基于Lyapunov方法的一类非线性系统分段线性化自适应控制

非仿射非线性系统在非线性系统领域的研究中还不够成熟.本文针对一类非仿射单输入单输出的非线性系统,采用分段线性化方法来处理对象的非线性,基于Lyapunov第二方法对分段线性化后的系统进行了自适应律的设计,并旦证明了其渐近稳定性,这为使用分段线性化方法来处理一类非线性系统提供了理论支持,基于所设计的自适应律,以电弧炉电极调节系统的自适应控制为例,进行了数字仿真.仿真结果表明了该设计方法的有效性,为处理一类非线性系统提供有益的思路.     

Feedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serial neuro-gray-box models

In this paper, discrete-time control schemes based on feedback linearization of serial gray-box models are considered for partially known nonlinear processes. These techniques combine the benefits of feedback linearization, neural networks, and serial gray-box modeling, which result in larger dynamic operating ranges, better extrapolation properties, and fewer data acquisition efforts in comparison with the corresponding black-box-based schemes. First-principles-based serial gray-box models are classified into invertible and non-invertible structures for training purposes, and an improved approximate feedback linearization scheme based on Taylor series terms of a non-affine gray-box model is proposed. Moreover, an affine gray-box model is developed for applying the exact feedback linearization scheme. Simulation results on a fermentation process show that the proposed methods yield significant improvement in modeling and control performance in comparison with that of the black-box feedback linearization schemes.     

Omni-directional mobile robot controller based on trajectory linearization

In this paper, a nonlinear controller design for an omni-directional mobile robot is presented. The robot controller consists of an outer-loop (kinematics) controller and an inner-loop (dynamics) controller, which are both designed using the Trajectory Linearization Control (TLC) method based on a nonlinear robot dynamic model. The TLC controller design combines a nonlinear dynamic inversion and a linear time-varying regulator in a novel way, thereby achieving robust stability and performance along the trajectory without interpolating controller gains. A sensor fusion method, which combines the onboard sensor and the vision system data, is employed to provide accurate and reliable robot position and orientation measurements, thereby reducing the wheel slippage induced tracking error. A time-varying command filter is employed to reshape an abrupt command trajectory for control saturation avoidance. The real-time hardware-in-the-loop (HIL) test results show that with a set of fixed controller design parameters, the TLC robot controller is able to follow a large class of 3-degrees-of-freedom (3DOF) trajectory commands accurately.     

Model order reduction via real Schur-form decomposition

A new algorithm is presented for computing Moore's reduced-order transfer-function matrix without calculating the balancing transformation, which tends to be ill-conditioned, especially when the original system is non-minimal or when it has very nearly uncontrollable or unobservable modes. The algorithm is based on finding the eigenspaces associated with large eigenvalues of the cross-gramian matrix W_co using the real Schur-form decomposition. The algorithm does not require a minimal model to start with. The state-space realization obtained by this method is related to the balanced realization by a non-singular matrix. An example is presented to illustrate the proposed algorithm     

A nonlinear model predictive control system based on Wiener piecewise linear models

In this paper a nonlinear model predictive control (NMPC) based on a Wiener model with a piecewise linear gain is presented. This approach retains all the interested properties of the classical linear model predictive control (MPC) and keeps computations easy to solve due to the canonical structure of the nonlinear gain. Some guidelines for the identification of the nominal model as well as the uncertainty bounds are discussed, and two examples that show the possibility of application of this control scheme to real life problems are presented.     

基于分片线性化方法的非线性系统多模型自适应控制

基于分片线性化方法辨识一类非线性系统 ,给出了非线性系统的多线性模型表示。基于线性模型建立多个控制器 ,基于最大最小指标切换函数构成多模型自适应控制器。给出了非线性系统多模型自适应控制算法的优化模型集建立方法 ,解决了多模型自适应控制模型多、计算量大的问题。仿真结果证明了算法的有效性     

Compact thermoelectric coupled models of micromachined thermal sensors using trajectory piecewise-linear model order reduction

Numerical simulation has become an effective way to design and optimize micromachined thermal sensors. To improve the speed of development process, fast simulation is indispensable. This paper investigates compact models, which are accurate low order representations of high order finite element models, for micromachined thermal sensors. Because the thermal field and the electric field act on and influence each other, the compact models should be established from the thermoelectric coupled full models. Thermoelectric coupling and temperature dependent resistivity make the problems strong nonlinearity. Therefore a powerful nonlinear model order reduction method, named trajectory piecewise-linear (TPWL) method, is employed. Its core idea is approximating the nonlinear model piecewise-linearly along a training trajectory. The performance of the TPWL method and fast TPWL method are compared. And the effects of linearization point number and local reduced basis order on accuracy, efficiency and size of the TPWL compact models are studied. Moreover, the expandability of the TPWL compact models is also discussed. Results show that the TPWL compact models are suitable for the design and optimization of micromachined thermal sensors.     

Input linearization of nonlinear systems via pulse-width control

In this note, it is shown that a general nonlinear system can be transformed to an affine nonlinear system by virtue of the use of pulsewidth control. Therefore, the combined system from the pulse width control input to the nonlinear system output behaves as an affine (linear-in-control) system. By this way, a cumbersome nonlinear system model can be transformed to a simpler linear-in-control form without increasing the system dimension; this in turn enables simpler control design. Furthermore, using this methodology, some control design methods developed only for affine systems can be adapted to general nonlinear systems.     

Global external linearization of nonlinear systems via feedback

This note presents necessary conditions and sufficient conditions for an affine nonlinear system to be globally feedback equivalent to a controllable linear system over an open subsetVof Rⁿ. WhenVequals Rⁿ, necessary and sufficient conditions are obtained.     

Adaptive control of nonlinear systems via approximate linearization

This paper presents an adaptive control scheme for nonlinear systems that violates some of the common regularity and structural conditions of current nonlinear adaptive schemes such as involutivity, existence of a well-defined relative degree, and minimum phase property. While the controller is designed using an approximate model with suitable properties, the parameter update law is derived from an observation error based on the exact model described in suitable coordinates. The authors show that this approach results in a stable, closed-loop system and achieves adaptive tracking with bounds on the tracking error and parameter estimates. The authors also present a constructive procedure for adaptive state regulation which is based on the quadratic linearization technique via dynamic state feedback. This regulation scheme does not impose any restriction on the location of the unknown parameters and is applicable to any linearly controllable nonlinear system     

一类不确定非线性系统的鲁棒自适应轨迹线性化控制

针对一类不确定非线性系统,研究了一种新的鲁棒自适应轨迹线性化控制方案.利用径向基神经网络的在线逼近能力以及被控对象分析模型的有用信息设计一种径向基神经网络干扰观测器来估计系统中存在的不确定性.观测器输出用于设计补偿控制律抵消不确定性对系统性能的影响,鲁棒自适应控制律用于克服逼近误差.采用Lyapunov方法严格证明了在自适应调节律作用下闭环系统所有误差信号最终有界.最后利用倒立摆系统验证了新方法的有效性.     

Parameter estimation of two-level nonlinear mixed effects models using first order conditional linearization and the EM algorithm

Multi-level nonlinear mixed effects (ML-NLME) models have received a great deal of attention in recent years because of the flexibility they offer in handling the repeated-measures data arising from various disciplines. In this study, we propose both maximum likelihood and restricted maximum likelihood estimations of ML-NLME models with two-level random effects, using first order conditional expansion (FOCE) and the expectation–maximization (EM) algorithm. The FOCE–EM algorithm was compared with the most popular Lindstrom and Bates (LB) method in terms of computational and statistical properties. Basal area growth series data measured from Chinese fir (Cunninghamia lanceolata) experimental stands and simulated data were used for evaluation. The FOCE–EM and LB algorithms given the same parameter estimates and fit statistics for models that converged by both. However, FOCE–EM converged for all the models, while LB did not, especially for the models in which two-level random effects are simultaneously considered in several base parameters to account for between-group variation. We recommend the use of FOCE–EM in ML-NLME models, particularly when convergence is a concern in model selection.     

Synthesis of sliding-mode controllers for nonlinear systems via extended linearization

In this article, a general synthesis method is proposed for the design of discontinuous feedback strategies leading to asymptotically stabilizing sliding regimes. The method is applicable to the class of nonlinear dynamical systems possessing constant equilibrium points. A family of nonlinear stabilizing sliding manifolds, parametrized by generic desired equilibrium point, is specified on the basis of the extended linearization approach. Some examples including simulations are presented for illustrative purposes. Editor: S. Zak     

基于平衡截断方法的高超声速飞行器模型降阶

本文提出了一种适用于高超声速飞行器数学模型的模型降阶方法.该方法采用基于奇异值分解的投影技术,对高阶的高超声速飞行器数学模型进行平衡变换,进而通过截断获得低阶的微分方程,方便控制器的设计,达到模型降阶的目的.相比于传统的只适用于稳定系统的模型降阶方法,本文提出的模型降阶方法通过右互质分解可以应用于不稳定的系统的模型降阶.为了证明该模型降阶方法的准确性,本文通过平均灰色关联系数的计算,给出基于时域分析的定量验证结果.仿真部分成功应用该方法对美国空军实验室提出的弹性纵向模型实现了降阶,证明了该方法的有效性.     

Identification of nonlinear systems via piecewise general orthogonal polynomials operator

Based on a hybrid orthogonal function, a new linear, continuous and bounded operator, piecewise general orthogonal polynomials operator (PGOPO), is proposed. Its main properties and operational rules have been strictly constructed based on the theory of convergence in the mean square, and are useful to discuss the orthogonal polynomial approach in the proper mathematics frame. Then applying the PGOPO method to solve the identification problem of nonlinear systems, the convergence analysis of PGOPO approximation method is given. Finally, using the PGOPO method to solve the parameter identification of two kinds of time-varying systems, the simulation studies show that the algorithm is simple and more effective than that of general orthogonal polynomials.     

Joint order and parameter estimation of multivariate autoregressive models using multi-model partitioning theory

In this paper the multi-model partitioning theory is used for simultaneous order and parameter estimation of multivariate autoregressive models. Simulation experiments show that the proposed method successfully selects the correct model order and estimates the parameters accurately, in very few steps, even with a small sample size. They also show that the proposed method performs equally well when the complexity of the model is increased. The results are compared to those obtained using well-established order selection criteria. Finally, it is shown that the method is also successful in tracking model order changes, in real time.     

Gain scheduling control of nonlinear systems based on approximate input-output linearization

The gain scheduling control mostly has been developed based on Jacobian linearization around the operating points related with scheduling variables. In this paper, We introduce a gain scheduling control method based on approximate input-output linearization. First, the nonlinear system is approximately input-output linearized via a diffeomorphism. Then, a gain scheduling controller with derivative information is developed. The proposed controller consists of two parts. The outer loop controller is like a feedback linearizing controller and the internal controller is a gain scheduling controller. It is shown that the overall resulting controller has a simple structure and at the same time achieves better tracking performance over the existing Jacobian-based gain scheduling controller.     

Composite control of nonlinear singularly perturbed systems via approximate feedback linearization

Machine Intelligence Research - This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed (SP) system using approximate feedback linearization...     

Non-regular feedback linearization of nonlinear systems via a normal form algorithm

In this paper, the problem of non-regular static state feedback linearization of affine nonlinear systems is considered. First of all, a new canonical form for non-regular feedback linear systems is proposed. Using this form, a recursive algorithm is presented, which yields a condition for single input linearization. Then the left semi-tensor product of matrices is introduced and several new properties are developed. Using the recursive framework and new matrix product, a formula is presented for normal form algorithm. Based on it, a set of conditions for single-input (approximate) linearizability is presented.     

Local observability of nonlinear differential-algebraic equations(DAEs) from the linearization along a trajectory

The main results of this note establish sufficient rank conditions for local observability of nonlinear differential-algebraic equations (DAE) systems near a known trajectory associated with a given control. Verification of the observability rank condition is addressed, and the relationship with previous work on observability of DAE is indicated