Finite-time observability of probabilistic Boolean control networks

In this paper, the finite-time observability (FO ) of probabilistic Boolean control networks (PBCNs ) based on set reachability and parallel extension is investigated. Under algebraic state space representation of PBCNs , finite-time set reachability (FSR ), finite-time single input sequence set reachability (FSSSR ), finite-time arbitrary input sequence set reachability (FASSR ), as well as finite-time output feedback set reachability (FOSR ) are addressed, where some efficient criteria are proposed. In the second part of this paper, several types of FO are provided, which can be converted to the corresponding FSR based on the parallel extension technique. Consequently, the obtained results for FSR are utilized to deal with FO . Finally, two examples including a biological network are given to demonstrate the theoretical results.     

Finite-time output feedback control for a class of stochastic low-order nonlinear systems

This paper discusses the problem of finite-time stabilisation for a class of stochastic low-order nonlinear systems via output feedback. By generalising the adding a power integrator technique, constructing an implementable reduced-order observer and using the stochastic finite-time stability criterion, a finite-time output feedback controller is presented to guarantee that the closed-loop system is finite-time stable in probability. A simulation example is provided to verify the effectiveness of the proposed design method.     

Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems

This article considers the problem of global finite-time stabilisation by output feedback for a class of nonlinear systems comprised of a chain of power integrators perturbed by an uncertain vector field. To solve the problem, we first construct a homogeneous observer and controller in a recursive way for the nominal system without the perturbing nonlinearities. Then, using the homogeneous domination approach, we scale the homogeneous observer and controller with an appropriate choice of gain to render the uncertain nonlinear system globally finite-time stable. Due to the use of a reduced-order observer, the proposed output feedback controller is applicable to those systems with unknown gains associated with the power integrators.     

Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems

This note studies the problem of global finite-time stabilization by dynamic output feedback for a class of continuous but nonsmooth nonlinear systems. By extending the adding-a-power-integrator technique and a special continuous observer design, a dynamic output feedback controller is explicitly constructed to render the systems globally finite-time stable. The novelty of the note is the development of a recursive design procedure, which takes full advantage of the continuous structure of the systems in constructing the state feedback stabilizer and the continuous observer with rigorously selected gains.     

Global finite-time stabilization for a class of switched nonlinear systems via output feedback

This paper addresses the problem of global finite-time stabilization for a class of uncertain switched nonlinear systems via output feedback under arbitrary switchings. Based on the adding a power integrator approach, we design a homogeneous observer and controller for the nominal switched system without the perturbing nonlinearities. Then, a scaling gain is introduced into the proposed output feedback stabilizer to implement global finite-time stability of the closed-loop system. In addition, the proposed approach can be also extended to a class of switched nonlinear systems with upper-triangular growth condition. Two examples are given to illustrate the effectiveness of the proposed method.     

Observability Analysis and Improved Zero‐Speed Position Observer Design of Synchronous Motor with Experimental Results

This paper deals with the permanent magnet synchronous motor (PMSM) observability analysis for sensorless control design. The problem of loss of observability at low frequency range is always recognized in experimental settings. Nevertheless, there are no sufficient theoretical observability analyses for the PMSM. In the literature, only the sufficient observability condition has been presented. Therefore, the current work is aimed especially towords the necessary observability condition analysis. Furthermore, improved zero‐speed observation is presented here for a surface PMSM (SPMSM) to overcome position observability problems at zero‐speed which is an unobservable state point. The proposed observer based on higher order sliding mode (HOSM) is designed in order to ensure robustness against disturbances and to avoid the chattering phenomenon which is inherent in standard first order sliding modes. The stability and finite time convergence of the developed observer are studied and discussed. Experimental results are carried out to illustrate the effectiveness and robustness of the proposed observer.     

Global finite-time output feedback stabilisation for a class of uncertain nontriangular nonlinear systems

This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.     

A separation principle for a class of non-UCO systems

This paper introduces a new approach to output feedback stabilization of single-input-single-output systems which, unlike other techniques found in the literature, does not use quasilinear high-gain observers and control input saturation to achieve separation between the state feedback and observer designs. Rather, we show that by using nonlinear high-gain observers working in state coordinates, together with a dynamic projection algorithm, the same kind of separation principle is achieved for a larger class of systems which are not uniformly completely observable. By working in state coordinates, this approach avoids using knowledge of the inverse of the observability mapping to estimate the state of the plant, which is otherwise needed when using high-gain observers to estimate the output time derivatives.     

Higher Order Sliding Mode Controllers With Optimal Reaching

Higher order sliding mode (HOSM) control design is considered for systems with a known permanent relative degree. In this paper, we introduce the robust Fuller's problem that is a robust generalization of the Fuller's problem, a standard optimal control problem for a chain of integrators with bounded control. By solving the robust Fuller's problem it is possible to obtain feedback laws that are HOSM algorithms of generic order and, in addition, provide optimal finite-time reaching of the sliding manifold. A common difficulty in the use of existing HOSM algorithms is the tuning of design parameters: our methodology proves useful for the tuning of HOSM controller parameters in order to assure desired performances and prevent instabilities. The convergence and stability properties of the proposed family of controllers are theoretically analyzed. Simulation evidence demonstrates their effectiveness.     

A system decomposition approach to the design of functional observers

This paper reports a system decomposition that allows the construction of a minimum-order functional observer using a state observer design approach. The system decomposition translates the functional observer design problem to that of a state observer for a smaller decomposed subsystem. Functional observability indices are introduced, and a closed-form expression for the minimum order required for a functional observer is derived in terms of those functional observability indices.     

Kalman decomposition for implicit linear systems

The Kalman decomposition for a general class of implicit systems is introduced and studied. The properties of strong reachability, observability, acceptance of all inputs and outer sequences, output-uniqueness, uniqueness, and trajectory observability of the original system are related to the properties of its subsystems obtained via the Kalman decomposition. The problems of transfer relation, regularizability by feedback, output feedback, and output injection are studied by means of this decomposition     

Finite-time observers for multi-agent systems without velocity measurements and with input saturations

This paper is devoted to the distributed finite-time observers for multi-agent systems, where the control inputs are required to be bounded and the velocities are assumed to be not available for feedback. An effective framework through defining a class of coordinated saturation functions is introduced, under which both a first-order finite-time observer and a high-order finite-time observer are constructed. By applying the homogeneous theory for stability analysis, it is proven that all the states of the followers can converge to that of the leader in finite time under our proposed observers. With mild modifications of our control strategies, the foregoing results are then extended to the distributed finite-time containment control problem, where the states of the followers converge to the convex hull spanned by the multiple dynamic leaders. Numerical simulations are presented to demonstrate the efficiency of our methods.     

任意传递函数最小实现的代数方法

本文用代数方法讨论了传递函数的最小实现问题.首先从传递函数可否约分的概念出 发,提出了可控可观测新的代数判据;讨论了梯形网络的状态公式、结构可控可观测性及状态 反馈和输出做最小实现的代数方法,并给出了例题.这种实现方法较状态空间法结构简单,有 源和无源元件个数少,而且梯形网络的元件值可任意给定,加法器各增益值计算简单.     

Adaptive output feedback control of nonlinear systems representedby input-output models

We consider a single-input-single-output nonlinear system which can be represented globally by an input-output model. The system is input-output linearizable by feedback and is required to satisfy a minimum phase condition. The nonlinearities are not required to satisfy any global growth condition. The model depends linearly on unknown parameters which belong to a known compact convex set. We design a semiglobal adaptive output feedback controller which ensures that the output of the system tracks any given reference signal which is bounded and has bounded derivatives up to the nth order, where n is the order of the system. The reference signal and its derivatives are assumed to belong to a known compact set. It is also assumed to be sufficiently rich to satisfy a persistence of excitation condition. The design process is simple. First we assume that the output and its derivatives are available for feedback and design the adaptive controller as a state feedback controller in appropriate coordinates. Then we saturate the controller outside a domain of interest and use a high-gain observer to estimate the derivatives of the output. We prove, via asymptotic analysis, that when the speed of the high-gain observer is sufficiently high, the adaptive output feedback controller recovers the performance achieved under the state feedback one     

基于LMI的大型互联线性系统的分散有限时间镇定

借助于有限时间稳定性的定义,针对大型互联线性系统,引入了分散有限时间镇定的概念.对一类大型互联线性系统进行分散状态反馈和分散动态输出反馈控制器设计,利用线性矩阵不等式(LMI)的方法提出一个充分条件,当反馈控制律作用于该系统时,闭环系统是有限时间稳定的.仿真算例说明了所得结论的可行性和有效性.     

Global finite-time stabilization by output feedback for planar systems without observable linearization

This note considers the problem of global finite-time stabilization by output feedback for a class of planar systems without controllable/observable linearization. A sufficient condition for the solvability of the problem is established. By developing a nonsmooth observer and modifying the adding a power integrator technique, we show that an output feedback controller can be explicitly constructed to globally stabilize the systems in finite time. As a direct application of the main result, global output feedback finite-time stabilization is achieved for the double linear integrator systems perturbed by some nonlinear functions which are not necessarily homogeneous.     

Representation of dynamic output feedback control system variables via orthogonal functions

A general basis for using orthogonal functions to approximate the variables of a dynamic output feedback control system is presented. The use of an operational matrix of integration reduces the problem to a set of linear algebraic equations. The result is also useful for implementing open-loop approximation of derived closed-loop control. The flexible controller structure provides easy adaptation to feedback configurations using state, output, dynamic output or observer output, and feedback compensator. As an example, an approximation analysis of dynamic output feedback control via Fourier series is investigated.     

Non-linear observer design by transformation into a generalized observer canonical form

An observer design method for a certain class of non-linear single output systems is introduced. The characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non-linear system is approximated by a linear one. The present paper deals with the derivation of a transformation of the considered non-linear system into a generalized observer canonical form (GOCF) which enables a systematic observer design similar to the linear one based on the well-known linear observer canonical form. To assign conditions for its existence, the transformation into the GOCF is carried out in two steps via a generalized observability canonical form (GOBCF). In contrast to previous forms used for linear systems, the two non-linear canonical forms presented here also depend on the time derivatives of the input variables. This means that the resulting observer has to be supplied, not only with the input and output variables of the given system, but also with derivatives of the input variables. However, a final example shows that it is possible to eliminate those derivatives in special cases.     

具有干扰输入的大型互联线性系统的分散有限时间镇定

借助于大型互联线性系统有限时间稳定性的定义,对具有干扰输入的大型互联线性系统引入了分散有限时间镇定的概念,并对一类具有干扰输入的大型互联不确定线性系统进行了分散状态反馈和分散动态输出反馈控制器设计,利用线性矩阵不等式（LMI）方法,提出了一个充分条件.当反馈控制律作用于该系统时,闭环系统是有限时间稳定的.     

Generalized functional observer

A functional observer and state feedback are proposed for singular systems in the polynomial fraction form that requires no impulsive mode elimination. The order of the compensator is determined by the newly defined generalized observability index that is associated with the McMillan degree of the system. A new generalized Lyapunov equation is also proposed through a realization scheme that can be applied to both ordinary and singular systems. The solution to the equation provides an algebraic approach to the observer of singular systems in the generalized state-space form