We also obtain a new formula for the optimal performance and prove the existence of an optimal controller.

Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer

This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.

Semi-supervised learning based hybrid beamforming under time-varying propagation environments

Hybrid precoding is considered as a promising low-cost technique for millimeter wave(mm-wave)massive Multi-Input Multi-Output(MIMO)systems.In this work,referring to the time-varying propagation circumstances,with semi-supervised Incremental Learning(IL),we propose an online hybrid beamforming scheme.Firstly,given the constraint of constant modulus on analog beamformer and combiner,we propose a new broadnetwork-based structure for the design model of hybrid beamforming.Compared with the existing network structure,the proposed network structure can achieve better transmission performance and lower complexity.Moreover,to enhance the efficiency of IL further,by combining the semi-supervised graph with IL,we propose a hybrid beamforming scheme based on chunk-by-chunk semi-supervised learning,where only few transmissions are required to calculate the label and all other unlabelled transmissions would also be put into a training data chunk.Unlike the existing single-by-single approach where transmissions during the model update are not taken into the consideration of model update,all transmissions,even the ones during the model update,would make contributions to model update in the proposed method.During the model update,the amount of unlabelled transmissions is very large and they also carry some information,the prediction performance can be enhanced to some extent by these unlabelled channel data.Simulation results demonstrate the spectral efficiency of the proposed method outperforms that of the existing single-by-single approach.Besides,we prove the general complexity of the proposed method is lower than that of the existing approach and give the condition under which its absolute complexity outperforms that of the existing approach.

Nuclear magnetic resonance experiments on the time-varying law of oil viscosity and wettability in high-multiple waterflooding sandstone cores

A simulated oil viscosity prediction model is established according to the relationship between simulated oil viscosity and geometric mean value of T2spectrum,and the time-varying law of simulated oil viscosity in porous media is quantitatively characterized by nuclear magnetic resonance(NMR)experiments of high multiple waterflooding.A new NMR wettability index formula is derived based on NMR relaxation theory to quantitatively characterize the time-varying law of rock wettability during waterflooding combined with high-multiple waterflooding experiment in sandstone cores.The remaining oil viscosity in the core is positively correlated with the displacing water multiple.The remaining oil viscosity increases rapidly when the displacing water multiple is low,and increases slowly when the displacing water multiple is high.The variation of remaining oil viscosity is related to the reservoir heterogeneity.The stronger the reservoir homogeneity,the higher the content of heavy components in the remaining oil and the higher the viscosity.The reservoir wettability changes after water injection:the oil-wet reservoir changes into water-wet reservoir,while the water-wet reservoir becomes more hydrophilic;the degree of change enhances with the increase of displacing water multiple.There is a high correlation between the time-varying oil viscosity and the time-varying wettability,and the change of oil viscosity cannot be ignored.The NMR wettability index calculated by considering the change of oil viscosity is more consistent with the tested Amott(spontaneous imbibition)wettability index,which agrees more with the time-varying law of reservoir wettability.

Adaptive Event-Triggered Time-Varying Output Group Formation Containment Control of Heterogeneous Multiagent Systems

In this paper,a class of time-varying output group formation containment control problem of general linear hetero-geneous multiagent systems(MASs)is investigated under directed topology.The MAS is composed of a number of tracking leaders,formation leaders and followers,where two different types of leaders are used to provide reference trajectories for movement and to achieve certain formations,respectively.Firstly,compen-sators are designed whose states are estimations of tracking lead-ers,based on which,a controller is developed for each formation leader to accomplish the expected formation.Secondly,two event-triggered compensators are proposed for each follower to evalu-ate the state and formation information of the formation leaders in the same group,respectively.Subsequently,a control protocol is designed for each follower,utilizing the output information,to guide the output towards the convex hull generated by the forma-tion leaders within the group.Next,the triggering sequence in this paper is decomposed into two sequences,and the inter-event intervals of these two triggering conditions are provided to rule out the Zeno behavior.Finally,a numerical simulation is intro-duced to confirm the validity of the proposed results.

Time-dependent model for two-phase flow in ultra-high water-cut reservoirs:Time-varying permeability and relative permeability

For the ultra-high water-cut reservoirs,after long-term water injection exploitation,the physical properties of the reservoir change and the heterogeneity of the reservoir becomes increasingly severe,which further aggravates the spatial difference of the flow field.In this study,the displacement experiments were employed to investigate the variations in core permeability,porosity,and relative permeability after a large amount of water injection.A relative permeability endpoint model was proposed by utilizing the alternating conditional expectation(ACE)transformation to describe the variation in relative permeability based on the experimental data.Based on the time dependent models for permeability and relative permeability,the traditional oil-water two-phase model was improved and discretized using the mimetic finite difference method(MFD).The two cases were launched to confirm the validation of the proposed model.The impact of time-varying physical features on reservoir production performance was studied in a real water flooding reservoir.The experimental results indicate that the overall relative permeability curve shifts to the right as water injection increases.This shift corresponds to a transition towards a more hydrophilic wettability and a decrease in residual oil saturation.The endpoint model demonstrates excellent accuracy and can be applied to time-varying simulations of reservoir physics.The impact of variations in permeability and relative permeability on the reservoir production performance yields two distinct outcomes.The time-varying permeability of the reservoir results in intensified water channeling and poor development effects.On the other hand,the time-varying relative permeability enhances the oil phase seepage capacity,facilitating oil displacement.The comprehensive time-varying behavior is the result of the combined influence of these two parameters,which closely resemble the actual conditions observed in oil field exploitation.The time-varying simulation technique of reservoir physical properties proposed in this paper can continuously and stably characterize the dynamic changes of reservoir physical properties during water drive development.This approach ensures the reliability of the simulation results regarding residual oil distribution.

Set-Membership Filtering Approach to Dynamic Event-Triggered Fault Estimation for a Class of Nonlinear Time-Varying Complex Networks

The present study addresses the problem of fault estimation for a specific class of nonlinear time-varying complex networks,utilizing an unknown-input-observer approach within the framework of dynamic event-triggered mechanism(DETM).In order to optimize communication resource utilization,the DETM is employed to determine whether the current measurement data should be transmitted to the estimator or not.To guarantee a satisfactory estimation performance for the fault signal,an unknown-input-observer-based estimator is constructed to decouple the estimation error dynamics from the influence of fault signals.The aim of this paper is to find the suitable estimator parameters under the effects of DETM such that both the state estimates and fault estimates are confined within two sets of closed ellipsoid domains.The techniques of recursive matrix inequality are applied to derive sufficient conditions for the existence of the desired estimator,ensuring that the specified performance requirements are met under certain conditions.Then,the estimator gains are derived by minimizing the ellipsoid domain in the sense of trace and a recursive estimator parameter design algorithm is then provided.Finally,a numerical example is conducted to demonstrate the effectiveness of the designed estimator.