Low-order self-tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems

Based on the modified state-space self-tuning control (STC) via the observer/Kalman filter identification (OKID) method, an effective low-order tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems is proposed in this paper. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). Then, the above identified model in a general coordinate form is transformed to an observer form to provide a computationally effective initialization for a low-order on-line “auto-regressive moving average process with exogenous (ARMAX) model”-based identification. Furthermore, the proposed approach uses a modified Kalman filter estimate algorithm and the current-output-based observer to repair the drawback of the system multiple failures. Thus, the fault-tolerant control (FTC) performance can be significantly improved. As a result, a low-order state-space self-tuning control (STC) is constructed. Finally, the method is applied for a three-tank system with various faults to demonstrate the effectiveness of the proposed methodology.     

Some problems of linear differential equations on abstract spaces and unbounded perturbations of linear operator semigroup

This paper is a survey for development of linear distributed parameter system. At first we point out some questions existing in current study of control theory for the L^p linear system with an unbounded control operator and an unbounded observation operator, such as stabilization problem and observer theory that are closely relevant to state feedback operator. After then we survey briefly some results on relevant problems that are related to solvability of linear differential equations in general Banach space and semigroup perturbations. As a principle, we propose a concept of admissible state feedback operator for system (A, B). Finally we give an existence result of admissible state feedback operators, including semigroup generation and the equivalent conditions of admissibility of state feedback operators, for an L^p well-posed system.     

Asymptotic linearization and stabilization for a class of nonlinear systems

This paper presents a nonlinear output feedback which asymptotically linearizes the class of nonlinear, continuous-time, affine in the control systems having relative degree equal to the state space dimension. Moreover, we show that any set of eigenvalues can be assigned for the asymptotic closed-loop linear system. The controller is based on a nonlinear observer, presented in a previous paper, and on the linearizing state feedback proposed by Isidori and computed in the estimated state. The main result obtained is equivalent to the separation theorem in the linear case.This work was supported by the Italian Ministry for University and Scientific and Technological Research.     

State feedback for uncertain dynamical systems

We consider a linear dynamical system in which the system and input matrices, as well as the input, are uncertain. We present a control system consisting of a linear control to stabilize the nominal system, a nonlinear control to cope with the uncertainties, and an insensitive observer for the state estimation. Practical stability is guaranteed for uncertainties with known bounds. Furthermore, the control system is designed to achieve insensitivity against parameter variations. The theoretical results are illustrated by an application to the suspension control of a maglev vehicle.     

Multivariable state-feedback self-tuning controllers ∗

This paper describes a state-space approach for self-tuning control of a class of multivariable stochastic systems having the same number of inputs as outputs. A multivariable state-feedback self-tuning controller, based on pole-assignment concepts, is derived. The developed multivariable self-tuner can be applied to stable/unstable and minimum/non-minimum phase linear time-invariant multivariable systems. A multivariable reduced-order self-tuner and a state-feedback minimum-variance self-tuner are also derived. The simplicity and flexibility of the proposed state-space approach facilitate the practical applications of self-tuning control concepts to real systems     

广义连续系统极小极大控制反问题初探

将极小极大控制的反问题推广到广义系统.针对给定的性能指标,通过受限等价变换,得到判别广义连续系统控制器是极小极大控制器的充要条件及其等价的频率条件.最后针对广义系统H∞次优控制的反问题进行了讨论.     

Robust output-feedback SOSM control subject to unmatched disturbances and its application: A fixed-time observer-based method

This paper investigates the output-feedback control for a general class of multi-input multi-output (MIMO) linear systems in the presence of unmatched disturbances. Firstly, a new observer composed of a Luenberger observer and a novel hierarchical high-order sliding mode (HOSM) observer is proposed to identify the system states and disturbances, simultaneously. As one of the most remarkable properties, the convergence time of the proposed observer is bounded by a positive constant which is free of the system initial error conditions. Secondly, based on the proposed observer, a new second-order sliding mode (SOSM) controller is constructed by using a novel sliding surface with unmatched disturbances compensation. The proposed control law is a simply continuous function of time and thus can certainly reduce numerical chattering. Finally, to show the effectiveness of the theoretical results, an application to inverted pendulum system is used to make simulation comparison.     

Observer‐based dissipative control for networked control systems: A switched system approach

This article studies the problem of observer‐based dissipative control problem for wireless networked control systems (NCSs). The packet loss and time delay in the network are modeled by a set of switches, using that a discrete‐time switched system is formulated. First, results for the exponential dissipativity of discrete‐time switched system with time‐varying delays are proposed by using the average dwell time approach and multiple Lyapunov–Krasovskii function. Then, the results are extended to drive the controller design for considered wireless NCS. The attention is focused on designing an observer‐based state feedback controller which ensures that, for all network‐induced delay and packet loss, the resulting error system is exponentially stable and strictly dissipative. The sufficient conditions for existence of controllers are formulated in the form of linear matrix inequalities (LMIs), which can be easily solved using some standard numerical packages. Both observer and controller gains can be obtained by the solutions of set of LMIs. Finally, numerical examples are provided to illustrate the applicability and effectiveness of the proposed method. © 2014 Wiley Periodicals, Inc. Complexity 21: 297–308, 2015     

A NARMAX model-based state-space self-tuning control for nonlinear stochastic hybrid systems

A novel state-space self-tuning control methodology for a nonlinear stochastic hybrid system with stochastic noise/disturbances is proposed in this paper. via the optimal linearization approach, an adjustable NARMAX-based noise model with estimated states can be constructed for the state-space self-tuning control in nonlinear continuous-time stochastic systems. Then, a corresponding adaptive digital control scheme is proposed for continuous-time multivariable nonlinear stochastic systems, which have unknown system parameters, measurement noise/external disturbances, and inaccessible system states. The proposed method enables the development of a digitally implementable advanced control algorithm for nonlinear stochastic hybrid systems.     

Real-time nonlinear global state observer design for solar heating systems

Nowadays it is important to investigate and develop solar water heating systems as an environmentally friendly technology. For this reason we introduce a physically-based nonlinear mathematical model that applies to a wide range of solar heating systems. In commercial solar heating systems not all state variables are monitored by direct measurements, since some of them may be technically difficult or expensive to measure. For a better monitoring and more efficient control of the system it may be useful to estimate the unmeasured state variables.As a novelty, we apply a global nonlinear state observer to a solar domestic water heating system. The state observer has been established relatively recently in the field of control theory. The state observer we worked out enables us to estimate the unmeasured state variables in real-time. This observer is global in the sense that it works starting from any initial state. A further contribution of this work is a rather general algorithm for the practical application of the real-time estimation process, and we also give bounds of the estimation error and a practical method to decrease this error.Comparing calculated and measured values for a real particular solar heating system, we justify the usability of the state observer and the estimation process.On the basis of measured data, we show that the nonlinear mathematical model corresponding to the applied nonlinear observer is more accurate than the linear model corresponding to the classical linear Luenberger-type observer, so it is reasonable to apply the nonlinear observer.     

Design of observers for nonlinear systems with H ∞ performance analysis

This paper investigates the problem of observer design for nonlinear systems. By using differential mean value theorem, which allows transforming a nonlinear error dynamics into a linear parameter varying system, and based on Lyapunov stability theory, an approach of observer design for a class of nonlinear systems with time‐delay is proposed. The sufficient conditions, which guarantee the estimation error to asymptotically converge to zero, are given. Furthermore, an adaptive observer design for a class of nonlinear system with unknown parameter is considered. A method of H _∞ adaptive observer design is presented for this class of nonlinear systems; the sufficient conditions that guarantee the convergence of estimation error and the computing method for observer gain matrix are given. Finally, an example is given to show the effectiveness of our proposed approaches. Copyright © 2013 John Wiley & Sons, Ltd.     

线性脉冲控制系统的能控性与最优控制

首先讨论了一类线性随机脉冲控制系统的精确能控性质,给出了该类控制系统的脉冲精确能控的等价的代数判据.然后提出了一个确定性的二维线性脉冲控制系统的时间-脉冲强度最优控制问题;利用动态规划原理,给出了脉冲最优控制的反馈形式和值函数的显式表达式;说明了值函数在整个平面上是连续的,在左右两个半平面的内部还是连续可微的.     

Controllability and Controller-Observer Design for a Class of Linear Time-Varying Systems

In this paper a class of linear time-varying control systems is considered. The time variation consists of a scalar time-varying coefficient multiplying the state matrix of an otherwise time-invariant system. Under very weak assumptions of this coefficient, we show that the controllability can be assessed by an algebraic rank condition, Kalman canonical decomposition is possible, and we give a method for designing a linear state-feedback controller and Luenberger observer.     

多层介质的发汗冷却自适应控制

针对一维固定边界复合介质发汗冷却系统的自适应控制问题 ;给出了一个根据实际观测 .基于对气动加热面边界热流密度的估算 ,由热平衡方程及热阻滞函数的特征确定控制输入的自校正控制方法 .理论和数据试验显示 ,对时变的热流及未知的热阻滞函数 ,此方法可以取得很好的控制效果 .     

Robust fault tolerant control of continuous-time switched systems: An LMI approach

The present paper proposes a new robust fault tolerant control (RFTC) design for continuous-time switched systems. The main objective is to design in an integrated way the couple (controller, observer) that allows to stabilize switched systems even in the presence of actuator faults. A state/fault estimation observer is designed to simultaneously estimate system state and actuator faults. Based on this observer, a fault tolerant controller is developed to stabilize the system and accommodate the actuator faults automatically. The RFTC problem is formalized in the form of linear matrix inequalities (LMI) rather than bilinear matrix inequalities (BMI), to avoid the difficulty of solving BMIs. Finally, a numerical example composed of unstable subsystems is studied to show the applicability and efficiency of the obtained results.     

Approximate controllability for semilinear retarded systems

This paper deals with the approximate controllability for the semilinear retarded control system. We will also derive the equivalent relation between controllability and stabilizability of the solution for the corresponding linear control system.     

Minimum-order observers for discrete-time systems

We consider the synthesis of a minimum-order state or functional observer for a linear dynamical system. The synthesis problem is solved for completely certain systems of general form and for some classes of uncertain systems. Various approaches are described, which ultimately lead to the same task: finding a minimum-dimension Hurwitz solution for a system of linear equations with a Hankel matrix. For scalar and vector linear systems, prior upper and lower bounds on the observer dimension are derived, which makes it possible to switch to an iterative procedure of finding an optimal solution. The discussion is set out for discrete-time dynamical systems.