一类有输入噪声扰动的逆系统无偏参数辨识算法研究

对逆系统建模时,原系统的输出作为逆系统参数辨识时的输入.由于原系统输出存在测量噪声,且噪声方差未知,采用普通最小二乘法辨识,无法得到逆系统参数的一致无偏估计.为此,本文研究了一种有输入扰动的的逆系统无偏参数辨识算法,该算法先通过小波变换估计输入信号噪声的方差,再由估计得到的方差,通过偏差消除的递推最小_乘法,对逆系统的参数进行无偏辨识.该算法降低了对输入辨识信号为白噪声的要求,具有较强的实用性.由于采用递推运算,该算法也可以用于逆系统参数的在线辨识.最后,通过实验验证了该算法的有效性.     

An inverse Hollis-Paulos artificial neural network

The Hollis-Paulos artificial neural network (1990) [HPANN] is convenient in terms of its possibility for realization of variable weight artificial neural networks in VLSI by MOS transistor circuits, though it is nondynamical and not driven by external inputs. Here we introduce dynamics and inputs into the HPANN and show that over the range of operation covered by the Hollis-Paulos theory the system has an inverse. In particular, we derive that inverse, in semistate form, and give simulation results on its operation, showing how well the input to the original HPANN can be recovered from the output of the HPANN when fed into the inverse system. A comparison is made with the previous inverse of the Hopfield ANN. Possible applications of these inverse systems are to decoding of transmitted ANN signals and to inverse filtering for the extraction of input signals from processed signals.     

改进的逆向组合算法在图像配准中的应用

逆向组合算法在进行图像配准时精度很高,但对模板图像在待配准图像中的初始位置敏感。针对该问题,提出一种改进的逆向组合算法,通过计算巴氏系数进行模板匹配,实现输入图像的粗定位后,应用逆向组合算法进行精确定位。实验结果证明,改进的算法对图像发生形变的情况具有较好的鲁棒性,相比原算法,配准能力更强。     

Inverse Dyamics of Non-Minimum Phase Systems with Non-Zero Initial Conditions

A method is presented forcomputing the inverse dynamics of a linear non-minimum phasesystem with non-zero initial conditions. The method is also usedto change or correct a trajectory after it is already in motion,and consequently, it will allow for real time control by continuallyupdating the inverse dynamics computation.Frequency domain techniques are used to compute the input functionneeded to produce a desired output trajectory at a particulardegree of freedom. An output profile based on the differencebetween the desired trajectory and either a homogeneous responseor a forced response to a previous forcing function is used tocompute the required input function. The resulting input functionactively damps out initial conditions in the system and makesit track the desired trajectory.The method is applied to a non-collocated single-link flexiblerobot arm. The finite element method using Timoshenko beam theoryis used to discretize the equations of motion. Torque profilesare computed to control the tip displacement for several problems.The first problem is to control the tip to a desired trajectorywhen starting with non-zero initial conditions. The second problemis to change the desired trajectory while the previous desiredtrajectory is already in motion. The third problem is to correctthe trajectory after a disturbance is added to the system. Thefourth problem is to analyze sensitivity to errors in the modeland initial conditions. The last problem is to compare tip responsesfor rigid and flexible link assumptions in the inverse dynamicscomputation.     

一种新型神经网络广义逆系统

提出一种新型带有反馈环节的广义逆系统方法,并给出了其存在性的证明．该方法首先利用神经网络构造被控对象的α 阶逆系统,通过改变反馈环节参数可随时任意配置复合系统极点,无需重新构造广义逆系统．分别对ＳＩＳＯ 和ＭＩＭＯ 非线性系统进行仿真研究．仿真结果表明,在配置极点变换时,利用该方法构造的广义逆系统仍可对原系统实现有效的线性化和解耦．     

Continuous-time adaptive control of systems with unknown backlash

This paper addresses one of the nondifferentiable nonlinearities which appear very often in industrial control applications: backlash. The authors first present a right inverse of backlash and then give one of its possible implementations. Characteristics like backlash are seldom known, so an adaptive version of the authors' backlash inverse is more suitable for applications. The authors develop an adaptive backlash inverse scheme and apply it to feedback control of a known linear plant with an unknown backlash at its input. The authors use simulation results to illustrate achieved performance improvements     

Inverse optimal control for strict‐feedforward nonlinear systems with input delays

We consider inverse optimal control for strict‐feedforward systems with input delays. A basic predictor control is designed for compensation for this class of nonlinear systems. Furthermore, the proposed predictor control is inverse optimal with respect to a meaningful differential game problem. For a class of linearizable strict‐feedforward system, an explicit formula for compensation for input delay, which is also inverse optimal with respect to a meaningful differential game problem, is also acquired. A cart with an inverted pendulum system is given to illustrate the validity of the proposed method.     

Discrete-time controller design to attenuate effects of external disturbances

This paper presents a discrete time controller to attenuate influence of external disturbances. The proposed controller elevates tracking performance by suppressing a peak of a plant input sensitivity function. The controller is computed from an inverse model of a conventional plant input sensitivity function. For a stable and casual inverse model, we introduce all-pass filters and unit delays. In addition, high pass filters are utilized to avoid amplification of high frequency disturbance, which is a different approach from traditional design methods. Experimental verifications demonstrate the effectiveness of this design method and it is confirmed that the controller suppresses the sensitivity peak and enhances tracking performance obviously.     

输入平稳的快速无超调预测控制算法

针对输入要求平稳的系统设备,提出了一种快速无超调预测控制新算法。该算法通过对输入增量引入柔化系数矩阵从而进行约束,防止了输入的剧烈变化;既达到了系统输入平稳的要求,又克服了传统控制律中求解逆矩阵的缺点,提高了系统响应的快速性。其次,控制算法中改善了传统广义预测控制算法的单一性,充分利用预测信息的补偿作用进行加权平均,很好地抑制了超调的出现。通过对水下航行器航向系统的仿真试验比较,试验结果验证了该算法的有效性。     

Finite‐time stabilization of stochastic low‐order nonlinear systems with FT‐SISS inverse dynamics

This paper studies finite‐time stabilization problem for stochastic low‐order nonlinear systems with stochastic inverse dynamics. By characterizing unmeasured stochastic inverse dynamics with finite‐time stochastic input‐to‐state stability, combining the Lyapunov function and adding a power integrator technique, and using the stochastic finite‐time stability theory, a state feedback controller is designed to guarantee global finite‐time stability in probability of stochastic low‐order nonlinear systems with finite‐time stochastic input‐to‐state stability inverse dynamics.     

基于反双曲正弦函数的跟踪微分器

反双曲正弦函数是光滑连续函数,具有快速并消除速度高频震颤的作用.利用反双曲正弦函数构造加速度函数,设计二阶跟踪微分器,证明了跟踪微分器的收敛性,并分析了跟踪微分器频域特性.仿真实验表明,该跟踪微分器能对输入信号进行低通滤波,且跟踪精度高,响应速度快;同时,它较好地抑制了微分信号的噪声放大效应,可以得到输入函数理想的微分信号.     

Training with noise as a method to increase noise resilience of neural network solution of inverse problems

Inverse problems constitute a special class of problems, which consist in reconstruction of parameters of an object by the data of indirect measurements, which are affected by these parameters. Many inverse problems are ill-posed (incorrect), i.e., characterized by nonuniqueness and/or instability of the solution. Improvement in the stability of the solution of inverse problems is a very topical problem; one of the ways to solve it is the use of artificial neural networks. In the present study, at the example of a model 5-parameter inverse problem it is demonstrated that adding noise to the training set when training neural networks allows one to improve resilience of the neural network solution to noise in input data, with various distribution and intensity of noise.     

Nearly optimal solution of rational linear systems of equations with symbolic lifting and numerical initialization

Hensel’s symbolic lifting is a highly effective method for the solution of a general or structured (e.g. Toeplitz or Hankel) linear system of equations with integer or rational coefficients of bounded length. It can handle ill conditioned inputs, for which numerical methods become costly. Lifting amounts to recursive multiplications by vectors of the input coefficient matrices and its precomputed inverse modulo a fixed integer s. Such multiplications only involve small numbers of data movements and arithmetic operations with bounded precision. The known methods for precomputation of the inverse are more costly, however; in particular they involve more data movements. As our remedy for this bottleneck stage we create an auxiliary matrix sharing its inverse modulo s with the input matrix, and we readily compute this inverse by applying numerical iterative refinement, which is a numerical counterpart of lifting. In the case of general unstructured as well as Toeplitz, Hankel, and other popular structured inputs our hybrid algorithms involve a small number of data movements and optimal number of Boolean (that is bitwise) operations (up to a logarithmic factor). We extend the algorithms to nearly optimal computation of polynomial greatest common divisors (gcds), least common multiples (lcms) and Padé approximations, as well as the Berlekamp-Massey reconstruction of linear recurrences. We also cover Newton’s lifting for matrix inversion, specialize it to the case of structured input, and combine it with Hensel’s to enhance the overall efficiency. Our initialization techniques work for Newton’s lifting as well. Furthermore we extend all our lifting algorithms to allow their initialization modulo powers of two, thus implementing them in the binary base.     

Perfect tracking for maximum-phase nonlinear systems by iterative learning control

A method to track a desired trajectory by iterative learning control is proposed for uncertain maximum-phase nonlinear systems. The relation between the variations in the initial state, input and output is derived and it is shown that the inverse mapping from the desired output to the initial state and input is stable using the time reversal of unstable manifolds for a maximum-phase system as given by Doyle et al. Based on these facts, an input update law is proposed to find the initial state and the input for perfect tracking. Also, it is shown that perfect tracking can be made possible over a finite control horizon by using a non-causal input starting at any fixed state. Simulation results show that the proposed method works well.     

Dynamics of the 6-6 Stewart parallel manipulator

Recursive matrix relations in kinematics and dynamics of the 6-6 Stewart–Gough parallel manipulator having six mobile prismatic actuators are established in this paper. Controlled by six forces, the manipulator prototype is a spatial six-degrees-of-freedom mechanical system with six parallel legs connecting to the moving platform. Knowing the position and the general motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each manipulator’s link. Further, the inverse dynamics problem is solved using an approach based on the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations with their multipliers. Finally, compact matrix relations and graphs of simulation for the input velocities and accelerations, the input forces and powers are obtained.     

A Fuzzy Inverse Model Construction Method for General Monotonic Multi-Input-- Single-Output (MISO) Systems

This paper presents a novel method of systematically constructing a fuzzy inverse model for general multi-input--single-output (MISO) systems represented with triangular input membership functions, singleton output membership function, and fuzzy-mean defuzzification. The fuzzy inverse model construction method has the ability of uniquely determining the inverse relationship for each input–output pair. It is derived in a straightforward way and the required input variables can be simultaneously obtained by the fuzzy inferencing calculation to realize the desired output value. Simulation examples are provided to demonstrate the effectiveness of the proposed method to find the inverse kinematics solutions for complex multiple degree-of-freedom industrial robot manipulators.      

Hybrid control of a pneumatic artificial muscle (PAM) robot arm using an inverse NARX fuzzy model

We investigated the possibility of applying a hybrid feed-forward inverse nonlinear autoregressive with exogenous input (NARX) fuzzy model-PID controller to a nonlinear pneumatic artificial muscle (PAM) robot arm to improve its joint angle position output performance. The proposed hybrid inverse NARX fuzzy-PID controller is implemented to control a PAM robot arm that is subjected to nonlinear systematic features and load variations in real time. First the inverse NARX fuzzy model is modeled and identified by a modified genetic algorithm (MGA) based on input/output training data gathered experimentally from the PAM system. Second the performance of the optimized inverse NARX fuzzy model is experimentally demonstrated in a novel hybrid inverse NARX fuzzy-PID position controller of the PAM robot arm. The results of these experiments demonstrate the feasibility and benefits of the proposed control approach compared to traditional PID control strategies. Consequently, the good performance of the MGA-based inverse NARX fuzzy model in the proposed hybrid inverse NARX fuzzy-PID position control of the PAM robot arm is demonstrated. These results are also applied to model and to control other highly nonlinear systems.     

含有死区输入的Hammerstein系统的网络预测控制

文中对具有死区输人特性的一类Hamrnerstein系统提出了网络预测控制方法。此方法借鉴广义预测控制的思想,首先对Hammerstein模型的线性部分,求得中间变量的预测值,并通过对死区求逆得到控制信号的预测值。在被控对象的缓冲区中选取最靠近当前时刻的控制输入预测值作为当前的控制输入,以用来补偿网络诱导时延。实验结果表明,采用了广义预测控制之后,系统的响应速度明显提高。证明广义预测控制可以很好地补偿前向以及反馈通道的诱导时延。     

基于RBFN的伺服系统逆控制器设计及仿真研究

飞行仿真转台伺服系统中有一些诸如负载变化、机械摩擦等不确定和非线性因素，而神经网络逆控制对模型的不依赖性能较好的解决这些问题。该文给出了转台伺服系统速度跟踪的神经网络逆控制方案，它可以克服转台中负载变化及一些参数变化的影响，且能显著的提高动态精度。通过使用RBF神经网络实现了对象逆动态模型的在线辨识。并直接将该RBFN与PI环节构成一种神经网络逆控制制器，仿真结果表明这种方法具有较好的鲁棒性及较高的跟踪精度，有实际应用价值。     

Inverse systems for reproducing linear functions of inputs

Most of the previous studies on inverse systems have treated only the case where all components of the input of the original system are recoverable. However, even when not all components are recoverable, there is still a possibility of reproducing part of the input. As a generalization of the inverse of a linear time-invariant dynamical system to include such cases, ‘α-integral F-inverse’ is proposed in this paper which reproduces the αth integral of a linear function Fu of the input vector u. A necessary and sufficient condition for the existence of an α-integral F-inverse is derived. A construction procedure of such an inverse is also given along with a numerical example.