A novel scheme for output definition in feedback passivation of nonlinear systems

In this paper, a set of conditions for defining output functions is derived such that a system can become passive by static state feedback. A key feature of the proposed set of conditions is that several output functions that satisfy these conditions can be defined without any transformation into a normal form or any need of linearisation of the system. In essence, this paper introduces a new connection between the Lyapunov stability concept and minimum phase property which is indeed a necessary condition of feedback passivity.     

非最小相位SIMO系统的盲辨识方法

提出一种非最小相位SIMO系统的盲辨识方法.SIMO系统的多个输出可重新组合为具有循环平稳特性的输出序列,利用信号子空间与噪声子空间正交的特性,可求解系统的模型参数.该方法能辨识最小相位对象的结构参数,对非最小相位对象以及具有无限冲击响应的对象同样有效.该方法运算复杂度低,辨识速度快.仿真结果验证了其有效性.     

Minimum time output regulation problem of linear discrete-time systems

This paper deals with the minimum time output regulation problem of finite-dimensional linear time-invariant discrete-time systems with an incomplete state observation. First, the necessary and sufficient condition is obtained for the existence of controllers which regulate the system for any arbitrary initial state to a certain given subspace in finite steps. Then, the minimum time is obtained in which the system satisfying the above conditions can be regulated, and a minimum time regulating controller is designed. These are obtained by the geometric approach which is a powerful tool for the investigation of the structural property of linear systems.     

Using an Observer to Transform Linear Systems Into Strictly Positive Real Systems

In this note, we study the extension of the class of linear time invariant plants that may be transformed into SPR systems introducing an observer. It is shown that for open loop stable systems a cascaded observer achieves the result. For open loop unstable systems an observer-based feedback is required to succeed. In general any stabilizable and observable system may be transformed into an SPR system defining a new output based on the observer state. This overcomes the old conditions of minimum phase and relative degree one for the case of keeping the original output. The result is illustrated with some examples.     

不确定非线性系统自适应镇定的充要条件

研究了一类相当广泛的包含未知参数的非线性控制系统的自适应鲁棒控制问题,这类系统的标称系统包含一些非最小相位非线性系统和一些不存在相对阶的非线性系统．其未知定常参数是线性的．在一定假设条件下,对该类系统给出了存在自适应控制器的充要条件,并采用backstepping方法给出了控制器的设计步骤．所得主要结论没有用到增长性假设、最小相位假设和相对阶的假设．同时,还给出了不存在相对阶及非最小相位的非线性系统的例子,对于后者给出了控制器的设计过程．     

Adaptive stabilization of single-input single-output delay systems

For the problem of adaptive stabilization of linear systems with unknown, noncommensurate, real delays, the existence of a smooth controller that regulates the output to zero is proven. The assumptions imposed on the system are natural generalizations of the familiar minimum phase and relative degree one conditions in nondelay systems.     

一类线性不可观非线性系统的动态输出反馈镇定

本文研究一类不可观非线性系统的动态输出反馈镇定,基于逼近渐近稳定性的概念,给出了动态输出反馈可镇定的充分条件,本文主要结果的直接推论是零动太逼近渐近稳定的最小相位系统能用动态输出反馈镇定,本文的方法也能处理非最小相位系统。     

Global adaptive output feedback stabilization of nonlinear systemsof any relative degree with unknown high-frequency gains

This paper presents an algorithm for adaptive output feedback stabilization of nonlinear single-input/single-output, minimum phase systems of any relative degree which are linear with respect to input and unknown constant parameter vector. The algorithm does not require the knowledge of the sign of the high-frequency gain     

Relaxation of output zeroing for bilinear non-minimum phase systems

Linear control design techniques for output setpoint tracking of regulation problems can be extended, through input output feedback linearization (IOFL), to non-linear, input-affine systems, but are not applicable to the case of equilibrium points that exhibit non-minimum phase characteristics. Rather than resort to minimum phase approximations, this paper instead proposes a relaxation of IOFL that does not require IOFL to be implemented at every sampling instant. The relaxation introduces degrees of freedom which, in the case of bilinear systems, can be used efficiently to achieve tracking/regulation, and to maintain this property (to within perturbations caused by the relaxation) until the desired state is reached. A way for expanding the region of attraction is considered and the results of the paper are demonstrated through simulation examples.     

双线性系统的自校正控制

本文分别对确定和随机双线性系统,首次建立了大范围渐近收敛和稳定的自校正控制算法。该算法具有渐近最优的控制效果,且适用于非最小相位系统情况。仿真实验表明了该算法的有效性。     

MIMO非线性最小相位系统的光滑调节

本文研究多输入多输出非线性最小相位系统的光滑调节问题,得到的主要结论是:对合 的在原点具有相对阶的局部双曲最小相位系统能渐近跟踪满足某种有界条件的局部Lyapunov 稳定的信号.一类具有一致相对阶的全局指数稳定的最小相位系统,若满足某种类似的 Lipschitz条件,则能渐近跟踪一类很广泛的信号,既可以是Poisson稳定的,也可以是无界 的.     

A note on the problem of semiglobal practical stabilization of uncertain nonlinear systems via dynamic output feedback

It is known that if a system can be (robustly) globally asymptotically stabilized by means of a feedback that is driven by functions that are uniformly completely observable (UCO), then this system can be practically semiglobally stabilized by means of (possibly dynamic) output feedback. This papers discusses a significant structural hypothesis under which the existence of a dynamic feedback driven by UCO functions is guaranteed. The class of systems which satisfy this hypothesis includes any stabilizable and detectable linear system and any relative degree one nonlinear system which is stabilizable by dynamic output feedback. In particular, the hypothesis does not require the system to be minimum phase.     

Output deadbeat controllers with stability for discrete-time multivariable linear systems

This short paper Treats the problem of designing output deadbeat controllers having the property that the control input to the system converges to zero as time goes to infinity, for discrete-time multivariable linear systems. Two configurations of controllers are considered: one is of state feedback; the other is a dynamic controller using an observer. The existence of such controllers is examined, and the methods are presented for designing such controllers when they exist. The controller using a state feedback obtained in this paper is optimal in the sense that the controller settles the output in zero for any initial state in the minimum number of steps. On the other hand, the dynamic controller is not optimal in that sense, but it minimizest, wheretis defined as an integer such that the controller drives the output to zero in no more thantsteps for any set of initial conditions of the system and the observer.     

Adaptive control of nonlinear systems via approximate linearization

This paper presents an adaptive control scheme for nonlinear systems that violates some of the common regularity and structural conditions of current nonlinear adaptive schemes such as involutivity, existence of a well-defined relative degree, and minimum phase property. While the controller is designed using an approximate model with suitable properties, the parameter update law is derived from an observation error based on the exact model described in suitable coordinates. The authors show that this approach results in a stable, closed-loop system and achieves adaptive tracking with bounds on the tracking error and parameter estimates. The authors also present a constructive procedure for adaptive state regulation which is based on the quadratic linearization technique via dynamic state feedback. This regulation scheme does not impose any restriction on the location of the unknown parameters and is applicable to any linearly controllable nonlinear system     

Design of stabilized digital inverse systems

As is well known, due to the existence of unstable limiting zeros and/or the minimum phase property of continuous-time systems, there are many cases that the discretized systems are of non-minimum phase. In this case, it is impossible to construct a stable digital inverse by usual methods. However, in this paper, we will show that if the inter-sample output is used in the design, one can always construct a stable digital inverse system.     

Stabilization of discrete time linear systems by static outputfeedback

This note proposes a systematic approach for the static output feedback control design for discrete time linear systems. It is shown that if the open loop system satisfies some particular structural conditions, a static output feedback gain can be calculated easily, using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the stronger relies on a minimum phase argument. Square and nonsquare systems are considered     

Global asymptotic tracking for nonminimum‐phase nonlinear systems in output feedback form

The problem of global asymptotic tracking by output feedback is studied for a class of nonminimum‐phase nonlinear systems in output feedback form. It is proved that the problem is solvable by an n‐dimensional output feedback controller under the two conditions: (a) the nonminimum‐phase nonlinear system can be rendered minimum‐phase by a virtual output; and (b) the internal dynamics of the nonlinear system driven by a desired signal and its derivatives has a bounded solution trajectory. With the help of a new coordinate transformation, a constructive method is presented for the design of a dynamic output tracking controller. An example is given to validate the proposed output feedback tracking control scheme.     

Global adaptive output-feedback control of nonlinear systems. I.Linear parameterization

The problem of designing global adaptive output-feedback tracking controls for single-input single-output nonlinear systems which are linear with respect to the input and an unknown constant parameter vector is addressed. A class of systems which can be globally controlled by adaptive observer-based output-feedback compensators is identified by geometric coordinate-free conditions. The nonlinearities depend on the output only: growth conditions are not required. Each system in the class admits observers with linear error dynamics and is minimum phase, i.e., it has linear asymptotically stable zero dynamics. When the parameters are known, new sufficient conditions for global output-feedback tracking control are obtained as a special case. For linear systems the result recovers a well-known fundamental adaptive result. Three examples are discussed     

A robust sliding-mode output tracking control for a class of relative degree zero and non-minimum phase plants: A chemical process application

A well-known robust observer-based sliding-mode output tracking control developed for strictly proper, minimum phase systems is extended to the control of relative degree zero, MIMO non-minimum phase plants. By assuming that the class of uncertainty is limited to an appropriate sub-space of the actuator range-space, a sliding-mode tracking control for non-minimum phase systems is posed. By introducing some dynamics, in the form of a plant output filter, relative degree zero plants are proved to be robustly controllable. The design of the linear components of the tracking control and the observer gains is posed in an H ₂-framework. The control law is exemplified on the control of a highly non-linear, benzene producing, large scale chemical process.     

Deadbeat output regulators for decouplable recursive non-linear systems

The deadbeat output regulator problem is formulated and solved in a straight-forward way for a class of decouplable multivarialbe recursive non-linear systems. It is shown that the decoupling control sequences drive each regulated output to zero and remain at zero thereafter in a minimum number of control iterations; this number is equal to the relative degree of the corresponding output. In addition, we show that the internal stability of a deadbeat closed-loop system is guaranteed only if the system is minimum phase.