非参数不确定动力学建模研究综述

在工程应用中不可避免存在各种不确定因素,采用不确定模型能够更为准确反映动力学系统的特性。参数不确定动力学建模在过去三十多年得到了充分关注和研究,而非参数不确定动力学建模作为一个比较新的研究领域,直到近年来才逐渐得到重视。该领域至今已取得了大量的研究成果,有必要对国内外研究和发展现状进行全面的总结。从非参数不确定动力学建模的方法、理论基础、建模过程及应用等方面系统综述了其研究现状,归纳现阶段存在的问题,并指出了未来研究的发展方向。

非参数不确定时滞系统的重复控制

针对非参数不确定时滞系统,给出能够实现跟踪误差本身沿整个周期完全跟踪的重复控制器设计.针对系统不确定特性的界函数已知和未知两种情形,分别分析闭环系统的稳定性与收敛性.控制器中学习部分采用完全饱和形式,使得参数估计囿于一预先给定的范围内.该控制律可保证闭环系统内所有信号有界以及跟踪误差本身趋于零.数值仿真表明算法的有效性.

一类非参数不确定运动系统的自适应空间重复学习控制

针对一类在空间区间内重复运行的非参数不确定运动系统,本文提出一种基于李雅普诺夫方法的自适应空间重复学习控制(SRLC)策略。首先,引入空间微分算子将系统从时间域转换到空间域形式,并将系统非参数不确定性划分为空间周期不确定和非周期不确定两部分。其次,设计全饱和空间重复学习律估计和补偿空间周期非参数不确定部分,同时保证被估计值的连续性和有界性。此外,将非周期不确定部分转换为参数化不确定形式,并设计其上界参数的空间自适应更新律用以补偿系统非周期不确定。最后,设计控制器确保系统输出能够精确跟踪空间周期性期望信号。仿真结果验证了所提方法的有效性。

输入增益未知非参数不确定系统的准最优学习控制

为解决一类非参数不确定系统在任意初态且输入增益未知情形下的轨迹跟踪问题,提出准最优误差跟踪学习控制方法.该方法综合准最优控制和迭代学习控制两种技术设计控制器,在构造期望误差轨迹的基础上,根据控制Lyapunov函数及Sontag公式给出标称系统的优化控制,以鲁棒方法和学习方法相结合的策略处理非参数不确定性.闭环系统经过足够次迭代运行后,经由实现系统误差对期望误差轨迹在整个作业区间上的精确跟踪,获得系统状态对参考信号在预设的部分作业区间上的精确跟踪.仿真结果表明所设计学习系统在收敛速度方面快于非优化设计.

具有死区输入的非参数不确定系统误差跟踪迭代学习控制

本文针对一类具有非对称死区输入的非参数不确定系统设计了一种误差跟踪迭代学习控制(ILC)算法。首先,构造一种新型的期望误差轨迹放宽经典迭代学习控制的初值一致条件。其次,利用微分中值定理将非对称死区转换为线性形式,并利用径向基函数(RBF)神经网络对系统不确定性和死区参数进行估计和补偿。在此基础上,设计误差跟踪迭代学习控制器和组合自适应律,实现系统在指定区间对期望轨迹的高精度跟踪。最后,基于Lyapunov-Like理论进行稳定性分析,并通过仿真验证了本文所提方法的有效性。

一类非参数不确定系统的自适应神经网络重复学习控制

本文针对一类非参数不确定系统提出一种自适应神经网络重复学习控制方法。利用期望轨迹的周期特性,构造周期性期望控制输入,并设计重复学习律估计未知期望控制输入并补偿系统周期不确定,实现系统对期望轨迹的高精度跟踪。在此基础上,利用神经网络估计系统未知状态和补偿非周期性不确定,进而提高系统鲁棒性。与已有的部分限幅学习律相比,本文提出的全限幅重复学习律可以保证估计值的连续性且能够被限制在指定的界内。最后,基于Lyapunov方法分析误差的收敛性能,并给出仿真结果验证了本文所提方法的有效性。

非参数不确定系统的自适应迭代学习控制

针对一类含非参数不确定的受限非线性系统,提出一种新的自适应迭代学习控制算法.该算法利用神经网络(neural network)逼近系统中的非参数不确定性,神经网络的权值通过迭代轴上的自适应算法进行更新.控制器设计补偿项对神经网络逼近误差上界进行估计以此消除其影响.采用一种新的障碍李雅普诺夫函数(barrier Lyapunov functions)并与组合能量函数(composite energy function)方法相结合,当系统中同时存在非参数不确定性,随机初始误差,及非严格重复外部扰动时,能够保证系统同时满足输入和状态受限要求.将所提出的算法应用于高速列车运行控制系统,仿真结果验证了算法的有效性.

基于系统侵入与不变流行的非线性系统自适应控制

考虑了一类具有非参数不确定非线性系统的自适应控制问题,基于系统侵入与不变流行概念,选用含有系统状态的参数误差表达式,应用非线性阻尼方法,处理参数估计误差中的不确定项,确保参数估计对外界干扰的鲁棒性。应用滑模积分反推法,确定了系统的控制率,证明了在该控制律的作用下系统平衡点全局渐近稳定。该方法设计过程简单,参数估计误差具有良好的动态性能,而且避免了积分反推法无自适应调节时出现的系统不稳定问题。仿真结果表明,所设计的控制器对非参数不确定性具有很强的稳定性和鲁棒性。

基于扩张状态观测器的永磁同步电机重复学习控制

本文针对非参数不确定永磁同步电机系统,提出一种基于扩张状态观测器的重复学习控制方法,实现对周期期望轨迹的高精度跟踪.首先,将永磁同步电机中的非参数不确定性分为周期不确定与非周期不确定两部分.其次,构造包含周期不确定的未知期望控制输入,并设计重复学习律估计未知期望控制输入并补偿系统周期不确定.在此基础上,设计扩张状态观测器,估计系统未知状态和补偿非周期性不确定,进而提高系统鲁棒性.与已有的部分限幅学习律相比,本文提出的全限幅重复学习律可以保证估计值的连续性且能够被限制在指定的界内.最后,基于李雅普诺夫方法分析误差的收敛性能,并给出仿真和实验结果验证本文所提方法的有效性.

A non-parametric indicator Kriging method for generating coastal sediment type map

Coastal sediment type map has been widely used in marine economic and engineering activities, but the traditional mapping methods had some limitations due to their intrinsic assumption or subjectivity. In this paper, a non-parametric indicator Kriging method has been proposed for generating coastal sediment map. The method can effectively avoid mapping subjectivity, has no special requirements for the sample data to meet second-order stationary or normal distribution, and can also provide useful information on the quantitative evaluation of mapping uncertainty. The application of the method in the southern sea area of Lianyungang showed that much more convincing mapping results could be obtained compared with the traditional methods such as IDW, Kriging and Voronoi diagram under the same condition, so the proposed method was applicable with great utilization value.

ROBUST CONTROL OF A CLASS OF NONLINEAR SYSTEM WITH TIME-VARYING PAR AMETRIC UNCERTAINTIES

A class of triangular non li near system with disturbances which has unknown multiplicative time varying par ametric uncertainties in each virtual control is treated by a backstepping techn ique. The controller designed for all admissible uncertainties can guarantee tha t all states of its closed loop system are uniformly bounded. The robust contro ller design algorithm and a sufficient condition of the system stability are giv en. In addition, the closed loop system has an ISS property when the multiplica tive time varying parametric uncertainties are viewed as inputs to the system. Thus, this design provides a way to prevent a destabilizing effect of the multip licative time varying parametric uncertainties. Finally, simulational example i s given and simulational result shows that the controller exhibits effectiveness and excellent robustness.

Disturbance observer based position tracking of electro-hydraulic actuator

A nonlinear controller based on an extended second-order disturbance observer is presented to track desired position for an electro-hydraulic single-rod actuator in the presence of both external disturbances and parameter uncertainties. The proposed extended second-order disturbance observer deals with not only the external perturbations, but also parameter uncertainties which are commonly regarded as lumped disturbances in previous researches. Besides, the outer position tracking loop is designed with cylinder load pressure as output; and the inner pressure control loop provides the hydraulic actuator the characteristic of a force generator. The stability of the closed-loop system is provided based on Lyapunov theory. The performance of the controller is verified through simulations and experiments. The results demonstrate that the proposed nonlinear position tracking controller, together with the extended second-order disturbance observer, gives an excellent tracking performance in the presence of parameter uncertainties and external disturbance.

Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input

This paper presents a sliding mode (SM) based identifier to deal with the parameter identification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system; an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.

Design for robust stabilization of nonlinear systems with uncertain parameters

Based on Lyapunov stability theory, a design method for the robust stabilization problem of a class of nonlinear systems with uncertain parameters is presented. The design procedure is divided into two steps: the first is to design controllers for the nominal system and make the system asymptotically stabi1ize at the expected equilibrium point; the second is to construct closed-loop nominal system based on the first step, then design robust controller to make the error of state between the origina1 system and the nominal system converge to zero, thereby a dynamic controller with the constructed closed-loop nominal system served as interior dynamic is obtained. A numerical simulation verifies the correctness of the design method.

Robust tracking control design for a flexible air-breathing hypersonic vehicle

A nonlinear robust controller was presented to improve the tracking control performance of a flexible air-breathing hypersonic vehicle(AHV) which is subjected to system parametric uncertainties and unknown additive time-varying disturbances.The longitudinal dynamic model for the flexible AHV was used for the control development.High-gain observers were designed to compensate for the system uncertainties and additive disturbances.Small gain theorem and Lyapunov based stability analysis were utilized to prove the stability of the closed loop system.Locally uniformly ultimately bounded tracking of the vehicle's velocity,altitude and attack angle were achieved under aeroelastic effects,system parametric uncertainties and unknown additive disturbances.Matlab/Simulink simulation results were provided to validate the robustness of the proposed control design.The simulation results demonstrate that the tracking errors stay in a small region around zero.

Synchronization of hyperchaotic Rossler system with uncertain parameters via nonlinear control

Based on the Lyapunov stability theory,a new method for synchronization of hyperchaotic Rossler system with uncertain parameters is proposed. By this method, choosing appropriate control law and adaptive update law of uncertain parameters, all the errors of system variable synchronization and of uncertain param- eter track are asymptotically stable. The theoretical analysis and the numerical simulations prove the efffectiveness of the oroDosed method.

Robust flutter analysis based on genetic algorithm

Robust flutter analysis considering model uncertain parameters is very important in theory and engineering applications.Modern robust flutter solution based on structured singular value subject to real parametric uncertainties may become difficult because the discontinuity and increasing complexity in real mu analysis.It is crucial to solve the worst-case flutter speed accurately and efficiently for real parametric uncertainties.In this paper,robust flutter analysis is formulated as a nonlinear programming problem.With proper nonlinear programming technique and classical flutter analysis method,the worst-case parametric perturbations and the robust flutter solution will be captured by optimization approach.In the derived nonlinear programming problem,the parametric uncertainties are taken as design variables bounded with perturbed intervals,while the flutter speed is selected as the objective function.This model is optimized by the genetic algorithm with promising global optimum performance.The present approach avoids calculating purely real mu and makes robust flutter analysis a plain job.It is illustrated by a special test case that the robust flutter results coincide well with the exhaustive method.It is also demonstrated that the present method can solve the match-point robust flutter solution under constant Mach number accurately and efficiently.This method is implemented in problem with more uncertain parameters and asymmetric perturbation interval.

Integrated adaptive dynamic surface car-following control for nonholonomic autonomous electric vehicles

In this paper,the car-following control problem of nonholonomic autonomous electric vehicles in the curved highway is studied.Owing to the fact that the nonholonomic autonomous electric vehicles have the features of strong coupling,parametric uncertainties,nonlinearities and external disturbances,a novel integrated adaptive car-following control system is constructed to supervise the longitudinal and lateral motions of vehicles.Firstly,an adaptive fuzzy dynamic surface car-following control strategy is presented to determine a vector of total forces and torque of autonomous electric vehicles,which can guarantee the uniform ultimate boundedness of close-loop control signals.Then,an optimal tire forces distribution law is proposed to dynamically allocate the desired coupled tire longitudinal and lateral forces in real-time.Finally,simulation results illustrate the effectiveness and robustness of the proposed car-following control approach.

Fast changing processes in radiotelemetry systems of space vehicles

The method of processing of the non-stationary casual processes with the use of nonparametric methods of the theory of decisions is considered. The use of such methods is admissible in telemetry systems in need of processing at real rate of time of fast-changing casual processes in the conditions of aprioristic uncertainty about probabilistic properties of measured process.