Simultaneous identification of unknown time delays and model parameters in uncertain dynamical systems with linear or nonlinear parameterization by autosynchronization

In this paper, we propose a general method to simultaneously identify both unknown time delays and unknown model parameters in delayed dynamical systems based on the autosynchronization technique. The design procedure is presented in detail by constructing a specific Lyapunov function and linearizing the model function with nonlinear parameterization. The obtained result can be directly extended to the identification problem of linearly parameterized dynamical systems. Two Wpical numerical examples confirming the effectiveness of the identification method are given.

Robust Adaptive Control of Nonholonomic Systems with Nonlinear Parameterization

全球适应的州的反馈控制策略与强壮的非线性的飘移和未知非线性的参数在锁住的形式为 nonholonomic 系统的一个类被介绍。一种参数分离技术被介绍把非线性的 parameterization nonholonomic 系统转变成一个象线性一样 parameterized nonholonomic 系统。然后，反馈支配设计被使用设计一个全球适应稳定控制器，切换的策略被开发消除 uncontrollability 的现象。建议控制器能保证那得到状态全球性集成到起源的所有系统，当另外的信号仍然保持围住时。模拟例子表明有效性和建议控制器的柔韧的特征。

Numerical Analysis of the Nonlinear Parameterization of Waves in Currents over a Submerged Sill with a Non-Hydrostatic Model

An investigation of the effects of a uniform current strength direction(following or opposing wave propagation) on the nonlinear transformation of irregular waves over a submerged trapezoidal sill is carried out using SWASH,a non-hydrostatic numerical wave model.The nonlinear parameters(i.e.,asymmetry,skewness,and kurtosis) are calculated,and the empirical formulas for these parameters are presented as a function of the local Ursell number based on the present numerical data measured.In the shoaling area of the submerged sill,the nonlinear characteristics of waves are more obvious when waves propagate in the same direction as the currents than when waves propagate in the opposite direction.Whereas nonlinear parameters grow with the strengthening of the following currents over the crest,they tend to decrease as the adverse current velocity increases over the crest area of the submerged sill.

Self-heating tendency evaluation of sulfide ores based on nonlinear multi-parameters fusion

In order to reveal the nonlinear dynamics characteristics of unsteady self-heating process of sulfide ores, nine different kinds of sulfide ore samples from a pyrite mine in China were taken as experimental materials and their self-heating characteristics were measured in laboratory. Furthermore, the measured temperature was studied by integrating wavelet transform, nonlinear characteristic parameters extraction and fuzzy comprehensive evaluation. The results indicate that only the ore samples 1, 2, 6 and 9 have obvious self-heating phenomenon, and their self-heating initiative temperatures are 220 ℃, 239 ℃, 220 ℃ and 220 ℃, respectively, which means that they are difficult to produce self-heating under normal mining conditions. The correlation dimension of self-heating process is fraction and the maximum Lyapunov exponent is positive, which means that it is feasible to study the self-heating process based on chaotic dynamics theory. The nonlinearities of self-heating process of these four samples （ore samples 1, 2, 6 and 9） are 0.8227, 0.7521, 0.9401 and 0.8827 respectively and the order of the samples according to these results is： sample 6, sample 9, sample 1, sample 2, which is consistent with the measured results of self-heating characteristics. Therefore, the nonlinearity method can be used to evaluate the self-heating tendency of sulfide ores, and it is an effective verification of the reliability of measured results.

Computer simulation of acoustic nonlinear parameter tomography

Acoustic nonlinearity paramcter B / A is a new important parameter in ultrasonic tissue characterization. In this paper, we present the nonlinear theory of a finite amplitude plane sound wave propagating in a layer medium by Burgers' equation and apply this analysis in the case of imaging with the second harmonic wave. A computer simulation of acoustic nonlinear parameter imaging was carried out from the second harmonic data in a conventional CT algorithm. The reconstructed imagcs were obtained by using filtered back projection algorithm. The tomography of acoustic nonlinear parameter for simple phantoms was reconstructed with quite good quality.

FBFN-based adaptive repetitive control of nonlinearly parameterized systems

An adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on the fuzzy basis function network （FBFN）. The parameters of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control term is approximated by an adaptive PI control structure. The bound of the discontinuous control term is assumed to be unknown and estimated by an adaptive mechanism. Based on the Lyapunov stability theory, an adaptive repetitive control law is proposed to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, which avoid the nonlinear parameterization from entering into the adaptive repetitive control, the controller singularity problem is solved. The proposed approach does not require an exact structure of the system dynamics, and the proposed controller is utilized to control a model of permanent-magnet linear synchronous motor subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method.

A Novel Nonlinear Parameter Estimation Method of Soft Tissues

The elastic parameters of soft tissues are important for medical diagnosis and virtual surgery simulation. In this study, we propose a novel nonlinear parameter estimation method for soft tissues. Firstly, an in-house data acquisition platform was used to obtain external forces and their corresponding deformation values, To provide highly precise data for estimating nonlinear param- eters, the measured forces were corrected using the constructed weighted combination forecasting model based on a support vector machine （WCFM_SVM）. Secondly, a tetrahedral finite element parameter estimation model was established to describe the physical characteristics of soft tissues, using the substitution parameters of Young＇s modulus and Poisson＇s ratio to avoid solving compli- cated nonlinear problems. To improve the robustness of our model and avoid poor local minima, the initial parameters solved by a linear finite element model were introduced into the parameter estimation model. Finally, a self-adapting Levenberg-Marquardt （LM） algorithm was presented, which is capable of adaptively adjusting iterative parameters to solve the established parameter estimation model. The maximum absolute error of our WCFM SVM model was less than 0.03 Newton, resulting in more accurate forces in comparison with other correction models tested. The maximum absolute error between the calculated and measured nodal displacements was less than 1.5 mm, demonstrating that our nonlinear parameters are precise.

ON THE SINGULAR PERTURBATION OF A NONLINEAR ORDINARY DIFFERENTIAL EQUATION WITH TWO PARAMETERS

In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchro-nization of two different chaotic systems with fully unknown parameters and nonlinear inputs. We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero. We assume that both the master＇s and the slave＇s system parameters are unknown in advance. Proper adaptation laws are derived to tackle the unknown parameters. An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time. We prove that both reaching and sliding mode phases are stable in finite time. An estimation of convergence time is given. Two illustrative examples show the effectiveness and usefulness of the proposed technique. It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.

Parameterized design of nonlinear feedback controllers for servo positioning systems

To achieve fast, smooth and accurate set point tracking in servo positioning systems, a parameterized design of nonlinear feedback controllers is presented, based on a so-called composite nonlinear feedback （CNF） control technique. The controller designed here consists of a linear feedback part and a nonlinear part. The linear part is responsible for stability and fast response of the closed-loop system. The nonlinear part serves to increase the damping ratio of closed-loop poles as the controlled output approaches the target reference. The CNF control brings together the good points of both the small and the large damping ratio cases, by continuously scheduling the damping ratio of the dominant closed-loop poles and thus has the capability for superior transient performance, i.e. a fast output response with low overshoot. In the presence of constant disturbances, an integral action is included so as to remove the static bias. An explicitly parameterized controller is derived for servo positioning systems characterized by second-order model. Practical application in a micro hard disk drive servo system is then presented, together with some discussion of the rationale and characteristics of such design. Simulation and experimental results demonstrate the effectiveness of this control design methodology.

THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION “ON-OFF” SWITCHES INCLUDED BY A MODEL

In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.

Molecular structure dependence of acoustic nonlinearity parameter B/A for silicone oils

Exploring new acoustic parameters is essential to develop a noninvasive imaging technique for the surgery of silicone oil tamponades. In this study, the acoustic nonlinearity parameters B/A of varied silicone oil samples （e.g., linear or hyper-branched） are experimentally measured by using a modified thermodynamic method. The results show that： （i） when the concentration of the silicone oil with a molecular weight of 5 × 10^4 increases from 0.5 g/100 ml to 8 g/100 ml, the corresponding B/A value increases by about 18%, but the acoustic velocity only increases by about 0.1%; （ii） when the molecular weight of the hyper-branched silicone oil is enhanced from 2 × 10^5 to 1 × 10^6, the B/A value increases by about 22%, while the acoustic velocity is only raised by about 0.2%. This study suggests that the B/A parameter of the silicone oil is more sensitive to the change in its molecular structure than that of the acoustic velocity. Thus, the B/A parameter might be utilized as an effective index for the development and optimization of the noninvasive imaging of the surgery of silicone oil tamponades.

Experimental Evaluation of Parameterized Nonlinear MPC Applied to PEM Fuel Cell

This paper proposes a parameterized nonlinear model-based predictive control (NMPC) strategy to tackle the oxygen excess ratio regulation challenge of a proton exchange membrane fuel cell. In practice, the most challenging part regarding NMPC strategies remains the on-line implementation. In fact, NMPC strategies, at least in their basic form, involve heavy computation to solve the optimization problem. In this work, a specific parameterization of control actions has been designed to address this limitation and achieve on-line implementation. To assess the effectiveness and relevance of the proposed strategy, the controller has been implemented on-line, experimentally validated on a real fuel cell and compared to the built-in controller. Performance of the parameterized NMPC controller in terms of setpoint tracking accuracy, disturbances rejection and computational cost, have tested under several control scenarios. Experimental results have shown the excellent tracking capability, disturbances rejection ability and low computational cost of the NMPC controller, regardless of the operating conditions. Moreover, compared to the built-in controller the proposed strategy has demonstrated better disturbances rejection capability. Overall, the proposed parameterized NMPC controller appears as an excellent candidate to address the oxygen excess ratio regulation issue.

过载和攻击时间约束下的非线性最优制导方法

考虑导弹过载受限条件下,对以期望时间为攻击目标的非线性最优制导问题进行了研究。首先,建立了非线性最优制导问题的理论模型,基于庞特里亚金极大值原理和饱和函数方法建立了最优轨迹的最优性条件。其次,根据最优性条件和哈密尔顿轨迹参数化方法,建立了最优轨迹的参数化微分方程组,使得通过数值积分即可生成从飞行状态到最优制导指令映射关系的数据集。然后,通过前馈神经网络对上述映射关系进行近似,实现了非线性最优制导指令的毫秒量级实时生成。最后,通过数值仿真验证了所提非线性最优制导指令生成方法的有效性。

Nonlinear characteristics of induced spontaneous combustion process of sulfide ores

To investigate the relationship between nonlinear parameters and spontaneous combustion tendency of sulfide ores, nine different sulfide ore samples were taken from a pyrite mine in China, and induced spontaneous combustion experiment was carried out in the laboratory. Different stages of the induced spontaneous combustion process were studied by integrating wavelet technology and nonlinear dynamics theory. The results show that ignition points of all the ore samples are above 330 ℃, indicating that sulfide ores of the pyrite mine are difficult to combust spontaneously under normal mining conditions. Spontaneous combustion process includes three stages： incubation stage, development stage and approaching stage. The average temperature rising rate of the three stages are 1.0 ~C/min, 2.0 ~C/min and 4.2 ~C/min, respectively. During the spontaneous combustion process, mean values of approximate entropy and correlation dimension increase at first, and then decrease in the following stage. The mean value of the maximum Lyapunov exponent increases with the passage of reaction time. In a whole, correlation among the three nonlinear parameters firstly weakens, then enhances, and the best correlation period is at approaching stage. As ignition point increases, the maximum Lyapunov exponent of approaching stage decreases. Therefore, combustible tendency of sulfide ores could be qualitatively evaluated based on the maximum Lyapunov exponent of this stage.

考虑自动驾驶仪延迟的非线性最优末制导方法

针对过载受限和自动驾驶仪延迟等条件下的非线性最优末制导指令在线生成方法进行研究。首先,基于庞特里亚金极大值原理,建立了目标静止的非线性最优末制导问题的最优性条件,并利用饱和函数将过载约束嵌入最优性条件。其次,应用参数化方法使得通过数值积分即可快速生成满足最优性条件的飞行轨迹数据集。然后,利用该数据集训练神经网络,使其拟合弹-目相对运动状态到最优制导指令的映射关系,实现过载约束下制导指令的毫秒量级在线生成。针对自动驾驶仪的延迟响应,通过微分补偿法估计神经网络下一时刻输出的制导指令以实现快速跟踪。最后,仿真结果表明,本文所提出方法针对静止目标与小机动目标都能够在线生成最优制导指令。

基于最小二乘法的欠驱动水面船舶模型预测控制

针对欠驱动水面船舶轨迹跟踪控制问题,根据模型预测控制(Model Predictive Control, MPC)原理,提出一种基于参数化模型的非线性模型预测控制(Parameterized Model-Nonlinear Model Predictive Control, PM-NMPC)方法。采用最小二乘法对船舶的参数化模型进行辩识,设计PM-NMPC控制器。对环境干扰下的某集装箱船艏向角控制和轨迹跟踪进行试验,验证控制算法的有效性,并将该控制器与比例积分微分控制器(Proportional plus Integral plus Derivative cotroller, PID cotroller)控制器进行对比。仿真结果表明,PM-NMPC控制器轨迹跟踪效果更好,对未知干扰具有更强的稳健性。

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton＇s principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed- parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

Impacts of parameter uncertainties on deep chlorophyll maximum simulation revealed by the CNOP-P approach

Parameter uncertainty is a primary source of uncertainty in ocean ecosystem simulations.The deep chlorophyll maximum(DCM)is a ubiquitous ecological phenomenon in the ocean.Using a theoretical nutrients-phytoplankton model and the conditional nonlinear optimal perturbation approach related to parameters,we investigated the eff ects of parameter uncertainties on DCM simulations.First,the sensitivity of single parameter was analyzed.The sensitivity ranking of 10 parameters was obtained by analyzing the top four specifi cally.The most sensitive parameter(background turbidity)aff ects the light supply for DCM formation,whereas the other three parameters(nutrient content of phytoplankton,nutrient recycling coeffi cient,and vertical turbulent diff usivity)control nutrient supply.To explore the interactions among diff erent parameters,the sensitivity of multiple parameters was further studied by examining combinations of four parameters.The results show that background turbidity is replaced by the phytoplankton loss rate in the optimal parameter combination.In addition,we found that interactions among these parameters are responsible for such diff erences.Finally,we found that reducing the uncertainties of sensitive parameters could improve DCM simulations remarkably.Compared with the sensitive parameters identifi ed in the single parameter analysis,reducing parameter uncertainties in the optimal combination produced better model performance.This study shows the importance of nonlinear interactions among various parameters in identifying sensitive parameters.In the future,the conditional nonlinear optimal perturbation approach related to parameters,especially optimal parameter combinations,is expected to greatly improve DCM simulations in complex ecosystem models.