Adaptive Non‐Backstepping Fuzzy Control for a Class of Uncertain Nonlinear Systems with Unknown Dead‐Zone Input

Based on the approximation property of fuzzy logic systems, we propose a novel non‐backstepping adaptive tracking control algorithm for a class of single input single output (SISO) strict‐feedback nonlinear systems with unknown dead‐zone input. In this algorithm, we introduce some novel state variables and coordinate transforms to convert the strict‐feedback form into a normal one, and it is not necessary to consider the traditional approximation‐based the backstepping scheme. Due to new states variables being unavailable, the tracking control is changed from a state‐feedback one to an output‐feedback one. So, observers need to be designed to estimate the indirect nonmeasurable states. According to Lyapunov stability analysis method, the developed controller can guarantee that all of the signals in the closed‐loop system will be ultimately uniformly bounded (UUB), and the output can track the reference signal very well. Simulation results are presented to show the effectiveness of the proposed approach.     

DESIGN MODIFICATION OF SLIDING MODE OBSERVERS FOR UNCERTAIN MIMO SYSTEMS WITHOUT AND WITH TIME‐DELAY

In this paper, the sliding mode observers design techniques for MIMO and as a simple example for SISO systems are systematically advanced as a first purpose. Design parameters are selected such that on the defined switching surface always is generated asymptotically stable sliding mode. Moreover, observer state error dynamics is globally robustly asymptotically stable. Then, advanced design techniques are generalized to the design of a new modification of sliding mode observers for uncertain MIMO systems with time‐delay. Robust sliding and global asymptotic stability conditions are derived by using Lyapunov‐Krasovskii V‐functional method. By these conditions observer parameters are designed such that an asymptotically stable sliding mode always is generated in observer and observer state error dynamics is robustly globally asymptotically stable. The main results are formulated in terms of Lyapunov matrix equations and inequalities. Design example for AV‐8A Harrier VTOL aircraft with simulation results using MATLAB‐Simulink show the effectiveness of proposed design approaches.     

A closed‐loop nonlinear control and sliding mode estimation strategy for fluid flow regulation

Novel sliding mode observer (SMO) and robust nonlinear control methods are presented, which are shown to achieve finite‐time state estimation and asymptotic regulation of a fluid flow system. To facilitate the design and analysis of the closed‐loop active flow control (AFC) system, proper orthogonal decomposition–based model order reduction is utilized to express the Navier‐Stokes partial differential equations as a set of nonlinear ordinary differential equations. The resulting reduced‐order model contains a measurement equation that is in a nonstandard mathematical form. This challenge is mitigated through the detailed design and analysis of an SMO. The observer is shown to achieve finite‐time estimation of the unmeasurable states of the reduced‐order model using direct sensor measurements of the flow field velocity. The estimated states are utilized as feedback measurements in a closed‐loop AFC system. To address the practical challenge of actuator bandwidth limitations, the control law is designed to be continuous. A rigorous Lyapunov‐based stability analysis is presented to prove that the closed‐loop flow estimation and control method achieves asymptotic regulation of a fluid flow field to a prescribed state. Numerical simulation results are also provided to demonstrate the performance of the proposed closed‐loop AFC system, comparing 2 different designs for the SMO.     

A Robust Backstepping Sensorless Control for Interior Permanent Magnet Synchronous Motor Using a Super‐Twisting Based Torque Observer

In order to achieve high‐performance speed regulation for sensorless interior permanent magnet synchronous motors (IPMSMS), a robust backstepping sensorless control is presented in this paper. Firstly, instead of a real mechanical sensor, a robust terminal sliding mode observer is used to provide the rotor position. Then, a new super‐twisting algorithm (STA) based observer is designed to obtain estimates of load torque and speed. The proposed observer ensures finite‐time convergence, maintains robust to uncertainties, and eliminates the common assumption of constant or piece‐wise constant load torque. Finally, a sensorless scheme is designed to realize speed control despite parameter uncertainties, by combining the robust backstepping control with sliding mode actions and the presented sliding mode observers. The stability of the observer and controller are verified by using Lyapunov's second method to determine the design gains. Simulation results show the effectiveness of the proposed approach.     

Application of the dynamic high‐gain scaling methodology to servocompensator design

The error‐feedback servomechanism problem is addressed for a general class of strict‐feedback‐like systems. We provide two error‐feedback control designs based on our recent results on adaptive output‐feedback based on dynamic high‐gain scaling. One control design is of a dual high‐gain observer/controller structure, whereas the other control design utilizes a backstepping‐based controller in conjunction with a dynamic high‐gain scaling‐based observer. Owing to the particular robustness properties offered by a dynamic high‐gain scaling‐based controller and a backstepping‐based controller, the two designs require slightly different sets of assumptions on the system. Both design techniques allow the system to contain both unknown functions and uncertain appended input‐to‐state stable dynamics. Copyright © 2008 John Wiley & Sons, Ltd.     

Real‐time nonlinear moving horizon observer with pre‐estimation for aircraft sensor fault detection and estimation

This paper presents a real‐time nonlinear moving horizon observer (MHO) with pre‐estimation and its application to aircraft sensor fault detection and estimation. An MHO determines the state estimates by minimizing the output estimation errors online, considering a finite sequence of current and past measured data and the available system model. To achieve the real‐time implementability of such an online optimization–based observer, 2 particular strategies are adopted. First, a pre‐estimating observer is embedded to compensate for model uncertainties so that the calculation of disturbance estimates in a standard MHO can be avoided without losing much estimation performance. This strategy significantly reduces the online computational complexity. Second, a real‐time iteration scheme is proposed by performing only 1 iteration of sequential quadratic programming with local Gauss‐Newton approximation to the nonlinear optimization problem. Since existing stability analyses of real‐time moving horizon observers cannot address the incorporation of the pre‐estimating observer, a new stability analysis is performed in the presence of bounded disturbances and noises. Using a nonlinear passenger aircraft benchmark simulator, the simulation results show that the proposed approach achieves a good compromise between estimation performance and computational complexity compared with the extended Kalman filtering and 2 other moving horizon observers.     

Adaptive Impulsive Observers for a Class of Switched Nonlinear Systems with Unknown Parameter

This work investigates and solves the design of adaptive impulsive observers for a class of uncertain switched nonlinear systems with unknown parameter. Sufficient conditions are derived for designing such observers for each subsystem to reconstruct asymptotically and update system states in real time. The state observer is represented in terms of impulsive differential equations. The parameter estimation law is modelled by an impulse‐free, time‐varying differential equation associated with the impulse time sequence in order to determine when the observer estimated state is updated. The asymptotic convergence to zero of the observation errors is established by applying the method of multiple time‐varying Lyapunov functions. Sufficient conditions are derived that guarantee the convergence of parameter estimation. An example of switched Lorenz system along with numeric and simulation results is presented to demonstrate the effectiveness of the proposed method.     

Global output regulation for strict‐feedback nonlinear systems with mismatched nonvanishing disturbances

This paper concerns the problem of global output regulation for a class of strict‐feedback nonlinear systems subject to mismatched nonvanishing disturbances. A composite control scheme is developed using a nonlinear disturbance observer‐based control approach. A novel idea is that the disturbance estimation is introduced into the design of virtual control laws in each step. Global stability analysis for the closed‐loop system is presented by the direct Lyapunov function method. It is shown that the system output asymptotically converges to zero in the presence of mismatched nonvanishing disturbances without the requirement of solving any partial differential equations involved with the traditional output regulation theory. An application design example of a single‐machine infinite‐bus system with static var compensator is presented with simulation results to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Observer‐Based Reliable Control for Discrete‐Time Switched Linear Systems with Faulty Actuators

This paper deals with the issue of reliable control for discrete‐time switched linear systems with faulty actuators by utilizing a multiple Lyapunov functions method and estimate state‐dependent switching technique. A solvability condition for the reliable control problem is given in terms of matrix inequality with an extra matrix variable. This condition allows the reliable control problem for each individual subsystem to be unsolvable. For each subsystem of such a switched system, we design an observer and an observer‐based controller. A switching rule depending on the observer state is designed which, together with the controllers, can guarantee the stability of the closed‐loop switched system for all admissible actuator failures. The observers, controllers, and switching law are explicitly computed by solving linear matrix inequalities (LMIs). The proposed design method is illustrated by two numerical examples.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

Controller design based on similar skew‐symmetric structure for nonlinear plants

This paper proposes a novel controller design approach for nonlinear plants. A class of stable nonlinear systems with a similar skew‐symmetric structure is chosen as the objective closed loop system, and two design methods are proposed with backstepping and direct construction. Compared with the conventional backstepping method, the proposed backstepping method need not construct a Lyapunov function step by step, thus the design procedure is simplified. The direct construction method can be applied to some nonlinear plants for which the conventional backstepping is not feasible; and the design can be accomplished in only one step. Furthermore, for some nonlinear plants which have a lower triangular structure with two subsystems, simpler controllers can be derived by the proposed direct construction method than those derived by backstepping design. In addition, the proposed methods are both system structure oriented, therefore their designs are more intuitive than the conventional backstepping design. Two controllers are derived for satellite attitude control by employing the proposed methods; simulation results demonstrate their effectiveness. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Design of a nonlinear distributed parameter observer for a pressure swing adsorption plant

As an integral part of an advanced process monitoring and control scheme, the reconstruction of the spatial concentration, temperature, and pressure profiles of an oxygen production plant is studied by the design of a nonlinear observer with distributed parameters. The considered pressure swing adsorption process consists of two adsorbers and each adsorber of two layers. The design of the nonlinear observer with distributed parameters is illustrated for a single adsorption layer, which is described by six quasilinear partial differential equations and related boundary conditions. Thereby, a late lumping approach is used in order to design the injected correction functions in the observer equations and to introduce tuning parameters with a physical meaning. The observer is extended to the entire adsorption process and its simulation shows an excellent convergence behavior.     

Backstepping control with speed estimation of PMSM based on MRAS

This paper presents a backstepping control method with speed estimation of permanent magnet synchronous motor (PMSM) based on model reference adaptive system (MRAS). First, a comprehensive dynamical model of PMSM in d–q axis and its space state equations are established. Next, using Lyapunov stability theorem, based on the backstepping control theory, the PMSM rotor speed and current backstepping controllers are designed. Furthermore, using Popov stability theory, based on MRAS, the PMSM rotor speed observer is designed. Finally, Matlab/Simulink simulation results show that the backstepping control and speed observer are effective and feasible.     

一种网络拥塞的反步控制算法

针对Internet网络拥塞控制中的TCP动态非线性流体模型,提出用于网络主动队列管理（AQM）的拥塞控制算法,设计用于估计未知状态的状态观测器,采用反步法技术和Lyapunov直接方法,通过输出反馈实现闭环系统的渐近稳定。仿真实验结果表明,基于反步法的AQM控制算法调整时间小、丢包率低、链路利用率高。     

Small gain problem in coupled differential‐difference equations,time‐varying delays,and direct Lyapunov method

This article presents a Lyapunov–Krasovskii formulation of scaled small gain problem for systems described by coupled differential‐difference equations. This problem includes H_∞ problem with block‐diagonal uncertainty as a special case. A discretization may be applied to reduce the conditions into linear matrix inequalities. As an application, the stability problem of systems with time‐varying delays is transformed into the scaled small gain problem through a process of either one‐term approximation or two‐term approximation. The cases of time‐varying delays with and without derivative upper‐bound are compared. Finally, it is shown that similar conditions can also be obtained by a direct Lyapunov–Krasovskii functional method for coupled differential‐functional equations. Numerical examples are presented to illustrate the effectiveness of the method in tackling systems with time‐varying delays. Copyright © 2010 John Wiley & Sons, Ltd.     

非线性系统大范围渐近稳定状态观测器设计

提出了一类化工过程中非线性系统大范围渐近稳定状态观测器的构造方法。通过配置极点选择时变状态反馈增益阵保证观测器的性能,使观测器能在大范围内稳定工作。其稳定性可由Lyaptmov理论得到证明,存在模型误差和噪声干扰时也有较好的鲁棒性。从工程应用的角度,提出了分区域配置矩阵的策略,大大减少了在线计算量。同时改进了算法,保证能在应用中正确离线计算。在CSPR仿真器上的应用结果证明了该方法的良好性能。     

Full‐Order and Reduced‐order Observer Design for a Class of Fractional‐order Nonlinear Systems

The paper is concerned with problem of the full‐order and reduced‐order observer design for a class of fractional‐order one‐sided Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using indirect Lyapunov approach, the sufficient condition for asymptotic stability of the full‐order observer error dynamic system is presented. Furthermore, the proposed design method was extended to reduced‐order observer design for fractional‐order nonlinear systems. All the stability conditions are obtained in terms of LMI, which are less conservative than some existing ones. Finally, a numerical example demonstrates the validity of this approach.     

Fault estimation observer design for discrete‐time systems in finite‐frequency domain

This paper proposes a framework of fault estimation observer design in finite‐frequency domain for discrete‐time systems. First, under the multiconstrained idea, a full‐order fault estimation observer in finite‐frequency domain is designed to achieve fault estimation by using the generalized Kalman–Yakubovich–Popov lemma to reduce conservatism generated by the entire frequency domain. Then, a reduced‐order fault estimation observer is constructed, which results in a new fault estimator to realize fault estimation using current output information. Furthermore, by introducing slack variables, improved results on full‐order fault estimation observer and reduced‐order fault estimation observer design with finite‐frequency specifications are obtained such that different Lyapunov matrices can be separately designed for each constraint. Simulation results are presented to illustrate the advantages of the theoretic results obtained. Copyright © 2014 John Wiley & Sons, Ltd.