共查询到20条相似文献,搜索用时 0 毫秒
1.
Given two nonlinear input–output systems written in terms of Chen–Fliess functional expansions, i.e., Fliess operators, it is known that the feedback interconnected system is always well defined and in the same class. An explicit formula for the generating series of a single-input, single-output closed-loop system was provided by the first two authors in earlier work via Hopf algebra methods. This paper is a sequel. It has four main innovations. First, the full multivariable extension of the theory is presented. Next, a major simplification of the basic setup is introduced using a new type of grading that has recently appeared in the literature. This grading also facilitates a fully recursive algorithm to compute the antipode of the Hopf algebra of the output feedback group, and thus, the corresponding feedback product can be computed much more efficiently. The final innovation is an improved convergence analysis of the antipode operation, namely, the radius of convergence of the antipode is computed. 相似文献
2.
Fliess operators as input–output mappings are particularly useful in a number of fundamental problems concerning nonlinear realization theory. In the classical analysis of these operators, certain growth conditions on the coefficients in their series representations insure uniform and absolute convergence, provided every input is uniformly bounded by some fixed upperbound. In some emerging applications, however, it is more natural to consider other classes of inputs. In this paper, Lp function spaces are considered. In particular, it is shown that the classic growth conditions also provide sufficient conditions for convergence and continuity when the admissible inputs are from a ball in Lp[t0,t0+T], where T is bounded and p1. In addition, stronger global growth conditions are given that apply even for the case where T is unbounded. When the coefficients of a Fliess operator have a state space representation, it is shown that the state space model will always locally realize the corresponding input–output map on Lp[t0,t0+T] for sufficiently small T>0. If certain well-posedness conditions are satisfied then the state space model will globally realized the input–output mapping for unbounded T when the coefficients satisfy the global growth condition. 相似文献
3.
The present work proposes a new approach to the nonlinear discrete-time feedback stabilization problem with pole-placement. The problem's formulation is realized through a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived. Using tools from functional equations theory, one can prove that the solution to the above system of nonlinear functional equations is locally analytic, and an easily programmable series solution method can be developed. Under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear discrete-time state feedback control law that are both computed through the solution of the system of nonlinear functional equations, the feedback stabilization with pole-placement design objective can be attained under rather general conditions. The key idea of the proposed single-step design approach is to bypass the intermediate step of transforming the original system into a linear controllable one with an external reference input associated with the classical exact feedback linearization approach. However, since the proposed method does not involve an external reference input, it cannot meet other control objectives such as trajectory tracking and model matching. 相似文献
4.
For a fixed-time free endpoint optimal control problem it is shown that the optimal feedback control satisfies a system of ordinary differential equations. They are obtained using an elimination procedure of the adjoint vector which appears linearly in a set of differential equations. These equations, involving Lie brackets of vector fields, are derived from the Maximum Principle. An application of this approach to robotics is given. 相似文献
5.
J. Tsinias 《Systems & Control Letters》1999,36(3):47
This paper presents a version of the well-known Sontag’s ‘input-to-state-stability’ property for stochastic systems. This concept is used to derive sufficient conditions for global stabilization for certain class of stochastic nonlinear systems by means of static and dynamic output feedback. 相似文献
6.
The problem of control design for a system represented as linear stationary and static nonlinear parts is considered. It is assumed that the linear part is unknown and strictly minimum phase. The nonlinear part is known inaccurately, it is irreducible to an input of the linear block, and generally does not satisfy sector restrictions. An adaptive regulator ensuring asymptotic stability is synthesized. The output of a control system, but not its derivatives, is used as a measured variable. 相似文献
7.
Andrzej Banaszuk Andrzej Święch John Hauser 《Mathematics of Control, Signals, and Systems (MCSS)》1996,9(3):207-241
We study the problem of approximating one-dimensional nonintegrable codistributions by integrable ones and apply the resulting
approximations to approximate feedback linearization of single-input systems. The approach derived in this paper allows a
linearizable nonlinear system to be found that is close to the given system in a least-squares (L
2) sense. A linearly controllable single-input affine nonlinear system is feedback linearizable if and only if its characteristic
distribution is involutive (hence integrable) or, equivalently, any characteristic one-form (a one-form that annihilates the
characteristic distribution) is integrable. We study the problem of finding (least-squares approximate) integrating factors
that make a fixed characteristic one-form close to being exact in anL
2 sense. A given one-form can be decomposed into exact and inexact parts using the Hodge decomposition. We derive an upper
bound on the size of the inexact part of a scaled characteristic one-form and show that a least-squares integrating factor
provides the minimum value for this upper bound. We also consider higher-order approximate integrating factors that scale
a nonintegrable one-form in a way that the scaled form is closer to being integrable inL
2 together with some derivatives and derive similar bounds for the inexact part. This allows a linearizable nonlinear system
that is close to the given system in a least-squares (L
2) sense together with some derivatives to be found. The Sobolev embedding techniques allow us to obtain an upper bound on
the uniform (L
∞) distance between the nonlinear system and its linearizable approximation.
This research was supported in part by NSF under Grant PYI ECS-9396296, by AFOSR under Grant AFOSR F49620-94-1-0183, and by
a grant from the Hughes Aircraft Company. 相似文献
8.
9.
Jesus Gonzalez-Trejo Jose Alvarez Ramirez Guillermo Fernandez 《Journal of Process Control》1999,9(3):221-231
The goal of this paper is to describe a linearizing feedback adaptive control structure which leads to a high quality regulation of the output error in the presence of uncertainties and external disturbances. The controller consists of three elements: a nominal input–output linearizing compensator, a state observer and an uncertainty estimator, which provides the adaptive part of the control structure. In this way, the feedback controller, based on the disturbance observer, compensates for external disturbances and plant uncertainties. The effectiveness of the controller is demonstrated on a distillation column via numerical simulations. © 相似文献
10.
ZHANG Li WANG HuaiLei & HU HaiYan MOE Key Lab of Mechanics Control of Aerospace Structures Nanjing University of Aeronautics Astronautics Nanjing China School of Aerospace Engineering Beijing Institute of Technology Beijing 《中国科学:信息科学(英文版)》2010,(3)
This paper presents both analytical and numerical studies on the global view of Hopf bifurcations of a van der Pol oscillator with delayed state feedback.Based on a detailed analysis of the stability switches of the trivial equilibrium of the system,the stability charts are given in a parameter space consisting of the time delay and the feedback gains.The center manifold reduc-tion and the normal form method are used to study Hopf bifurcations with respect to the time delay.To gain an insight into the persi... 相似文献
11.
In this paper, we investigate the problem of global stabilization for a general class of high-order and non-smoothly stabilizable nonlinear systems with both lower-order and higher-order growth conditions. The designed continuous state feedback controller is recursively constructed to guarantee the global strong stabilization of the closed-loop system. 相似文献
12.
Bogdan Marinescu Author Vitae 《Automatica》2010,46(9):1524-1530
The output feedback pole placement problem is solved in an input-output algebraic formalism for linear time-varying (LTV) systems. The recent extensions of the notions of transfer matrices and poles of the system to the case of LTV systems are exploited here to provide constructive solutions based, as in the linear time-invariant (LTI) case, on the solutions of diophantine equations. Also, differences with the results known in the LTI case are pointed out, especially concerning the possibilities to assign specific dynamics to the closed-loop system and the conditions for tracking and disturbance rejection. This approach is applied to the control of nonlinear systems by linearization around a given trajectory. Several examples are treated in detail to show the computation and implementation issues. 相似文献
13.
An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters’ weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm. 相似文献
14.
The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous state feedback. The approach is independent of the selection of a Lyapunov type function, but requires the solution of a nonlinear programming satisficing problem stated in terms of the logarithmic coordinates of flows. As opposed to other approaches, point-to-point steering is not required to achieve asymptotic stability. Instead, the flow of the controlled system is required to intersect periodically a certain reachable set in the space of the logarithmic coordinates. 相似文献
15.
16.
R. Pothin 《Systems & Control Letters》2001,43(2):1328
In this paper, the disturbance decoupling problem for a square-invertible nonlinear system is stated and solved by static feedback of measured variables only, in contrast with standard solutions which assume that the full state is available for feedback. The results are valid for left-invertible systems as well. 相似文献
17.
Smooth output feedback stabilization for a class of nonlinear systems with time‐varying powers
下载免费PDF全文
![点击此处可从《国际强度与非线性控制杂志<br>》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Chih‐Chiang Chen Chunjiang Qian Xiangze Lin Zong‐Yao Sun Yew‐Wen Liang 《国际强度与非线性控制杂志
》2017,27(18):5113-5128
》2017,27(18):5113-5128
This paper investigates the global asymptotic stabilization problem for a class of nonlinear systems with time‐varying powers. First, adding a power integrator technique is revamped to design a smooth state feedback controller, which is implementable with only upper and lower bounds of the time‐varying powers. When the system state is not fully available and the time‐varying power is exactly known, a smooth output feedback controller constituted by a state feedback and a nonlinear state observer is constructed to globally stabilize the system. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
18.
The robust global stabilization problem of a class of uncertain nonlinear systems with input unmodeled dynamics is considered using output feedback, where the uncertain nonlinear terms satisfy a far more relaxed condition than the existing triangulartype condition. Under the assumption that the input unmodeled dynamics is minimum-phase and of relative degree zero, a dynamic output compensator is explicitly constructed based on the nonseparation principle. An example illustrates the usefulness of the proposed method. 相似文献
19.
一类非线性时滞互联系统模糊分散输出反馈控制 总被引:1,自引:0,他引:1
对于一类状态不可测非线性互联时滞系统,给出一种基于观测器的模糊分散输出反馈控制方法.首先采用模糊T-S模型对非线性互联时滞系统进行模糊建模,在此基础上给出了模糊分散观测器和基于观测器的模糊分散输出控制器的设计.应用李亚普诺夫函数法和线性矩阵不等式方法给出了模糊分散控制系统稳定的充分条件.仿真结果进一步验证了所提出的模糊分散控制方法的有效性. 相似文献
20.
The principal contribution of this paper is that it shows how much the controllability condition can be weakened, while still providing the possibility of stabilization. A result concerning stabilization with respect to a target set for affine control systems in the lack of the full rank condition is proved. 相似文献