On approximate linearization of nonlinear control systems

A method for the approximate linearization of nonlinear control systems based on the ‘state-space exact linearization’ method is presented. An explicit procedure, both for the single-input and for the multiple-input case, is given, which is straightforward to implement.     

基于输入输出线性化的连续系统非线性模型预测控制

非线性约束预测控制关键是求得可行性优化解. 输入输出反馈线性化是非线性控制一种常用的方法, 其系统的初始线性输入约束转化成非线性基于状态的约束, 因而无法采用常规的二次规划(QP)求解优化问题. 针对连续状态空间模型系统, 本文提出迭代二次规划方法来寻求非线性优化解. 为了保证算法的收敛性, 系统加入另外一种迭代算法来保证其在整个预测时域上能得到可行解. 仿真控制结果表明了该方法的有效性.     

一种新的多输入非线性控制系统线性化的计算方法

通常, 即使对于一个可逼近反馈线性化的非线性系统, 求得一个所需的坐标变换和反馈仍然是困难的, 原因在于需要求解一组偏微分方程. 在本文中, 为了求得逼近反馈线性化所需的非线性反馈及坐标变换, 首先引入了一个扩展的坐标空间, 针对一类线性可控的多输入非线性系统, 推导了系统新的矩阵表达式. 然后, 提出了一种新的有效的构造化算法, 它降低了计算所需的运算量. 最后通过一个例子介绍了本方法的应用.     

一种新的多输入非线性控制系统高阶逼近线性化的计算方法

通常,即使对于一个可逼近反馈线性化的非线性系统,求得一 个所需的坐标变换和反馈仍然是困难的,原因在于需要求解一组偏微分 方程. 在本文中, 为了求得逼近反馈线性化所需的非线性反馈及坐标变 换, 我们首先引入了一个扩展的坐标空间, 针对一类线性可控的多输入非 线性系统,推导了系统新的矩阵表达式。基于这些准备,我们提出了一种 新的有效的构造化算法,它降低了计算所需的运算量。最后通过一个例 子我们介绍了本方法的应用.     

A state space embedding approach to approximate feedback linearization of single input nonlinear control systems

This contribution presents a numerical approach to approximate feedback linearization which transforms the Taylor expansion of a single input nonlinear system into an approximately linear system by considering the terms of the Taylor expansion step by step. In the linearization procedure, higher degree terms are taken into account by using a state space embedding such that the corresponding system representation has not to be computed in every linearization step. Linear matrix equations are explicitly derived for determining the nonlinear change of coordinates and the nonlinear feedback that approximately linearize the nonlinear system. If these linear matrix equations are not solvable, a least square solution by applying the Moore–Penrose inverse is proposed. The results of the paper are illustrated by the approximate feedback linearization of an inverted pendulum on a cart. Copyright © 2006 John Wiley & Sons, Ltd.     

A‐Orbital feedback linearization of multiinput control affine systems

This article deals with transformations of multiinput nonlinear control systems into linear controllable systems. For multiinput control affine systems, the notion of A‐orbital feedback linearizability is introduced which generalizes the notion of orbital feedback linearizability and is based on input‐dependent time scalings. A necessary and sufficient condition for A‐orbital feedback linearizability is derived for multiinput control affine systems. On the basis of this condition, an A‐orbital feedback linearization algorithm is developed. It is revealed that the proposed concept extends the existing approaches to orbital feedback linearization. More precisely, it is proved that if a system is A‐orbitally feedback linearizable in a neighborhood of some point, the dimension of the state is greater than that of the input by at least three, and the time scaling essentially depends on the input, then the system cannot be orbitally feedback linearized around that point.     

Decentralized filtered feedback linearization for uncertain nonlinear systems

This paper presents decentralized filtered feedback linearization (D‐FFL), which is a decentralized controller for uncertain nonlinear systems with potentially unknown disturbance. Moreover, D‐FFL uses only local‐state feedback (or, in certain cases, local‐output feedback) and local reference‐model‐input feedforward and requires limited model information. For sufficiently small initial conditions and sufficiently large choice of a scalar control parameter, D‐FFL makes the norm of the command‐following error arbitrarily small.     

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.     

Output feedback control for a class of nonlinear systems

This paper studies the global stabilization problem by an output controller for a family of uncertain nonlinear systems satisfying some relaxed triangular-type conditions and with dynamics which may not be exactly known. Using a feedback domination design method, we explicitly construct a dynamic output compensator which globally stabilizes such an uncertain nonlinear system. The usefulness of our result is illustrated with an example.     

Uncertainty modeling and robust minimax LQR control of multivariable nonlinear systems with application to hypersonic flight

For a class of multi‐input and multi‐output nonlinear uncertainty systems, a novel approach to design a nonlinear controller using minimax linear quadratic regulator (LQR) control is proposed. The proposed method combines a feedback linearization method with the robust minimax LQR approach in the presence of time‐varying uncertain parameters. The uncertainties, which are assumed to satisfy a certain integral quadratic constraint condition, do not necessarily satisfy a generalized matching condition. The procedure consists of feedback linearization of the nominal model and linearization of the remaining nonlinear uncertain terms with respect to each individual uncertainty at a local operating point. This two‐stage linearization process, followed by a robust minimax LQR control design, provides a robustly stable closed loop system. To demonstrate the effectiveness of the proposed approach, an application study is provided for a flight control problem of an air‐breathing hypersonic flight vehicle (AHFV), where the outputs to be controlled are the longitudinal velocity and altitude, and the control variables are the throttle setting and elevator deflection. The proposed method is used to derive a linearized uncertainty model for the longitudinal motion dynamics of the AHFV first, and then a robust minimax LQR controller is designed, which is based on this uncertainty model. The controller is synthesized considering seven uncertain aerodynamic and inertial parameters. The stability and performance of the synthesized controller is evaluated numerically via single scenario simulations for particular cruise conditions as well as a Monte‐Carlo type simulation based on numerous cases. It is observed that the control scheme proposed in this paper performs better, especially from the aspect of robustness to large ranges of uncertainties, than some controller design schemes previously published in the literature. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Bifurcation suppression of nonlinear systems via dynamic output feedback and its applications to rotating stall control

1IntroductionBifurcation control has attracted great attention in thepast two decades[1].The study of bifurcation control atpresent mostly concerns bifurcation stabilization,delay ofthe onset of aninherent bifurcation,changingthe parametervalue of an existing bifurcation point,and so on[1~4].Fromthe stability point of view,a bifurcation point of anonlinear systemis very disadvantageous.Asystemthat hasa bifurcation point may have more than one equilibriumpoint in a neighborhood of the bifurcati…     

Bifurcation suppression of nonlinear systems via dynamic output feedback and its applications to rotating stall control

This paper deals with the problems of bifurcation suppression and bifurcation suppression with stability of nonlinear systems. Necessary conditions and sufficient conditions for bifurcation suppression via dynamic output feedback are presented; Sufficient conditions for bifurcation suppression with stability via dynamic output feedback are obtained. As an application, a dynamic compensator, which guarantees that the bifurcation point of rotating stall in axial flow compressors is stably suppressed, is constructed.     

基于状态反馈的一类非线性系统动态输出反馈镇定

针对一类具有线性不可测量状态的非线性系统,基于状态反馈稳定控制器,利用不变流形和滑模变结构控制技术设计了动态输出反馈镇定控制器.这类控制器的结构类似于系统的状态反馈稳定控制器,在较简单的假定条件下,能够保证被控系统的状态得到渐近镇定.仿真算例表明该动态输出反馈控制器具有较强的镇定能力.     

Robust control of nonlinear feedback passive systems

In this paper we consider a class of nonlinear systems with uncertain parameters which enter the system nonlinearly. We assume that the uncertain nonlinear system is minimum phase and the uncertain parameters are from a bounded compact set. The problem under consideration is the design of a nonlinear static state feedback controller such that the closed-loop system is passive for all admissible uncertainties.     

Input-output linearization of nonlinear systems using multivariable Legendre polynomials

This contribution presents a new approach for the numeric computation of the input-output linearizing feedback law, which is obtained exactly in an analytical form. By using a state space embedding technique the nonlinear system to be controlled is described by a higher order system with solely polynomial nonlinearities. Consequently, the nonlinearities of this system can be represented by multivariable Legendre polynomials, so that the derivation of the input-output linearizing feedback controller can be accomplished using the operational matrices of multiplication and of differentiation for Legendre polynomials.     

Feedback affinization of nonlinear control systems

In this paper conditions for the nonlinear control system

to have a nonlinear feedback control

u=(x,v), vΩ′R^m′, m′m, 0Ω′

such that the nonlinear system takes a form of an affine system

are presented. All results require algebraic operations and differentiation of functions only.     

Feedback stabilization of nonlinear systems by locally bounded controls

In this paper results are presented on output regulation and stabilization of nonlinear control systems using Lyapunov-based methods. Sufficient conditions for global output regulation and stabilization using locally bounded state feedback are obtained. The approach used here is motivated by the work of Artstein (1983), Sontag (1989) and Tsinias (1989) on the relationship between control Lyapunov functions and feedback stabilization.     

Neural Network Based Feedback Linearization Control of an Unmanned Aerial Vehicle

This paper presents a flight control design for an unmanned aerial vehicle (UAV) using a nonlinear autoregressive moving average (NARMA-L2) neural network based feedback linearization and output redefinition technique.The UAV investigated is non- minimum phase.The output redefinition technique is used in such a way that the resulting system to be inverted is a minimum phase system.The NARMA-L2 neural network is trained off-line for forward dynamics of the UAV model with redefined output and is then inverted to force the real output to approximately track a command input.Simulation results show that the proposed approaches have good performance.     

Nonsmooth stabilizability and feedback linearization of discrete-time nonlinear systems

We consider the problem of stabilizing a discrete-time nonlinear system using a feedback which is not necessarily smooth. A sufficient condition for global dynamical stabilizability of single-input triangular systems is given. We obtain conditions expressed in terms of distributions for the nonsmooth feedback triangularization and linearization of discrete-time systems. Relations between stabilization and linearization of discrete-time systems are given.     

Input-Output linearization using approximate process models

An approach to approximate feedback linearization is presented which utilizes an approximate input-output normal form model for the process. The approach is valid for minimjm phase systems, and yields a dynamic output feedback controller of order 2N − R + 1, where N is the dynamic approximation order and R is the relative degree of the approximation model. Conditions are presented under which local (linear) stability can be guaranteed despite the plant-model mismatch. Two reactor control case studies are presented to show how the approach can be used both when a fundamental process model is available and when only process input-output data are available.