仿射非线性奇异系统的受控分布

研究非线性奇异系统的受控不变分布问题.讨论了非线性奇异系统的受控不变分布算法与该系统经过状态反馈转化为正常非线性系统的受控不变分布算法的关系.得到了在一定条件下,正则非线性奇异系统的受控不变分布算法与该系统经过状态反馈转化为正常非线性系统的受控不变分布算法的一致性.并给出一个例子说明本文的结果.     

非线性奇异系统的能控性子分布

研究非线性奇异控制系统的能控性子分布问题.提出了非线性奇异系统的能控性子分 布的概念;研究了非线性奇异系统能控性子分布的反馈不变性质;给出了非线性奇异系统能控 性子分布的算法,并讨论这个算法的一些性质;证明了在一定条件下,该算法给出的分布确为包 含在某给定分布中的非线性奇异系统的最大能控性子分布.     

一类非线性微分代数系统的能控性子分布

能控性子分布在系统的能控性分解中起着重要作用.针对一类非线性微分代数系统,利用M导数方法,提出了能控性子分布的概念.给出了一个计算包含在某些分布内的最大能控性子分布的算法,同时讨论了该算法的一些性质.最后,给出一个例子说明如何利用本文给出的算法计算此类微分代数系统的包含在某给定分布内的最大能控性子分布.     

局部具有指数稳定性的干扰解耦问题

本文研究了含于输出映射的核空间中最大受控不变分布里不含非零能控性分布的非线性系统性质,提出了包含干扰的最小受控不变分布的概念并用之解决这类系统局部具有指数稳定性的干扰解耦问题,得到充分必要的条件,并对一般的非线性系统作了推广。     

对称系统可逆性的简化条件

给出对称系统可逆性的一个充要条件.用这个条件检验对称系统的可逆性,可不必计算 包含在输出核中的最大能控性子分布,而只需计算较为简单的最大对称性子分布.     

一类受控Petri网的反馈控制

受控Petri网是离散事件动态系统(DEDS)的一种控制理论模型.通过模型来研究实现 禁止状态避免的最大允许反馈控制是DEDS控制理论中的一个重要课题.文中对受控Petri网 的一个子类(非受控变迁子集的外延子网为TC网)讨论控制综合问题,给出求这类受控网中实 现禁止状态避免的最大允许反馈控制的一个算法.     

时滞系统的输出反馈滑模控制的一种奇异系统方法

利用一种奇异系统方法讨论了时滞系统的输出反馈滑模控制问题. 时滞系统的非线性项满足范数有界约束.首先,将滑动模态与线性切换面作为一个奇异时滞系统,基于奇异时滞系统的稳定性理论, 给出滑动模态稳定及切换面存在的线性矩阵不等式(Linear matrix inequality, LMI)充分条件.然后,给出使得系统闭环渐近稳定的静态输出反馈滑模控制器的设计方法,此控制器保证闭环 系统有限时间到达切换面.最后,用数值算例验证本文方法的有效性和正确性.     

多胞约束LPV系统多面体不变集RMPC算法

针对一类输入和输出受约束且具有多胞结构的离散LPV 系统, 提出一种基于多面体不变集的鲁棒模型预测控制(RMPC) 算法. 选取一系列收敛于原点的离散状态点, 计算每个状态的反馈控制率, 构建相应的多面体不变集. 在每一个采样时刻, 确定包含当前状态的最小多面体不变集, 通过计算与相邻两个多面体不变集的位置关系, 执行连续的状态反馈控制率. 仿真结果表明, 相比椭圆不变集离线RMPC算法, 所提出算法扩大了系统的稳定区域, 取得了保守性较小的结果.

     

基于多面体终端域的Hammerstein-Wiener非线性预测控制

许多实际系统都可以表示成一种中间为线性动态子系统、输入输出端为非线性静态子系统的Hammerstein-Wiener型非线性模型. 针对输入和输出受约束的Hammerstein-Wiener型非线性系统, 提出一种基于多面体终端域的预测控制综合算法. 离线设计时, 通过构造一系列多面体不变集, 扩大了终端域; 在多面体不变集内, 设计非线性控制律, 减少了常规线性控制律设计的保守性. 在线计算时, 通过求解有限个线性矩阵不等式(Linear matrix inequalities, LMIs)优化问题, 不仅可以满足实时性要求, 而且能够改善控制性能. 仿真结果表明了采用多面体不变集的优越性.     

广义连续随机非线性系统的递推算法*

讨论了广义连续随机非线性系统的最优递推问题,利用矩阵的奇异值分解理论,给出了广义连续随机非线性系统的奇异值标准形式.基于标准形式,在两种情况下将系统分解成两个子系统,通过对子系统状态估计的研究,得到了该系统的最优递推算法.     

一类非线性系统最大可控不变集求解

针对非线性系统线性化在状态约束下最优鲁棒控制求解问题,提出了一种基于混合系统的非线性系统最大鲁棒控制不变集的方法.对于一类非线性系统通过平衡点线性化的方法转化为多模态的混合系统,并进行了混合逻辑动态模型(MLD)的建模,在不变集基本理论的基础上,通过多参数规划的混合整数规划(MIQP)的方法迭代求解最大可控不变集,并求得不变集内的最优控制器,解决系统的状态约束问题.通过一个非线性系统的实例进行建模、仿真,证明了本方法的可行性.     

Gradient-Like Observers for Invariant Dynamics on a Lie Group

This paper proposes a design methodology for non-linear state observers for invariant kinematic systems posed on finite dimensional connected Lie groups, and studies the associated fundamental system structure. The concept of synchrony of two dynamical systems is specialized to systems on Lie groups. For invariant systems this leads to a general factorization theorem of a nonlinear observer into a synchronous (internal model) term and an innovation term. The synchronous term is fully specified by the system model. We propose a design methodology for the innovation term based on gradient-like terms derived from invariant or non-invariant cost functions. The resulting nonlinear observers have strong (almost) global convergence properties and examples are used to demonstrate the relevance of the proposed approach.      

Parameterization of decoupling control laws for affine nonlinearsystems

The problem of parameterizing all the decoupling feedbacks is investigated and applied to the design of a stable noninteracting control for affine nonlinear systems. An algebraic study of controlled invariance is presented. It covers a new criterion for controlled invariance, parameterization and novel properties of the friend set, and computational aspects of the maximal controlled invariant distribution. This analysis is used to derive Falb-Wolovich-like conditions for general decoupling (including disturbance decoupling and noninteracting control) problems. It is shown that to determine all the decoupling feedbacks one usually needs infinitely many (sets of) controlled invariant or controllability distributions that can arise as solutions to the problems. It is also shown that under certain conditions, stable noninteracting design based on first parameterizing the decoupling feedbacks is still a feasible approach in the sense that a feedback can be chosen from the friend set of the maximal solution for the exponentially stable and noninteracting design problem     

Rotation Invariant Kernels and Their Application to Shape Analysis

Shape analysis requires invariance under translation, scale, and rotation. Translation and scale invariance can be realized by normalizing shape vectors with respect to their mean and norm. This maps the shape feature vectors onto the surface of a hypersphere. After normalization, the shape vectors can be made rotational invariant by modeling the resulting data using complex scalar-rotation invariant distributions defined on the complex hypersphere, e.g., using the complex Bingham distribution. However, the use of these distributions is hampered by the difficulty in estimating their parameters and the nonlinear nature of their formulation. In the present paper, we show how a set of kernel functions that we refer to as rotation invariant kernels can be used to convert the original nonlinear problem into a linear one. As their name implies, these kernels are defined to provide the much needed rotation invariance property allowing one to bypass the difficulty of working with complex spherical distributions. The resulting approach provides an easy, fast mechanism for 2D & 3D shape analysis. Extensive validation using a variety of shape modeling and classification problems demonstrates the accuracy of this proposed approach.     

Control synthesis for invariant sets of families of linear and nonlinear discrete systems with bounded disturbances

Two sets of controlled linear and nonlinear discrete-time systems under bounded disturbances are analyzed. The control synthesis problem for these two sets of systems, including systems with nonlinear functions of a certain class, is constructively solved. The optimal control minimizes the radius of the invariant set. An illustrative example is presented.     

A geometric characterization of feedforward forms

This note addresses the problem of (local) coordinates and feedback equivalence of single-input affine nonlinear systems to feedforward forms. In particular, using the notions of invariant and controlled invariant distributions we provide necessary and sufficient conditions for a general affine in control nonlinear system to be (locally) coordinates or feedback equivalent to a system in (strict) feedforward form. For illustration, the general theory is applied to a simple four-dimensional system describing the dynamics of a food-chain.     

Invariant Observer Design of Attitude and Heading Reference System

An attitude and heading reference system (AHRS) is a nonlinear state estimator unit for computing orientation in 3D space. This paper designs an AHRS using three approaches: an invariant observer, an invariant extended Kalman filter (IEKF), and a conventional extended Kalman filter (EKF). The three designs are validated in experiment versus a ground truth, demonstrating the practical interest of the invariant observer methodology and the advantage of the IEKF over the EKF under model uncertainty.     

Invariant sets for families of linear and nonlinear discrete systems with bounded disturbances

We use difference inclusions to describe the dynamics of a family of nonlinear discrete systems subject to bounded disturbances. For a family of linear discrete systems, we get an analytic solution of the problem of finding the invariant set, and for families of nonlinear systems, we propose an iterative process that finds their invariant set and converges with the speed of a geometric progression. We also provide illustrative examples.     

Inversion of nonlinear time-varying systems

A procedure for inverting nonlinear systems that presents some computational advantages when applied to flexible robot arms or, more generally, to mechanical structures, is given. The procedure is presented in a general setting, for nonlinear time-varying systems. An iterative algorithm that computes a smooth controlled invariant time-varying manifold, the mathematical properties of which are illustrated and exploited, is also proposed. An application to a flexible two-link manipulator illustrates the algorithm and its computational advantages