Global external linearization of nonlinear systems via feedback

This note presents necessary conditions and sufficient conditions for an affine nonlinear system to be globally feedback equivalent to a controllable linear system over an open subsetVof Rⁿ. WhenVequals Rⁿ, necessary and sufficient conditions are obtained.     

Robust nonlinear feedback design via quantifier elimination theory

In this note symbolic-computation methods are used to design simple, fixed-structure, robust controllers for nonlinear systems. Design specifications are reduced to logically quantified polynomial inequalities. The quantifier-elimination (QE) software package QEPCAD is used to eliminate quantifiers on state and plant parameters, to obtain regions of admissible controllers parameters, that guarantee robust stability and performance. Copyright © 1999 John Wiley & Sons, Ltd.     

超混沌系统同步非线性反馈控制

在将超混沌系统的控制、同步及反同步问题统一处理的基础上,给出了一种可实现超混沌系统同步的非线性状态反馈方法。该方法以非线性系统的线性化方法和极点配置理论为基础,把控制律分解为非线性和线性两部分之和,使超混沌系统得以控制、同步和反同步。对超混沌Newton-Leipnik系统的仿真实验表明了控制策略的有效性。     

On feedback equivalence to port controlled Hamiltonian systems

In the last few years port controlled Hamiltonian (PCH) systems have emerged as an interesting class of nonlinear models suitable for a large number of physical applications. In this paper we study the question of feedback equivalence of nonlinear systems to PCH systems. More precisely, we give conditions under which a general nonlinear system can be transformed into a PCH system via static state feedback. We consider the two extreme cases where the target PCH system is completely a priori fixed or completely free, as well as the case where it is only partially predetermined. When the energy function is free a set of partial differential equations needs to be solved, on the other hand, if it is fixed we have to deal with a set of algebraic equations. In the former case, we give some verifiable necessary and sufficient conditions for solvability. As a by-product of our analysis we obtain some stabilization results for nonlinear systems.     

包含SVC和非线性负荷的电力系统耗散实现与控制

采用Hamilton函数方法研究了包含静止无功补偿器(SVC)和非线性负荷的电力系统的反馈控制问题. 首先建立了系统的非线性微分代数方程模型, 通过预置状态反馈完成了耗散Hamilton实现. 然后利用该耗散实现结构,通过阻尼注入方式设计了基于能量的SVC非线性控制器. 本文所设计的控制器结构简单, 物理意义明确. 仿真结果表明该控制器能有效提高电力系统的暂态稳定性.     

Passivity and disturbance attenuation via output feedback foruncertain nonlinear systems

The authors address the problem of disturbance attenuation with internal stability via output feedback for a class of passive systems with uncertainties. The problem is approached by means of adaptive output feedback control which does not require any state observer. The results obtained extend an earlier result of Steinberg and Corless (1985). Sufficient conditions are proposed under which a nonlinear system can be made locally or globally passive via output feedback     

Robust H∞ nonlinear control via measurement feedback

This paper deals with the problem of finite-time-horizon robust H_∞ control via measurement feedback, for affine nonlinear systems with nonlinear time-varying parameter uncertainty. The problem addressed is the design of a control law, which processes the measured output and guarantees a prescribed level of closed-loop disturbance attenuation. Conditions for the existence of such a controller are obtained by solving an auxiliary control problem for a related system which is obtained from the original one by converting the parameter uncertainty into exogenous bounded energy signals. This approach allows us to apply the recently developed H_∞ nonlinear control techniques to solve the robust control problem. The problem is investigated in both the continuous- and discrete-time cases. The results are demonstrated by a simple example. © 1997 by John Wiley & Sons, Ltd.     

Output feedback stabilization of SISO nonlinear systems via dynamic sliding modes

Previous work on asymptotic stabilization of SISO nonlinear systems using dynamic sliding mode control to produce dynamic state feedback has been developed further to produce dynamic output feedback. All the states in the feedback controller are replaced with estimated states which come from a semi-high gain observer. An upper bound of the semi-high gain parameter is explicitly given. It is proved that if the given differential I-O system is minimum phase and proper, local uniform asymptotic output feedback stabilization can be achieved. Pertinent examples are given to show how the method works for both differential inputoutput models and state space models.     

一类非线性系统的自适应抗测量噪声的输出反馈镇定

本文研究一类非线性系统的自适应抗测量噪声的输出反馈镇定问题. 所研究的非线性系统输出中存在正的且 有界的乘性噪声. 非线性项的增长率为一个未知常数乘以输出的幂函数加上带有时滞输出的幂函数. 首先, 证明一个矩 阵不等式. 其次, 设计含有3个时变增益的输出反馈控制器, 并给出增益的自适应律, 然后, 构造适当的Lyapunov-Krasovskii 泛函, 给出确保闭环系统渐近稳定的充分条件. 最后, 仿真实验验证该方法的可行性和有效性.     

Construction of optimal feedback control for nonlinear systems via Chebyshev polynomials

A method is proposed to determine the optimal feedback control law of a class of nonlinear optimal control problems. The method is based on two steps. The first step is to determine the open-hop optimal control and trajectories, by using the quasilinearization and the state variables parametrization via Chebyshev polynomials of the first type. Therefore the nonlinear optimal control problem is replaced by a sequence of small quadratic programming problems which can easily be solved. The second step is to use the results of the last quasilinearization iteration, when an acceptable convergence error is achieved, to obtain the optimal feedback control law. To this end, the matrix Riccati equation and another n linear differential equations are solved using the Chebyshev polynomials of the first type. Moreover, the differentiation operational matrix of Chebyshev polynomials is introduced. To show the effectiveness of the proposed method, the simulation results of a nonlinear optimal control problem are shown.     

Asymptotic output stabilization for nonlinear systems via dynamical variable-structure feedback control

In this article, the problem of asymptotic output stabilization in nonlinear controlled systems is approached from the perspective of dynamical sliding-mode control. The proposed controller is based on Fliess's Generalized Observability Canonical Form, recently derived from the differential algebraic approach to system dynamics.     

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...     

Recursive scaling design for robust global nonlinear stabilization via output feedback

This paper proposes a novel approach to robust backstepping for global stabilization of uncertain nonlinear systems via output feedback. The design procedure developed in this paper is based on the concept of state‐dependent scaling, which handles output‐feedback stabilization problems of strict‐feedback systems with various structures of uncertainties in a unified way. The proposed method is suitable for numerical computation. The theory of the method employs the Schur complements formula instead of Young's inequality and completing the squares. This paper shows a condition of allowable uncertainty size under which an uncertain system is globally stabilized by output feedback. A class of systems is shown to be always globally stabilizable for arbitrarily large nonlinear size of uncertainties. A recursive procedure of robust observer design for such a class of uncertain systems is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Asymptotic stabilization via output feedback for nonlinear systems with delayed output

We propose a novel and simple design scheme of output feedback controller for a class of nonlinear systems with delayed output. The nonlinear systems considered here are more general than feedforward systems (upper triangular systems). By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and solving linear matrix inequalities (LMIs), the delay-dependent controller making the closed-loop system globally asymptotically stable (GAS) is explicitly constructed. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

基于双增益方法的不确定非线性系统的输出反馈调节问题

研究一类具有多种不确定性的非线性系统的全局输出反馈调节问题.所研究系统的一个显著特点是非线性项被未知增长率和多项式形式的输出函数的乘积界定,难点是在输出受不确定参数摄动的情况下如何抑制非线性项.提出一种改进的双增益方法来设计输出反馈控制器,可以确保闭环系统所有信号全局一致有界并且原系统状态收敛到零.最后,采用质量弹簧机械系统的输出反馈镇定问题来说明控制策略的有效性.     

Decentralized and adaptive nonlinear tracking of large-scale systems via output feedback

Presents a solution to the problem of decentralized adaptive asymptotic tracking for a class of large-scale systems using nonlinear output feedback. The proposed constructive approach does not require any matching conditions on the parametric uncertainties nor growth conditions of any kind on the subsystem and interacting output nonlinearities. Any decentralized system in the family may have an unknown, nonzero equilibrium point. Partially decentralized reduced-order filters are presented to recover the unmeasured states. The recursive, decentralized, output-feedback design procedure is illustrated in a practical example of two inverted pendulums on carts without velocity measurements. The effectiveness of the decentralized algorithm is supported by simulation results.