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.     

Observers and output feedback stabilising controllers for nonlinear strict-feedback systems with sampled observation

The design of observers and output feedback stabilising controllers for continuous-time strict-feedback systems with sampled observation is considered. First two types of observers are designed. One is a discrete-time semiglobal and practical reduced-order observer for the exact model and the other is a continuous-time semiglobal and practical full-order observer for continuous-time strict feedback systems with sampled observation. Then by combining the designed continuous-time observers and continuous-time state feedback laws that are continuous, zero at the origin, and uniformly globally asymptotically stabilise continuous-time systems, output feedback semiglobally practically uniformly asymptotically stabilising controllers are constructed. Numerical examples are given to illustrate the proposed design of observers and output feedback controllers.     

Asymptotic H∞ disturbance attenuationbased on perfect observation

A design method of controllers which ensure internal stability and attain asymptotically H^∞ disturbance attenuation is presented. The design procedure consists of two steps: (1) to design an H^∞ state feedback control via an algebraic Riccati equation approach; and (2) under a certain minimum-phase condition, to recover the achievable performance asymptotically by applying high-gain observers. It makes use of the perfect observation for the design of high-gain observers. It is shown that the asymptotic recovery can be attained by using reduced-order observers, provided there is no direct feedthrough of controls and disturbances in observations     

Cascade Design of State Observers

A block approach to designing state observers for nonlinear multivariate systems is developed. A block-observable form of nonlinear systems is elaborated, in which the design of dynamic observation devices is subdivided into sequentially and independently solved elementary subproblems of reduced dimension. Stepwise procedures for choosing state observer controls from high-gain feedback systems are developed. Lower estimates for the finite coefficients of state observers are used in estimating the state vector components with given accuracy via synthesis decomposition. The designed algorithms ensure the invariance of the control operator to parametric uncertainties. By way of application, the state variables of an asynchronous sensorless drive motor are estimated from stator current measurements.     

On observer design for nonlinear systems

The main weakness of all control methodologies is the dependency of feedbacks to full state measurements. In practical situations, measuring the states of a given system may fail because sometimes the measurements are impossible and sometimes, possible, but too expensive. Observer design for highly nonlinear dynamics is an important issue, particularly when the locally observable dynamics are not linearly observable. In such circumstances the ability to reduce the system to observable or observer form is key to observer design. This paper provides two observers for nonlinear systems given in Brunovski form. The first observer is a high-gain observer with a classical output injection form, while the second is a high-gain observer with a q-integral path. Finally, the discrete-time implementation of the high-gain observer is discussed in linear matrix inequality framework. A motivating example is shown to highlight the efficacy of the developed observers.     

一类带不确定输入动态非线性系统的输出反馈鲁棒镇定

研究一类带不确定输入动态非线性系统的输出反馈鲁棒镇定问题.通过在高增益观测器引入新的设计参数,改进了通常的高增益反馈控制的设计方法.在输入动态满足零相对阶最小相位的假设下,基于非分离设计原则给出了动态输出反馈控制器的设计方法,所设计的控制器实现了对任意可允许不确定输入动态的全局鲁棒镇定.     

具有未知动态的船舶编队输出反馈控制

研究了仅利用相对位置信息和相对航向信息的船舶编队输出反馈控制问题.首先使用leader-follower策略,建立了船舶编队的运动学模型.然后应用微分同胚变换将系统解耦成3个子系统.根据船舶低频运动的特点,在跟随船水动力学模型中粘性水动力和力矩未知以及所有船舶速度都不可测量的假定下,提出了一种高增益广义比例积分观测器来估计这些未知和不可测量动态.在高增益广义比例积分观测器的基础上,分别设计了线性输出反馈控制器和输入饱和受限的输出反馈控制器,并分析了闭环系统的稳定性.最后仿真结果表明了方法的有效性.     

Sliding-mode observers for systems with unknown inputs: A high-gain approach

Sliding-mode observers can be constructed for systems with unknown inputs if the so-called observer matching condition is satisfied. However, most systems do not satisfy this condition. To construct sliding-mode observers for systems that do not satisfy the observer matching condition, auxiliary outputs are generated using high-gain approximate differentiators and then employed in the design of sliding-mode observers. The state estimation error of the proposed high-gain approximate differentiator based sliding-mode observer is shown to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. Finally, the unknown input reconstruction using the proposed observer is analyzed and then illustrated with a numerical example.     

Semi-global stabilization and output regulation of constrained linear plants via measurement feedback

Semi-global stabilization and output regulation of linear systems subject to state and/or input constraints have been studied in our earlier work by using state feedback. For the same problems, observer based measurement feedback control designs are the topics of this paper. High-gain observers are used in the feedback design in order to obtain accurate estimates of the state so that the constraint violation can be avoided. Due to the peaking phenomenon associated with a high-gain observer, a special saturation protection is built in the control laws to avoid possible constraint violation. The results in this paper show that the semi-global stabilization and semi-global output regulation problems for constrained linear systems are solvable via measurement feedback under solvability conditions similar to those in the state feedback.     

Output feedback controller design of Takagi–Sugeno fuzzy systems

This paper presents new systematic design methods of two types of output feedback controllers for Takagi–Sugeno (T–S) fuzzy systems, one of which is constructed with a fuzzy regulator and a fuzzy observer, while the other is an output direct feedback controller. In order to use the structural information in the rule base to decrease the conservatism of the stability analysis, the standard fuzzy partition (SFP) is employed to the premise variables of fuzzy systems. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The concept of parallel distributed compensation (PDC) is employed to design fuzzy regulators and fuzzy observers from the T–S fuzzy models. New stability analysis and design methods of output direct feedback controllers are also presented. The output feedback controllers design and simulation results for a nonlinear mass-spring-damper mechanical system show that these methods are effective.     

Output feedback control of switched nonlinear systems using multiple Lyapunov functions

This work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints. The key feature of the proposed methodology is the integrated synthesis, via multiple Lyapunov functions, of “lower-level” bounded nonlinear feedback controllers together with “upper-level” switching laws that orchestrate the transitions between the constituent modes and their respective controllers. Both the state and output feedback control problems are addressed. Under the assumption of availability of full state measurements, a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding stability region for each mode. A set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed-loop system. When complete state measurements are unavailable, a family of output feedback controllers are synthesized, using a combination of bounded state feedback controllers, high-gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain. A different set of switching rules, based on the evolution of the state estimates generated by the observers, is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes. The differences between the state and output feedback switching strategies, and their implications for the switching logic, are discussed and a chemical process example is used to demonstrate the proposed approach.     

A high-gain scaling technique for adaptive output feedback control of feedforward systems

In this note, we propose an adaptive output feedback control design technique for feedforward systems based on our recent results on dynamic high-gain scaling techniques for controller design for strict-feedback systems. The system is allowed to contain uncertain functions of all the states and the input as long as the uncertainties satisfy certain bounds. Unknown parameters are allowed in the bounds assumed on the uncertain functions. If the uncertain functions involve the input, then the output-dependent functions in the bounds on the uncertain functions need to be polynomially bounded. It is also shown that if the uncertain functions can be bounded by a function independent of the input, then the polynomial boundedness requirement can be relaxed. The designed controllers have a very simple structure being essentially a linear feedback with state-dependent dynamic gains and do not involve any saturations or recursive computations. The observer utilized to estimate the unmeasured states is similar to a Luenberger observer with dynamic observer gains. The Lyapunov functions are quadratic in the state estimates, the observer errors, and the parameter estimation error. The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov equations. The controller design provides strong robustness properties both with respect to uncertain parameters in the system model and additive disturbances. This robustness is the key to the output feedback controller design. Global asymptotic results are obtained.     

High-gain observers in the presence of measurement noise: A switched-gain approach

This paper considers output feedback control using high-gain observers in the presence of measurement noise for a class of nonlinear systems. We study stability in the presence of measurement noise and illustrate the tradeoff when selecting the observer gain between state reconstruction speed and robustness to model uncertainty on the one hand versus amplification of noise on the other. Based on this tradeoff we propose a high-gain observer that switches between two gain values. This scheme is able to quickly recover the system states during large estimation error and reduce the effect of measurement noise in a neighborhood of the origin of the estimation error. We argue boundedness and ultimate boundedness of the closed-loop system under switched-gain output feedback.     

Certainty-equivalence output-feedback design with circle-criterion observers

We study how the class of observers introduced in a previous paper, here referred to as circle-criterion observers, can be incorporated in output-feedback control. Due to the absence of a controller-observer separation property for nonlinear systems, the certainty-equivalence implementation of a state-feedback design may lead to severe forms of instability. We show, on the contrary, that the state-dependent convergence properties of circle-criterion observers can prevent such instabilities. Exploiting these convergence properties we develop a modified circle-criterion observer design that guarantees global asymptotic stability for certainty-equivalence controllers.     

A pole-placement design approach for systems with multipleoperating conditions

The author proposes design procedures based on state-space pole-placement techniques for systems with multiple operating conditions. This is the so-called simultaneous pole-placement problem. First, the full state feedback problem is studied, in which a nonlinear local pole-placement solution is proposed. The design condition is formulated in terms of the rank condition of a multimode controllability matrix. Then, the output feedback problem is approached using a multimodel controller design, which is an extension of the observer design to multimode systems. The design is decomposed into separated global pole-placement subproblems and a local pole-placement subproblem. For a system with some operating conditions having modes on the j ω-axis, but no modes at the origin in the open right-half of the complex plane, stabilizability and detectability conditions for the design of an asymptotically stabilizing control are established, without any restriction on the number of inputs or outputs. Relations of this approach to other simultaneous control design approaches are pointed out     

Homogeneous observers, iterative design, and global stabilization of high-order nonlinear systems by smooth output feedback

We study the problem of global stabilization by smooth output feedback, for a class of n-dimensional homogeneous systems whose Jacobian linearization is neither controllable nor observable. A new output feedback control scheme is proposed for the explicit design of both homogeneous observers and controllers. While the smooth state feedback control law is constructed based on the tool of adding a power integrator, the observer design is new and carried out by developing a machinery, which makes it possible to assign the observer gains one-by-one, in an iterative manner. Such design philosophy is fundamentally different from that of the traditional "Luenberger" observer in which the observer gain is determined by observability. In the case of linear systems, our design method provides not only a new insight but also an alternative solution to the output feedback stabilization problem. For a class of high-order nonhomogeneous systems, we further show how the proposed design method, with an appropriate modification, can still achieve global output feedback stabilization. Examples and simulations are given to demonstrate the main features and effectiveness of the proposed output feedback control schemes.     

一类线性不确定组合系统的鲁棒控制器和观测器设计*

本文研究了一类带有结构不确定性的线性组合系统的鲁控制器和观测器设计问题，文中给出一种设计分散控制器和分散观测器的方法，其中状态反馈增益 观测器增益阵由两个黎卡提议方程的解给出。     

基于微分对策的最优状态观测器和最优状态反馈控制器的设计

研究了线性系统基于二次型指标的最优状态观测器和最优状态反馈控制器的设计问题．将观测状态的状态反馈和状态误差的输出反馈分别作为两个对局方,应用微分对策理论研究了系统的最优控制问题．给出了最优状态观测器和基于状态观测器的最优状态反馈控制的存在性条件．将系统的最优状态观测器和最优控制器的设计问题转化为一对Riccati方程的求解问题．研究表明最优状态观测器在一般情况下不存在．并进一步研究了基于状态观测器的次优控制问题,给出了基于LMI的优化算法．     

一类线性时变系统的输出反馈控制

基于线性时不变系统能控能观标准型变换及非线性系统高增益观测器方法,本文研究了一类线性时变系统 的输出反馈控制问题. 通过引入时变的状态变量坐标变换,分别设计了线性时变系统的状态反馈控制器、状态观测器以及基于 状态观测器的输出反馈控制器. 进一步地,本文分别证明了观测器动态误差是渐近收敛于零的,而状态反馈控制器以及输出反馈控制器可以 保证闭环系统的渐近稳定性.     

基于广义扩张状态观测器的干扰不匹配离散系统状态反馈控制

针对一类干扰不匹配的线性离散时间系统, 研究基于广义扩张状态观测器的稳定化状态反馈控制器设计问题. 在经典的自抗扰控制器中, 扩张状态观测器主要针对干扰匹配的积分串联型系统. 然而, 在许多实际系统中往往存在干扰不匹配的情况, 例如存在采样抖动的离散时间控制系统. 针对这一问题, 基于一类存在不匹配干扰的离散时间系统, 提出广义扩张状态观测器和相应的稳定化状态反馈控制器设计方法. 最后通过永磁同步电机调速控制仿真实例验证了所设计的观测器和控制器的有效性.