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.     

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     

On input-output linearization of discrete-time nonlinear systems

We consider a nonlinear discrete-time system of the form Σ: x(t+1)=f(x(t), u(t)), y(t) =h(x(t)), where x ε R^N, u ε R^m, y ε R^q and f and h are analytic. Necessary and sufficient conditions for local input-output linearizability are given. We show that these conditions are also sufficient for a formal solution to the global input-output linearization problem. Finally, we show that zeros at infinity of ε can be obtained by the structure algorithm for locally input-output linearizable systems.     

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...     

Nonlinear control via approximate input-output linearization: theball and beam example

Approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree is studied. For such systems, a method for constructing approximate systems that are input-output linearizable is provided. The analysis presented is motivated through its application to a common undergraduate control laboratory experiment-the ball and beam-where it is shown to be more effective for trajectory tracking than the standard Jacobian linearization     

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.     

基于输入输出线性化的船舶全局直线航迹控制

针对水面船舶直线航迹控制系统的非线性数学模型,基于输入输出线性化技术,给出了一类重定义输出变量和采用该输出变量的状态反馈控制律,并得到了保证系统全局渐近稳定的充分条件．数值仿真和模拟试验结果表明,所提出的充分条件能够保证船舶航迹控制全局渐近稳定,设计的控制律具有比较理想的控制效果．     

Approximate linearization of nonlinear control systems

The paper address the problem of approximate linearization of a nonlinear control system by state feedback or dynamic feedback. The main result proved is that if the fast k d-relative degrees are equal to each other, then the input-output response of a nonlinear control system can be linearized to degree k. Any system having linear d-relative degree can be linearized to any degree by dynamic feedbacks. One example of signal tracking using dynamic feedback linearization method to improve the performance is also given.     

基于动态非线性逼近的非线性系统预测控制

对于一类常见多重时滞非线性离散系统．提出基于动态非线性逼近的增量型最小化递推预测模型、广义预测控制律、噪声估计器以及参数自适应递推预报算法。实现了对存在较大滞后的时滞非线性系统的广义预测控制．仿真结果表明了该算法的正确性和有效性．     

Gain scheduling control of nonlinear singularly perturbed time-varying systems with derivative information

In this paper, we analyse the ultimate boundedness of nonlinear singularly perturbed time-varying systems and propose a control law using gain scheduling where the slow state and the exogenous signals are used as scheduling variables. In our control scheme, we have some flexibility in selecting the slow manifold of the system. Moreover, the derivative information can be properly engaged to manipulate the size of ultimate bound in tracking error of the controlled system.     

Dynamic input-output decoupling of nonlinear control systems

The problem of dynamic input-output decoupling of nonlinear control systems is studied. Based on an analytic algorithm the authors obtain necessary and sufficient conditions for the solvability of this problem. The solution of the problem is constructed by applying a series of simple precompensations and linking maps. Some interesting connections with other approaches in nonlinear control theory are discussed. The authors also give a few (simple) examples to illustrate the methods used     

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.     

An input-output based robust stabilization criterion forneural-network control of nonlinear systems

A stabilization method based on the input-output conicity criterion is presented. Conventional learning algorithms are applied to adjust the controller dynamics, and robust stability of the closed-loop system is guaranteed by modifying the training patterns which yield unstable behavior. The methodology developed expands the class of nonlinear systems to be controlled using neural control schemes, so that the stabilization of a broad class of neural-network-based control systems, even with unknown dynamics, is assured. Straightforwardness in the application of this method is evident in contrast to the Lyapunov function approach.     

基于自适应模糊与输入输出线性化的卫星姿态控制

将自适应模糊控制与输入输出线性化控制相结合，构成混合控制器，并将其应用于挠性卫星的姿态机动控制．给出了卫星姿态控制器的基本形式，分析了控制器参数的选取准则．在线调节自适应模糊控制器的参数，以补偿不确定性卫星的姿态跟踪误差．仿真结果表明，该控制算法通过在线学习能有效地克服挠性卫星的不确定性，具有较强的鲁棒性，从而有效地提高了挠性卫星的姿态控制精度．     

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.     

Feedback control of nonlinear systems by extended linearization

For single-input, multiple-output, nonlinear systems, we consider a design method based on the family of linearizations of the system, parameterized by constant operating points. Nonlinear state feedback control laws and observer/state feedback control laws are designed such that the eigenvalues of the family of linearized closed-loop systems are placed at specified values that are locally invariant with respect to the closed-loop operating point. The method is illustrated by application to the problem of automatically balancing an inverted pendulum.     

基于神经网络的非线性系统轨迹线性化自适应容错控制

针对一类仿射非线性系统,首先采用轨迹线性化方法将其等价表示为线性时变系统;然后利用神经网络构建伪逆模型以及动态故障模型：最后基于模型参数变化,应用李亚普诺夫稳定性理论构建标称系统控制器及故障补偿控制律,从而实现系统故障下的稳定有界容错控制．仿真结果表明了所提出算法的有效性．     

A normal form approach to approximate input-output linearizationfor maximum phase nonlinear SISO systems

A control synthesis scheme is presented for nonlinear single-input-single-output systems which have completely unstable (antistable) zero dynamics. The approach is similar in spirit to linear approaches for nonminimum phase systems and involves the derivation of an input-output linearizing controller for a suitably-defined nonlinear minimum phase approximation to the original system. The linearizing controller achieves an approximately linear input-output response and internal stability