Nondifferentiable optimization algorithm for designing control systems having singular value inequalities

It has been known for some time that many control system design requirements can be expressed as differentiable inequalities. More recently, it has been shown that important structural properties such as robustness and low noise sensitivity can be expressed as nondifferentiable inequalities involving the singular values of a system or return difference transfer function matrix. This paper presents an optimization algorithm which permits all these constraints to be considered.     

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.     

实参数摄动下结构奇异值计算的新方法

基于结构奇异值(μ)方法的鲁棒稳定性分析与综合设计的关键在于μ的准确计算,而MATLAB鲁棒工具箱中计算实参数摄动的μ的上下界差别太大.本文提出了具体针对实参数对角摄动下的μ的上界和数值准确值计算的新方法.利用实数摄动条件.通过奇异性约束展开的方法将实参数摄动的A计算问题转化为无约束的单目标全局优化问题,然后采用遗传算...     

A regularization algorithm for singular controls of parabolic systems

A practically convenient method of regularization is proposed to solve an optimal control problem for a parabolic equation with a delta function on its right-hand side. The corresponding regularized analogue is proved to converge to a delta function in a negative space. The differential characteristics of the performance criterion are analyzed. An algorithm for finding the optimal control is developed for a regularized problem. Results from a numerical testing of the algorithm are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 86–94, January–February 2006.     

A Jordan control canonical form for singular systems

A canonical form for controllable singular systems modulo restricted system equivalence is presented. The canonical form respects the decomposition of the singular system into a regular and an impulsive part. The construction is based on Popov's control canonical form and on the Jordan canonical form recently developed by Hinrichsen and Prätzel-Wolters. Continuity properties are analysed and the cellular partition of the orbit space induced by the canonical form is briefly discussed.     

Analysis and design for singular discrete linear systems subject to actuator saturation

A method to estimate the domain of attraction for a singular discrete linear system under a saturated linear feedback is established. Simple conditions are derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant. These conditions are expressed in terms of linear matrix inequalities. The largest contractively invariant ellipsoid can also be determined by solving an optimization problem with linear matrix inequality constraints. This result is extended to the design of feedback gain that results in the largest contractively invariant ellipsoid, which is also a linear matrix inequality optimization problem. A numerical example demonstrates the applicability and effectiveness of the presented method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

奇异线性系统在执行器饱和受限下不变集条件的改进

本文考虑饱和线性反馈下奇异线性系统扩大吸引域估计的问题.根据每个输入是否饱和,将输入空间分成若干子区域.在每个子区域内部,系统模型中没有显示的部分状态的时间导数可被显式表达.利用含有全部系统状态的二次Lyapunov函数,建立一组双线性矩阵不等式形式的改进的不变集条件.该组条件下,二次Lyapunov函数的水平集可诱导出一个吸引域估计.为得到最大的吸引域估计,构建了以这些双线性矩阵不等式为约束条件的优化问题,并为其求解给出了迭代算法.仿真结果表明本文得到的吸引域估计明显大于现有结果.     

A frequency domain approach to control of singular systems

In this paper, singular control systems are studied from the frequency domain point of view. The proper stable factorization of a singular system is derived. The stability of the closed-loop system consisting of a singular system and controller is addressed. Most significantly, all proper stabilizing controllers are parameterized for a given singular system     

Algebraic properties of singular systems subject to decentralized output feedback

This paper investigates algebraic properties of decentralized singular systems (DSSs) under local static output feedback. New concepts of the geometric multiplicity (GM) of the finite decentralized fixed mode (DFM), the decentralized output feedback variable polynomial (DVP), and the finite decentralized output feedback cycle index (DCI) of the DSS are defined. The formulas for determining the GM and the DCI are given in terms of the DFM and the system matrices. It is shown that almost any decentralized output feedback can make the zeros of the DVP (i.e., the closed-loop poles that are variable) distinct and away from any given finite set in the complex plane. It is also shown that the finite DFM of the DSS are those uncontrollable and/or observable finite modes of the closed-loop DSS through any single channel. Finally, the minimal number of the inputs and outputs that guarantee the finite modes of the closed-loop DSS controllable and observable is shown to be the finite DCI of the DSS. An illustrative example is provided.     

Feedback linearization control design for systems with fuzzyuncertainty

We derive a state feedback control design for nonlinear systems with fuzzy uncertainty. We use a fuzzy version of the Kolmogorov forward equation and an equivalent deterministic system to represent the effects of the fuzzy uncertainty. Feedback linearization of the equivalent deterministic system cancels both the system nonlinearities and the effects of the fuzzy uncertainty on the state membership function. Our controller obtains asymptotic stability and an approximation to our controller drives the system state to a small bounded set     

Feedback control for non-linear singular systems

An invertible non-linear map is developed, which transforms a non-linear singular system into a regular one and preserves local properties under the application of specific feedback control laws. The presented algorithm is easily implementable on a digital computer, since it is of closed form. An application of the above algorithm is presented on an autonomous vehicle.     

Rapid distributed model predictive control design using singular value decomposition for linear systems

The issue of model predictive control design of distribution systems using a popular singular value decomposition (SVD) technique is addressed. Namely, projection to a set of conjugate structure is dealt with in this paper. The structure of the resulting predictive model is decomposed into small sets of subsystems. The optimal inputs can be separately designed at each subsystem in parallel without any interaction problems. The optimal inputs can be directly obtained and the communication among the subsystems can be significantly reduced. In addition, the design of distribution model predictive control (DMPC) with constraints using the SVD framework is also presented. The unconstraint inputs are checked in parallel in the conjugate space. Without solving the QP problem of each subsystem, the suboptimal solution can be quickly obtained by selecting the bigger singular values and discarding the small singular values in the singular value space. The convergence condition of the proposed algorithm is also proved. Two case studies are used to illustrate the distribution control systems using the suggested approach. Comparisons between the centralized model predictive control method and the proposed DMPC method are carried out to show the advantages of the newly proposed method.     

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.     

Two singular value inequalities and their implications in H∞approach to control system design

In this note we prove that ifAandBare both nonnegative definite Hermitian matrices andA - Bis also nonnegative definite, then the singular values of A and B satisfy the inequalitiessigma_{i}(A)geq sigma_{i}(B), wherebar{sigma}(cdot) = sigma_{1}(cdot) geq sigma_{2}(cdot) geq '" geq sigma_{m}(cdot) = underbar{sigma}(.)denote the singular values of a matrix. A consequence of this property is that, in a nonsquare H^{infty} optimization problem, ifsup_{omega} bar{sigma}[Z(jsigma)] {underline{underline Delta}} sup_{omega} bar{sigma}[x(jomega)^{T}/ Y(jomega)^{T}]^{T} = lambda, then the singular values ofXandYsatisfy the inequalitylambda^{2} geq max_{i} sup_{omega} [sigma_{i}^{2}(X) + sigma_{m-i-1}^{2}(Y)]wheremis the number of columns of the matrixZ.     

A neural approach for control of nonlinear systems with feedback linearization.

Several schemes for feedback linearization using neural networks have been investigated and compared. Then an approach to design a neurocontroller in the sense of feedback linearization is introduced. The contents include: (1) full input-output linearization when a system has relative degree n; (2) partial input-output linearization when a system has relative degree r (r相似文献