Exponential observers for nonlinear systems

Exponentially converging observers are exhibited for a large class of multi-input multi-output (MIMO) nonlinear systems. Potential applications of these observers to mechanical systems and distillation columns are presented     

设计最低阶多线性函数观测器的新方法

本文讨论为连续线性时不变多输入多输出系统设计多线性函数观测器的时域方法.用此 法设计的观测器具有最低动态阶数,且极点可以任意配置.本文提供的算法不仅可用于设计 多输出系统的最低阶多线性函数观测器,而且也可用于设计多输出系统的降阶状态观测器.     

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.     

On the reliable decentralised stabilisation of n MIMO systems

In this paper, we consider the problem of reliable decentralised stabilisation for n multi-input multi-output (MIMO) systems when some of the shared controllers among these systems are faulty, in the sense that they fail to operate properly due to subsystem (module) failures that may occur in actuators, sensors or controllers. Specifically, we present a design framework using a dilated linear matrix inequalities (LMIs) technique for deriving reliable stabilising state-feedback gains for all n MIMO systems; while a set of decentralised unknown disturbance observers (UDOs) that are shared by all n MIMO systems is used for extending the result to the output-feedback case. Moreover, a sufficient condition for the solvability of the set of decentralised UDOs is given in terms of a minimum-phase condition of each subsystem and a lower-bounding condition on the number of outputs of each channel. We also present a numerical example that illustrates the applicability of the proposed technique.     

Adaptive observer for multiple-input-multiple-output (MIMO) lineartime-varying systems

For joint state-parameter estimation in linear time-varying (LTV) multiple-input-multiple-output (MIMO) systems, an approach to the design of adaptive observers is proposed. It is conceptually simple and computationally efficient. Its global exponential convergence is established for noise-free systems. In the presence of noises, it is proved that the estimation errors are bounded and converge in the mean to zero if the noises are bounded and have zero means. Potential applications are fault detection and isolation, and adaptive control     

Adaptive observers for nonlinearly parameterized class of nonlinear systems

In this paper, one proposes adaptive observers for a class of uniformly observable MIMO nonlinear systems with general nonlinear parameterizations. The state and the unknown parameters of the considered systems are supposed to lie in bounded domains which size can be arbitrarily large and the exponential convergence of the observers is shown to result under a well-defined persistent excitation condition. Moreover, the gain of the observers involves a design function that has to satisfy a simple condition which is given. Different expressions of such a function are proposed and it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function. The theory is supported by simulation results related to the estimation of the biomass concentration and the Contois model parameters in a bioreactor.     

Continuous–discrete adaptive observers for state affine systems

The observation of a class of multi-input multi-output (MIMO) state affine systems with constant unknown parameters and discrete time output measurements is addressed. Assuming some persistent excitation conditions to hold and the sampling steps to satisfy some boundedness hypotheses, system observability is ensured and a class of global exponential observers is synthesized.     

Output feedback stabilization of nonlinear MIMO systems having uncertain high-frequency gain matrix

The purpose of this paper is to provide a method for (semi-global) asymptotic stabilization of a nonlinear minimum-phase MIMO system, under a mild hypothesis of the so-called “high-frequency gain” matrix. This result is based on a non-trivial extension, to the MIMO setting, of the approach based on the use of extended observers. As a byproduct, a dynamic output feedback control is obtained, that asymptotically stabilizes the equilibrium of the closed-loop system, in spite of uncertainties in the high-frequency gain matrix.     

Linearization by generalized input-output injection

The problem under interest is the linearization of nonlinear MIMO systems by generalized input-output injection in order to design observers with linear error dynamics. The method is based on the study of the structure of the input-output differential equations; thus, the problem is solved as a realization problem. In this note, one considers the linearization under two kinds of inout-output injection. In the first case, the transformation depends on the output and time derivatives of the input, whereas in the second case, derivatives of both the input and the output are considered. Necessary and sufficient conditions are obtained which generalize the ones on standard input-output injection linearization.     

基于系数图法的多输入多输出系统控制器设计方法

多输入多输出系统的交互作用会限制适用于单输入单输出系统的多种先进设计方法的使用,且多数关于多输入多输出系统控制研究只重视消除交互作用的影响,忽略系统控制问题,这样不但弱化系统的鲁棒性,且设计过程复杂,解耦后系统阶次也较高.鉴于此,提出一种基于系数图法的多入多出系统的控制器设计方法,将多输入多输出系统解耦问题转化为参数优化问题.首先,给出目标函数和两个线性约束条件,通过在频域基于粒子群算法优化目标函数,从而设计补偿器实现解耦;其次,基于系数图法确定控制器结构及参数整定,兼顾系统的稳定性和鲁棒性;最后,通过仿真实验验证所提出方法的有效性.     

Application of the observer/Kalman filter identification method to unknown time-delay disturbed systems and the associated optimal digital tracker design

ABSTRACT

Many practical systems are described as unknown multi-input-multi-output (MIMO) time-delay systems with unknown disturbances. The properties and performance of multi-time-delay MIMO systems are quite different compared to delay-free systems, in particular if the time-delay is long. In addition, for practical implementation digital controllers are often required instead of analog controllers. This paper presents: (i) an overview of the mathematical modelling based on the observer/Kalman filter identification (OKID) method, with some insight on known/unknown MIMO systems; (ii) a study of the pole-zero maps of the identified delay-free system and the known/unknown time-delay system for various sampling periods; (iii) a development of the explicit pole-zero map of the sampled-data MIMO neutral system with multiple discrete and disturbed time delays; (iv) an utilisation of the OKID method for known/unknown time-delay sampled-data MIMO systems with unknown disturbances; (v) an extension of the existing equivalent-input-disturbance (EID) estimator, to determine a robust tracker for the unknown time-delay system with unknown disturbances; and (vi) an investigation on the unknown time-delay system with stable or unstable zeros to determine which traditional or customised tracker can be applied. In addition, simulation studies are performed on the relationship between pole-zero maps and delay times.     

Integration of support vector regression and annealing dynamical learning algorithm for MIMO system identification

This paper presents a robust approach to identify multi-input multi-output (MIMO) systems. Integrating support vector regression (SVR) and annealing dynamical learning algorithm (ADLA), the proposed method is adopted to optimize a radial basis function network (RBFN) for identification of MIMO systems. In the system identification, first, SVR is adopted to determine the number of hidden layer nodes, the initial structure of the RBFN. After initialization, ADLA with nonlinear time-varying learning rate is then applied to train the RBFN. In the ADLA, the determination of the learning rate would be an important work for the trade-off between stability and speed of convergence. A computationally efficient optimization method, particle swarm optimization (PSO) method, is adopted to simultaneously find optimal learning rates. Due to the advantages of SVR and ADLA (SVR-ADLA), the proposed RBFN (SVR-ADLA-RBFN) has good performance for MIMO system identification. Two examples are illustrated to show the feasibility and superiority of the proposed SVR-ADLA-RBFNs for identification of MIMO systems. Simulation results are provided to demonstrate the effectiveness of the proposed algorithm.     

An algorithm for the structural analysis of state space: synthesis of nonlinear observers

The problem addressed is the linearization of multi‐input multi‐output (MIMO) nonlinear systems by a generalized state coordinates transformation and generalized input–output injection, in order to design an observer. This observer will have linear error dynamics. The goal is to bring together two observers design approaches: a structural one and a numerical one. Necessary and sufficient conditions for the existence of a linearizing generalized state transformation are obtained by an algebraic way and without computing the input–output differential equations. The main result tests integrability conditions of differential one‐forms derived from the state space representation and is applicable to a large subclass of nonlinear systems. Copyright © 2001 John Wiley & Sons, Ltd.     

MIMO网络控制系统的控制器设计

研究了长时延有界的情况下,多输入多输出网络控制系统发生传感器故障时的控制器设计问题。首先,利用容错控制的思想建立了多输入多输出网络控制系统发生传感器故障时的模型。在此基础上,借助切换系统的理论,分析了闭环网络控制系统的稳定性,用线性矩阵不等式（LMI）形式给出了多输入多输出网络控制系统渐近稳定的充分条件和控制器的设计形式。仿真结果表明,该方法可以对多输入多输出网络控制系统中传感器故障问题进行有效的容错控制。     

Operator-Based Robust Nonlinear Control for SISO and MIMO Nonlinear Systems With PI Hysteresis

In this paper, operator based robust nonlinear control for single-input single-output (SISO) and multi-input multi-output (MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii (PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively. In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized. Finally, the effectiveness of the proposed method is confirmed by numerical simulations.      

Multiple sliding mode observers and unknown input estimations for Lipschitz nonlinear systems

Multiple sliding mode observers for state and unknown input estimations of a class of MIMO nonlinear systems are systematically developed in this paper. A new nonlinear transformation is formulated to divide the original system into two interconnected subsystems. The unknown inputs are assumed to be bounded and not necessarily Lipschitz, and do not require any matching condition. Under structural assumptions for the unknown input distribution matrix, the sliding mode terms of the nonlinear observer are designed to track their respective unknown inputs. Also, the unknown inputs can be reconstructed from the multiple sliding mode structurally. The conditions for asymptotic stability of estimation error dynamics are derived. Finally, simulation results are given to demonstrate the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

A New Algorithm to Design Minimal Multi‐Functional Observers for Linear Systems

Designing minimum possible order (minimal) observers for multi‐input multi‐output (MIMO) linear systems have always been an interesting subject. In this paper, a new methodology to design minimal multi‐functional observers for linear time invariant (LTI) systems is proposed. The approach is applicable, and it also helps in regulating the convergence rate of the observed functions. It is assumed that the system is functional observable or functional detectable, which is less conservative than assuming the observability or detectability of the system. To satisfy the minimality of the observer, a recursive algorithm is provided that increases the order of the observer by appending the minimum required auxiliary functions to the desired functions that are going to be estimated. The algorithm increases the number of functions such that the necessary and sufficient conditions for the existence of a functional observer are satisfied. Moreover, a new methodology to solve the observer design interconnected equations is elaborated. Our new algorithm has advantages with regard to the other available methods in designing minimal order functional observers. Specifically, it is compared with the most common schemes, which are transformation based. Using numerical examples it is shown that under special circumstances, the conventional methods have some drawbacks. The problem partly lies in the lack of sufficient numerical degrees of freedom proposed by the conventional methods. It is shown that our proposed algorithm can resolve this issue. A recursive algorithm is also proposed to summarize the observer design procedure. Several numerical examples and simulation results illustrate the efficacy, superiority and different aspects of the theoretical findings.     

Further results on variable output feedback controllers

Zak and Hui (1993) proposed a sliding mode controller for linear multiple-input-multiple-output (MIMO) systems using static output feedback. The author's previous paper (1996) provides an improvement of the output feedback controller of Zak-Hui for a class of linear single-input-single-output (SISO) systems that eliminated two important limitations: 1) system uncertainties must be bounded by the system output; and 2) a requirement of a matrix inequality. The controller developed previously can guarantee global closed-loop stability. This paper extends the previous results to linear MIMO systems. It is emphasized that the proposed MIMO controller yields global closed-loop stability whereas the one in Zak-Hui can only guarantee local stability. An application of the proposed MIMO controller to an aircraft model is included to show the effectiveness of the method     

Simultaneous state and unknown input reconstruction using cascaded high-gain observers

This paper presents a systematic routine for jointly reconstruct the state variables and the unknown inputs (UIs) for a large class of nonlinear MIMO systems. After an appropriate change of state coordinates, a set of cascade high-gain observers (CHGO) are designed in such a way that each of them provides an estimation of only one component of the UI vector, except the last one which gives a final adjustment of the whole state variables. Such design achieves a boundary of the state estimation error which can be arbitrarily small by properly specifying the sole synthesis parameter. An illustrative example verifies the effectiveness of the proposed scheme.     

Beamforming techniques for massive MIMO systems in 5G: overview,classification, and trends for future research

Massive multiple-input multiple-output (MIMO) systems combined with beamforming antenna array technologies are expected to play a key role in next-generation wireless communication systems (5G), which will be deployed in 2020 and beyond. The main objective of this review paper is to discuss the state-of-the-art research on the most favourable types of beamforming techniques that can be deployed in massive MIMO systems and to clarify the importance of beamforming techniques in massive MIMO systems for eliminating and resolving the many technical hitches that massive MIMO system implementation faces. Classifications of optimal beamforming techniques that are used in wireless communication systems are reviewed in detail to determine which techniques are more suitable for deployment in massive MIMO systems to improve system throughput and reduce intra- and inter-cell interference. To overcome the limitations in the literature, we have suggested an optimal beamforming technique that can provide the highest performance in massive MIMO systems, satisfying the requirements of next-generation wireless communication systems.