Time-varying Problem Research Articles

Optimal Semistable Control in Ad Hoc Network Systems: A Sequential Two-Stage Approach

Motivated by various problems such as distributed computation, multiagent coordination, wireless communication, and online search algorithms, a time-varying optimal coordinated information load balancing problem has been solved by means of a sequential, two-stage, optimal semistable control approach. Technically we formulate this information load balancing problem into a linear, time-varying quadratic semistabilization problem with time-dependent iterative algorithms for information load balancing in peer-to-peer networks. To solve this problem, we propose a novel, sequential two-stage design. The first stage is to guarantee the convergence of the optimal policy while the second stage is to derive the explicit recursive formulas for optimal strategies under a finite set of convergence-guaranteed candidate policies.

Discrete-time ZD, GD and NI for solving nonlinear time-varying equations

A special class of neural dynamics called Zhang dynamics (ZD), which is different from gradient dynamics (GD), has recently been proposed, generalized, and investigated for solving time-varying problems by following Zhang et al.'s design method. In view of potential digital hardware implemetation, discrete-time ZD (DTZD) models are proposed and investigated in this paper for solving nonlinear time-varying equations in the form of $f(x,t)=0$ . For comparative purposes, the discrete-time GD (DTGD) model and Newton iteration (NI) are also presented for solving such nonlinear time-varying equations. Numerical examples and results demonstrate the efficacy and superiority of the proposed DTZD models for solving nonlinear time-varying equations, as compared with the DTGD model and NI.

Different Zhang functions leading to different ZNN models illustrated via time-varying matrix square roots finding

In view of the great potential in parallel processing and ready implementation via hardware, neural networks are now often employed to solve online nonlinear matrix equation problems. Recently, a novel class of neural networks, termed Zhang neural network (ZNN), has been formally proposed by Zhang et al. for solving online time-varying problems. Such a neural-dynamic system is elegantly designed by defining an indefinite matrix-valued error-monitoring function, which is called Zhang function (ZF). The dynamical system is then cast in the form of a first-order differential equation by using matrix notation. In this paper, different indefinite ZFs, which lead to different ZNN models, are proposed and developed as the error-monitoring functions for time-varying matrix square roots finding. Towards the final purpose of field programmable gate array (FPGA) and application-specific integrated circuit (ASIC) realization, the MATLAB Simulink modeling and verifications of such ZNN models are further investigated for online solution of time-varying matrix square roots. Both theoretical analysis and modeling results substantiate the efficacy of the proposed ZNN models for time-varying matrix square roots finding.

Analyses of electromagnetic scattering characteristics for 3D time-varying plasma medium

To analyze the time-varying plasma, a modified finite-difference time-domain (LTJEC-FDTD) algorithm is derived. By using Laplace transform and inverse Laplace transform, we can deduce the FDTD iteration expression for calculating 3D time-varying problem from Maxwell equation and plasma constitutive equation. The iteration expression is proven to be correct by mode-coupling theory, while the correctness of the relevant boundary is tested by calculating the radar cross-section (RCS) of plasma sphere. So, the method is suitable to the calculation of time-varying plasma. Then, the RCS of complex time-varying plasma object is also analyzed.

Optimization of an Intelligent Controller for Parallel Autonomous Parking

Autonomous parking has become the research focus. Fuzzy controller was ofen used to solve the nonlinear and time-varying problem of the autonomous parking. According to the shortcomings of traditional fuzzy controller, a new ant colony algorithm based on idle ant effect was proposed. Firstly, the fuzzy controller was designed based on the kinematic equations. Then, multi-colony parallel optimization was adopted to improve the data initialization, path construction and pheromone update. The method guaranteed the completeness of the membership function and made the fuzzy parameters with higher precision. Finally, both traditional controller and the designed controller were used for the autonomous parking, the experimental results showed that, comparing with the traditional fuzzy controller, the designed controller can improve the stability problem with less error and faster response speed. DOI: http://dx.doi.org/10.11591/telkomnika.v11i2.1404 Full Text: PDF

Detection and Quantification of the Influence of Time Variation in Frequency Response Function Measurements Using Arbitrary Excitations

This paper presents a nonparametric method for detecting and quantifying the influence of time variation in frequency response function measurements. The method is based on the estimation of the best linear time-invariant (BLTI) approximation of a linear time-variant (LTV) system from known input, noisy output data. The key idea consists in reformulating the single-input, single-output time-variant problem as a multiple-input, single-output time-invariant problem. In addition to the BLTI approximation of the LTV system, the contribution of the disturbing noise, the leakage error, and the time-varying effects at the output is also quantified. As such, the approximation error of the time-invariant framework is known.

微纳卫星姿态控制系统的精细抗干扰容错控制方法

It is difficult to diagnose and accommodate the faults if disturbances and faults exist simultaneously in the controlled plants. This paper concerns the time-varying fault diagnosis problem for the attitude control system of microsatellites. First of all, a fault diagnosis observer for abrupt fault of the reaction flywheel is designed. In order to reject the disturbance of vibration from the reaction flywheel, a disturbance observer should be designed. Then a subtle fault diagnosis and tolerant control method is presented for the attitude control system including the parameter uncertainties due to the moment-of-inertia variation of microsatellites, fault of the reaction flywheel and the disturbance of vibration from the reaction flywheel simultaneously. A composite fault tolerant controller is constructed by integrating a fault accommodation from diagnosis observer with additional disturbance rejection and attenuation performance for two different types of disturbances. Then the fault can be accommodated and the multiple disturbances can be rejected and attenuated simultaneously. As a result, the controller can be easily solved via convex optimization based on linear matrix inequality. Simulations for an attitude control system of microsatellites are given to demonstrate that the fault can be accommodated readily and the disturbances can be rejected and attenuated simultaneously.

Novel Recurrent Neural Network for Time-Varying Problems Solving [Research Frontier

By following the inspirational work of McCulloch and Pitts [1], lots of neural networks have been proposed, developed and studied for scientific research and engineering applications [2][18]. For instance, one classical neural network is Hopfield neural network (HNN) which was proposed by Hopfield in the early 1980s [2]. Another classical neural network is based on the error back-propagation (BP) algorithm, i.e., BP neural network, which was developed by Rumelhart, McClelland and others in the mid-1980s [3]. Generally speaking, according to the nature of connectivity, these neural networks can be classified into two categories: feedback neural networks (or termed recurrent neural networks, RNN) and feed forward neural networks. Recently, due to the in-depth research on neural networks, the artificial neural-dynamic approach based on RNN has been viewed as a powerful alternative to online solution of mathematical problems arising in numerous fields of science and engineering, such as matrix inversion in robots redundancy resolution (as an essential part of the pseudoinversetype solution) [16], [18].

Creep Effects on the Reliability of a Concrete-Filled Steel Tube Arch Bridge

The deterioration and ageing process make the reliability of bridges a time-variant problem. However, most studies about time-dependent reliability focus on material corrosion and damage, less attention is given to the effects of concrete creep on the reliability of bridges. This paper presents a case study to investigate the influence of concrete creep on the serviceability reliability of concrete-filled steel tube (CFST) arch bridges, which have a wide application in China. The structural creep effect was analyzed by Model B3 and the age-adjusted effective modulus method; the reliability analysis was performed by Monte Carlo simulation with the Latin Hypercube sampling method, considering random variables involved in three aspects: creep model uncertainty, and variations of material and geometric properties. The analytic results show that the serviceability reliability of CFST arch bridges decreases due to creep, and creep model uncertainty is the most important factor for the structural creep effects and serviceability reliability.

Dynamic Multimode Process Modeling and Monitoring Using Adaptive Gaussian Mixture Models

For multimode processes, it is inevitable to encounter disturbances, such as equipment aging, catalyst deactivation, sensor drifting, reaction kinetics drifting, or adding new operating modes. The existing monitoring algorithms are established either for coping with multimode feature under time-invariant circumstance or for handling the time-varying problem of processes with single operating mode. The purpose of this article is to develop an effective modeling and monitoring approach for complex processes with both multimode and time-varying properties. We propose a novel adaptive monitoring scheme based on Gaussian Mixture Model (GMM). The new method is able to model different operating modes as well as trace process variations. The effectiveness and efficiency of the new method are validated by a numerical example and the Tennessee Eastman (TE) simulation platform in different scenarios.

A new variant of the Zhang neural network for solving online time-varying linear inequalities

Since March 2001, a special class of recurrent neural networks termed the Zhang neural network (ZNN) has been proposed by Zhang and co-workers for solving online a rich repertoire of time-varying problems. By extending Zhang et al. 's design formula (or say, the ZNN design formula), a (new) variant of the ZNN design formula is proposed and investigated in this paper, which is also based on a matrix/vector-valued indefinite error function. In addition, by employing such a novel design formula, a new variant of the ZNN (NVZNN) is proposed, developed and investigated for online solution of time-varying linear inequalities (LIs). The resultant NVZNN models are depicted in implicit dynamics and methodologically exploit the time-derivative information of time-varying coefficients. Computer simulation results further demonstrate the novelty, efficacy and superiority of the proposed NVZNN models for solving online time-varying LIs.

ARPOP: an appetitive reward-based pseudo-outer-product neural fuzzy inference system inspired from the operant conditioning of feeding behavior in Aplysia.

Appetitive operant conditioning in Aplysia for feeding behavior via the electrical stimulation of the esophageal nerve contingently reinforces each spontaneous bite during the feeding process. This results in the acquisition of operant memory by the contingently reinforced animals. Analysis of the cellular and molecular mechanisms of the feeding motor circuitry revealed that activity-dependent neuronal modulation occurs at the interneurons that mediate feeding behaviors. This provides evidence that interneurons are possible loci of plasticity and constitute another mechanism for memory storage in addition to memory storage attributed to activity-dependent synaptic plasticity. In this paper, an associative ambiguity correction-based neuro-fuzzy network, called appetitive reward-based pseudo-outer-product-compositional rule of inference [ARPOP-CRI(S)], is trained based on an appetitive reward-based learning algorithm which is biologically inspired by the appetitive operant conditioning of the feeding behavior in Aplysia. A variant of the Hebbian learning rule called Hebbian concomitant learning is proposed as the building block in the neuro-fuzzy network learning algorithm. The proposed algorithm possesses the distinguishing features of the sequential learning algorithm. In addition, the proposed ARPOP-CRI(S) neuro-fuzzy system encodes fuzzy knowledge in the form of linguistic rules that satisfies the semantic criteria for low-level fuzzy model interpretability. ARPOP-CRI(S) is evaluated and compared against other modeling techniques using benchmark time-series datasets. Experimental results are encouraging and show that ARPOP-CRI(S) is a viable modeling technique for time-variant problem domains.

The plane problem of the impact of a rigid body on a half-space modelled by a Cosserat medium

Abstract The formulation and method of solving of a plane time-varying contact problem with moving boundaries is developed for an absolutely rigid impactor and a half-space filled with a Cosserat medium. A new function, the surface influence function for a Cosserat medium, is constructed and investigated. An original algorithm for constructing it, based on the small-parameter method in conjunction with a simultaneous Fourier–Laplace integral transformation, is developed and implemented. The quantitative and qualitative differences between the influence function constructed and the well-known solution of the plane Lamb problem for an elastic half-space are indicated.

Range Doppler and chirp scaling processing of synthetic aperture radar data using the fractional Fourier transform

Synthetic aperture radar (SAR) systems are used to form high-resolution images from radar backscatter signals. The fractional Fourier transform (FrFT), which is a generalised form of the well-known Fourier transform, has opened up the possibility of a new range of potentially promising and useful applications that involve the use and detection of chirp signals that include pattern recognition and SAR imaging. In this study a time variant problem associated with the use of the FrFT for SAR processing is addressed and a new algorithm is presented that resolves this problem. Two new FrFT-based SAR processing algorithms are presented namely the FrRDA and the eFrCSA that are shown to improve the well-established range-Doppler and chirp-scaling algorithms for SAR processing. The performance of the algorithms are assessed using simulated and real Radarsat-1 data sets. The results confirm that the FrFT-based SAR processing methods provide enhanced resolution yielding both lower side lobes effects and improved target detection.

Time-varying uncertainty in shock and vibration applications using the impulse response

Design of mechanical systems often necessitates the use of dynamic simulations to calculate the displacements (and their derivatives) of the bodies in a system as a function of time in response to dynamic inputs. These types of simulations are especially prevalent in the shock and vibration community where simulations associated with models having complex inputs are routine. If the forcing functions as well as the parameters used in these simulations are subject to uncertainties, then these uncertainties will propagate through the models resulting in uncertainties in the outputs of interest. The uncertainty analysis procedure for these kinds of time-varying problems can be challenging, and in many instances, explicit data reduction equations (DRE's), i.e., analytical formulas, are not available because the outputs of interest are obtained from complex simulation software, e.g. FEA programs. Moreover, uncertainty propagation in systems modeled using nonlinear differential equations can prove to be difficult to analyze. However, if (1) the uncertainties propagate through the models in a linear manner, obeying the principle of superposition, then the complexity of the problem can be significantly simplified. If in addition, (2) the uncertainty in the model parameters do not change during the simulation and the manner in which the outputs of interest respond to small perturbations in the external input forces is not dependent on when the perturbations are applied, then the number of calculations required can be greatly reduced. Conditions (1) and (2) characterize a Linear Time Invariant (LTI) uncertainty model. This paper seeks to explain one possible approach to obtain the uncertainty results based on these assumptions.

Time-Varying Uncertainty in Shock and Vibration Applications Using the Impulse Response

Design of mechanical systems often necessitates the use of dynamic simulations to calculate the displacements (and their derivatives) of the bodies in a system as a function of time in response to dynamic inputs. These types of simulations are especially prevalent in the shock and vibration community where simulations associated with models having complex inputs are routine. If the forcing functions as well as the parameters used in these simulations are subject to uncertainties, then these uncertainties will propagate through the models resulting in uncertainties in the outputs of interest. The uncertainty analysis procedure for these kinds of time-varying problems can be challenging, and in many instances, explicit data reduction equations (DRE's), i.e., analytical formulas, are not available because the outputs of interest are obtained from complex simulation software, e.g. FEA programs. Moreover, uncertainty propagation in systems modeled using nonlinear differential equations can prove to be difficult to analyze. However, if (1) the uncertainties propagate through the models in a linear manner, obeying the principle of superposition, then the complexity of the problem can be significantly simplified. If in addition, (2) the uncertainty in the model parameters do not change during the simulation and the manner in which the outputs of interest respond to small perturbations in the external input forces is not dependent on when the perturbations are applied, then the number of calculations required can be greatly reduced. Conditions (1) and (2) characterize a Linear Time Invariant (LTI) uncertainty model. This paper seeks to explain one possible approach to obtain the uncertainty results based on these assumptions.

Different Zhang functions leading to different Zhang-dynamics models illustrated via time-varying reciprocal solving

Along with neural dynamics (based on analog solvers) widely arising in scientific computation and optimization fields in recent decades which attracts extensive interest and investigation of researchers, a novel type of neural dynamics, called Zhang dynamics (ZD), has been formally proposed by Zhang et al. for the online solution of time-varying problems. By following Zhang et al.’s neural-dynamics design method, the ZD model, which is based on an indefinite Zhang function (ZF), can guarantee the exponential convergence performance for the online time-varying problems solving. In this paper, different indefinite Zhang functions, which can lead to different ZD models, are proposed and developed as the error-monitoring functions for the time-varying reciprocal problem solving. Additionally, for the goal of developing the floating-point processors or coprocessors for the future generation of computers, the MATLAB Simulink modeling and simulative verifications of such different ZD models are further presented for online time-varying reciprocal solving. The modeling results substantiate the efficacy of such different ZD models for time-varying reciprocal solving.

The Leveling Position Control of a Four-Axial Active Pneumatic Isolation System Using PWM-Driving Parallel Dual-On/Off Valves

This study aims to develop a leveling position control of an active PWM-controlled pneumatic isolation table system. A novel concept using parallel dual-on/off valves with PWM control signals is implemented to realize active control and to improve the conventional pneumatic isolation table that supported by four pneumatic cushion isolators. In this study, the cushion isolators are not only passive vibration isolation devices, but also pneumatic actuators in active position control. Four independent closed-loop position feedback control system are designed and implemented for the four axial isolators. In this study, on/off valves are used, and PWM is realized by software. Therefore, additional hardware circuit is not required to implement PWM and not only cost down but also reach control precision of demand. In the controller design, the Fourier series-based adaptive sliding-mode controller with H∞ tracking performance is used to deal with the uncertainty and time-varying problems of pneumatic system. Finally, the experiments on the pneumatic isolation table system for synchronous position and trajectory tracking control, including no-load and loading conditions, and synchronous position control with master-slave method, are implemented in order to verify that the controller for each cushion isolator can realize good position and trajectory tracking performance.

Time-varying line-of-sight rate estimator with a single modified tracking index for RF homing guidance

A practical time-varying line-of-sight (LOS) rate estimator is proposed for surface-to-air missile (SAM) guidance using an RF seeker. The range-dependant LOS rate dynamics and variances of boresight error (BSE) measurements constitute the Kalman filtering problem associated with the timevarying matrix differential Riccati equation (DRE). Since the conventional gain-scheduled steady-state Kalman filter derived by solving an algebraic Riccati equation (ARE) cannot fully consider the time-varying nature of LOS rate dynamics, it might not be appropriate for volatile missile-target engagement scenarios. This motivates us to investigate a pseudo-analytic solution to the time-varying Kalman filtering problem based on the algebraic transform of the given DRE. Apart from the previous works, the explicit form of time-varying Kalman gain is expressed in terms of a single filter design parameter, called modified tracking index. The proposed time-varying filter is not only able to effectively handle the time-varying LOS rate dynamics but is also affordable for real-time implementation. Adjoint analysis results for a homing guidance loop show that the proposed LOS rate estimator could improve guidance performance and be an excellent choice for SAM applications.

Statistical properties of support vector machines with forgetting factor

Introducing a forgetting factor allows a support vector machine to solve time-varying problems adaptively. However, the exponential forgetting factor proposed in an earlier work does not ensure convergence of average generalization error even for a simple linearly separable problem. To guarantee convergence, we propose a factorial forgetting factor which decays factorially over time. We approximately derive the average generalization error of the factorial forgetting factor as well as that of the exponential forgetting factor using a simple one-dimensional problem, and confirm our theory by computer simulations. Finally, we show that our theory can be extended to arbitrary types of forgetting factors for simple linearly separable cases.