一般非线性系统的相关阶与标准形

一般非线性系统的相关阶与标准形佘焱（上海交通大学信控系上海２０００３０）张嗣瀛（东北大学自控系沈阳１１０００６）关键词一般非线性系统，标准形，相关阶．１）国家自然科学基金，中国博士后科学基金和辽宁省科学技术基金资助项目．收稿日期１９９６－０７－１５１...     

基于状态反馈的功率放大器线性化方法

笛卡尔座标反馈线性化技术是减小RF功率放大器非线性失真的一种有效方式,但在高频输入下信号传输延时使系统类似于一高阶系统,严重影响反馈系统的稳定性,一般只适用于窄带系统。为提高系统性能,提出了一种新的状态反馈的线性化技术,并通过二次优化实现参数的优化配置并进行仿真。仿真结果表明通过新方法设计的Cartesian回路增强了系统的稳定性,提高了反馈线性化技术的线性化带宽,而且设计的系统对延时的变化具有较强的鲁棒性。     

一类非线性多变量系统的解耦线性化

本文讨论了非线性多变量系统的解耦和完全线性化问题.利用微分几何理论中分布不变 性的概念,提出并证明了当系统的相对阶次之和小于系统维数时,非线性解耦系统实现完全线 性化并保持其解耦性不变的条件,还给出了这类系统完全线性化的具体求解方法.     

飞机着陆全面控制的直接反馈线性化设计及仿真

应用直接反馈线性化的方法来设计非线性飞机模型自动着陆全面控制系统。首先以飞机原始非线性十二阶微分方程为对象,利用直接反馈线性化(DFL)理论对飞机原始非线性方程进行线性化,将原系统等效于一个六阶的线性系统。然后设计了自动着陆控制系统控制律,并进行了仿真,仿真结果满足飞机自动着陆各项指标要求,表明所设计的自动着陆控制系统具有较强的鲁棒性。     

含有有色噪声的非线性分数阶系统自适应扩展卡尔曼滤波器

研究了含有未知参数的情况下，分别含有分数阶有色过程噪声和有色测量噪声的连续时间非线性分数阶系统状态估计问题.采用Grünwald-Letnikov （G-L）差分方法和1阶泰勒展开公式，对描述连续时间非线性分数阶系统的状态方程进行离散化和线性化.构造由状态量、未知参数和分数阶有色噪声的增广向量，设计自适应分数阶扩展卡尔曼滤波算法实现对有色噪声情况下的连续时间非线性分数阶系统的状态和参数的估计.最后，通过分析两个仿真实例，验证了提出算法的有效性.     

非线性控制系统的拓扑结构

本文的目的是描述与分析非线性控制系统的拓扑结构.文中首先定义可线性化系统,然 后引入Whitney拓扑,并用此定义非线性控制系统族上的拓扑.在这个拓扑下,证明了除单 输入二维系统外,在一般情况下能线性化的系统是一个零测集.最后讨论一般反馈线性化问 题.对输入数仅比系统维数少一的情况给出了充要条件,并证明了在此情况下几乎所有的系 统均可线性化.     

基于模糊子集合拟合对非线性系统的模糊控制

实际受控系统都存在非线性和不确定性，使得参数化模型控制算法难以实施．为此，提出一种非参数化模型的模糊控制算法，即在非线性系统中对局部过程实施模糊分段线性化，对分段线性化的过程进行联接，将分段线性化的模糊模型集合拟合为全局非线性模型．其控制律是由局部线性化的模糊控制律经模糊联接而构成整体非线性系统的模糊控制律．通过稳定性证明和仿真验证，论证了所给算法的有效性．     

基于逆系统方法的广义非线性系统控制及电力系统应用

对一般广义非线性系统的反馈线性化问题,通过将代数变量视为虚拟输入,给出了构造性递归求逆算法,实现了系统的精确反馈线性化.作为该算法的应用,讨论了带有非线性负荷的三节点电力系统的励磁控制问题,设计了非线性励磁控制器.仿真结果表明了方法的有效性.     

一种跟踪问题中的次优非线性预测控制算法

针对跟踪问题中无状态和输入约束的非线性预测控制最优解的求取问题,引入参考输入轨迹的概念,利用Ｓｔｉｒｌｉｎｇ插值公式,将非线性系统模型沿参考输入输出轨迹展开,取其一阶近似,处理成参数已知的线性模型．在此基础上,利用线性系统预测控制理论求解得到原系统的次优控制律．该方法不要求系统模型连续可导,且无需对线性化后的模型参数进行在线辨识,计算量小,易于实现．     

不对称信息理论与非线性鲁棒控制算法

针对非线性船舶航向保持系统,通过设计其精确反馈线性化控制器,给出一种物理意义更明显的解释,即非线性精确反馈线性化控制器由非线性函数项和常规线性控制器组成．将简化的精确反馈线性化法与闭环增益成形算法相结合,设计其非线性鲁棒控制器,增加了信息的传递量,在提高系统鲁棒性能的基础上,使该算法成为实际工程上可用的算法．仿真结果表明,当信息传递充分时,航向保持效果良好．     

Achieving vector relative degree for nonlinear systems with parametric uncertainties

Several algorithms for adaptive control, as well as for static state feedback decoupling, feedback linearization, or inversion of nonlinear multivariable systems require that the systems have full vector relative degree, in order to be applied. In this paper, we provide a parameter-independent method of achieving full vector relative degree for nonlinear multivariable systems which do not have it. We determine conditions under which a diagonal dynamic precompensation is sufficient to achieve vector relative degree for multivariable nonlinear systems, and describe a simple algorithm which determines such compensation.     

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     

Input-output pseudolinearization on controlled invariant submanifolds

The original notion of input-output pseudolinearization on equilibrium submanifolds is extended to general controlled invariant submanifolds for nonlinear systems. Input-output pseudolinearizing feedback laws render the input-output behavior of linearizations about nominal trajectories in the submanifold trajectory-independent and equal to that of a fixed linear time-invariant system, thereby facilitating the subsequent construction of control laws for stabilization and tracking. Sufficient existence conditions are derived that are weaker than the familiar relative degree conditions for nonlinear input-output decoupling that have come to be associated with exact input-output linearization.     

INPUT/OUTPUT LINEARIZATION FOR NONLINEAR SYSTEMS WITH UNCERTAINTIES AND DISTURBANCES USING TDC

In this paper, a class of nonlinear systems with uncertainties and disturbances considered is input output linearized without resorting to the coordinate transformation used in Isidori 1989 . Time delay control TDC is used to achieve input output linearization, when the systems considered have uncertain dynamics and disturbances, relating to the relative degree of the uncertain nonlinear systems and the matching condition.     

一类非线性时变系统的鲁棒输出跟踪控制

研究一类具有非匹配不确定性的非线性时变系统的鲁棒状态反馈输出跟踪控制器设计问题。通过引入非线性时变系统的相对阶将系统输入输出线性化,然后设计出一种基于标称系统和不确定性上界的连接型鲁棒输出跟踪控制器,利用该方案设计的控制器可保证整个闭环系统是一致有界稳定的,且闭环输出可以渐近跟踪期望的轨迹。     

一类非仿射非线性离散系统的改进无模型自适应控制

针对一类更广泛的非仿射非线性离散系统,提出一种改进的无模型自适应控制算法。该算法基于非参数动态线性化方法,运用观测器的思想,实现带有扰动系统的实时动态线性化,进而将无模型自适应控制方法的应用推广到更广泛的非仿射非线性离散系统。同时,对推广后的改进无模型自适应控制方法进行理论上的证明,并通过仿真实例验证了所提出的改进无模型自适应控制方法的可行性和有效性。     

On weak relative degree and the McGehee transformation

Points where jumps in relative degree occur are presented as singularities in the vector field of the internal dynamics of systems that are candidates for input-output linearization via nonlinear feedback. For a certain class of vector fields, it is shown that the point at which the relative degree is weak can be transformed to a saddle equilibrium point at the origin     

Input output linearization approach to state observer design fornonlinear system

Presents a state observer for a class of nonlinear systems based on the input output linearization. While the previous result presented state observers for nonlinear systems of full relative degree, we proposed a procedure fur the design of nonlinear state observers which do not require the hypothesis of full relative degree. Assuming that there exists a global state observer for internal dynamics and that some functions are globally Lipschitz, we can design a globally convergent state observer. It is also shown that if the zero dynamics are locally exponentially stable, then there exists a local state observer. An example is given to illustrate the proposed design of nonlinear state observers     

Generalized normal form and stabilization of non-linear systems

This paper considers the normal form of non-linear control systems. First we propose a generalized relative degree (relative degree vector) for non-linear single (respectively, multiple) input control system, which is called the point relative degree (respectively, point relative degree vector). For the systems without output, the concepts of essential relative degree (respectively, essential relative degree vector) and the essential point relative degree (respectively, essential point relative degree vector) are defined. Unlike the classical definition which requires regularity, the point relative degree (vector) is always well defined. Using these new concepts the generalized normal form is obtained. Its relationship with the Jacobian linearization is investigated. Using it, a straightforward computation algorithm is provided to achieve the generalized normal form. Based on the generalized normal form we prove that with an additional condition, if the zero-dynamics is stable the overall system is stabilizable by using pseudo-linear state feedback control. For the systems under generalized normal form with unstable zero dynamics, the centre manifold approach is applied. It is shown that the stabilization technique via a designed centre manifold is still applicable to this kind of general non-linear control system.     

一类非线性系统的次优控制研究

考虑一类关系度不确定且零动态稳定的非线性系统的控制器设计问题．利用预测控制概念,通过选用较为全面的二次型性能指标,对输出进行高阶泰勒级数展开,推导出一种非切换的解析次优控制律,进而得出了在该控制律下闭环系统局部稳定的充分条件．仿真例子验证了该控制算法具有较好的动态性能,与已有的近似线性化方法相比,显示了该控制策略的优越性．