Quantized H ∞ fault-tolerant control for networked control systems

Quantized H_∞ fault-tolerant control for networked control systems (NCSs) with partial actuator fault with respect to actuators is concerned in this paper. Considering transmission delay, packet dropout and quantization, a synthesis model with partial actuator fault is established. The piecewise constant controller is adopted to model NCS with the transmission delay and packet dropout. Due to data transmitted in practical NCSs should be quantized before they are sent to the next network node, the logarithmic static and time-invariant quantizers at the sensor and controller sides are proposed in the paper. For the established model, an appropriate type of Lyapunov functions is provided to investigate the delay-dependent H_∞ control problem. According to an optimal problem, the controller that makes the system achieve the best performance is designed. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach.     

Input-to-State Stability for Nonlinear Time-Varying Systems via Averaging

 We introduce two definitions of an averaged system for a time-varying ordinary differential equation with exogenous disturbances (“strong average” and “weak average”). The class of systems for which the strong average exists is shown to be strictly smaller than the class of systems for which the weak average exists. It is shown that input-to-state stability (ISS) of the strong average of a system implies uniform semi-global practical ISS of the actual system. This result generalizes the result of [TPA] which states that global asymptotic stability of the averaged system implies uniform semi-global practical stability of the actual system. On the other hand, we illustrate by an example that ISS of the weak average of a system does not necessarily imply uniform semi-global practical ISS of the actual system. However, ISS of the weak average of a system does imply a weaker semi-global practical “ISS-like” property for the actual system when the disturbances w are absolutely continuous and . ISS of the weak average of a system is shown to be useful in a stability analysis of time-varying cascaded systems. Date received: April 6, 1999. Date revised: April 11, 2000.     

Input-to-state stability for a class of hybrid dynamical systems via averaging

Input-to-state stability (ISS) properties for a class of time-varying hybrid dynamical systems via averaging method are considered. Two definitions of averages, strong average and weak average, are used to approximate the time-varying hybrid systems with time-invariant hybrid systems. Closeness of solutions between the time-varying system and solutions of its weak or strong average on compact time domains is given under the assumption of forward completeness for the average system. We also show that ISS of the strong average implies semi-global practical (SGP)-ISS of the actual system. In a similar fashion, ISS of the weak average implies semi-global practical derivative ISS (SGP-DISS) of the actual system. Through a power converter example, we show that the main results can be used in a framework for a systematic design of hybrid feedbacks for pulse-width modulated control systems.     

具有控制约束的网络控制系统的鲁棒H_∞控制

针对具有控制约束的网络控制系统(Networked Control Systems,NCS)的特点,建立了具有外部扰动的网络控制系统模型,对其H∞性能加以分析和研究,并验证所取得的理论成果.假设具有控制约束的网络控制系统的H∞控制器与执行器均为事件驱动,传感器为时间驱动,且网络诱导时延小于传感器的采样周期,然后将此类网络控制系统的广义被控对象建模为一类线性离散系统,运用Lyapunov函数和线性矩阵不等式(LMI),导出闭环系统渐近稳定且满足给定H∞性能指标的充分条件,并给出了控制器的具体求法.得到了系统的H∞控制器存在条件及具体方法,通过设计该控制器,使具有外部扰动的网络控制系统的性能有很大的改善,通过Matlab仿真证明该控制器行之有效.     

输入饱和及输出受限的纯反馈非线性系统控制

针对具有输入饱和和输出受限的纯反馈非线性系统,设计了神经网络自适应控制器.首先利用隐函数定理和中值定理将非仿射形式的纯反馈非线性系统转换成有显式输入的非线性系统,基于李雅普诺夫第二方法以及反推法并采用障碍型李雅普诺夫函数进行控制器的设计,最后通过稳定性分析证明了闭环控制系统是半全局一致最终有界的,利用仿真例子验证了控制...     

Discrete-time Lyapunov-based small-gain theorem for parameterized interconnected ISS systems

Input-to-state stability (ISS) of a feedback interconnection of two discrete-time ISS systems satisfying an appropriate small gain condition is investigated via the Lyapunov method. In particular, an ISS Lyapunov function for the overall system is constructed from the ISS Lyapunov functions of the two subsystems. We consider parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used in controller design for a sampled-data system.     

Dynamic high-gain scaling: State and output feedback with application to systems with ISS appended dynamics driven by all States

We propose a dynamic high-gain scaling technique and solutions to coupled Lyapunov equations leading to results on state-feedback, output-feedback, and input-to-state stable (ISS) appended dynamics with nonzero gains from all states and input. The observer and controller designs have a dual architecture and utilize a single dynamic scaling. A novel procedure for designing the dynamics of the high-gain parameter is introduced based on choosing a Lyapunov function whose derivative is negative if either the high-gain parameter or its derivative is large enough (compared to functions of the states). The system is allowed to contain uncertain terms dependent on all states and uncertain appended ISS dynamics with nonlinear gains from all system states and input. In contrast, previous results require uncertainties to be bounded by a function of the output and require the appended dynamics to be ISS with respect to the output, i.e., require the gains from other states and the input to be zero. The generated control laws have an algebraically simple structure and the associated Lyapunov functions have a simple quadratic form with a scaling. The design is based on the solution of two pairs of coupled Lyapunov equations for which a constructive procedure is provided. The proposed observer/controller structure provides a globally asymptotically stabilizing output-feedback solution for the benchmark open problem proposed in our earlier work with the provision that a magnitude bound on the unknown parameter be given.     

Input-to-state stability for discrete-time time-varying systems with applications to robust stabilization of systems in power form

Input-to-state stability (ISS) of a parameterized family of discrete-time time-varying nonlinear systems is investigated. A converse Lyapunov theorem for such systems is developed. We consider parameterized families of discrete-time systems and concentrate on a semiglobal practical type of stability that naturally arises when an approximate discrete-time model is used to design a controller for a sampled-data system. An application of our main result to time-varying periodic systems is presented, and this is used to solve a robust stabilization problem, namely to design a control law for systems in power form yielding semiglobal practical ISS (SP-ISS).     

等式约束的网络化控制系统的稳定性设计

研究了等式约束的网络化控制系统的稳定性问题．在假设网络时滞是随机变化的，并且假设网络化控制系统的被控对象为一个具有等式约束的时滞系统的情况下，将网络化控制系统模型化为一个混合系统．然后采用李亚普诺夫函数、线性矩阵不等式的方法推导出了该混合系统渐近稳定的一个充分条件．根据此充分条件，通过求解一个线性矩阵不等式，较容易地获得系统的最大允许网络时滞以及此时的控制器．最后给出一个具体的数值和仿真实例说明了此设计方法是有效的．     

Input-to-state stability for networked control systems via an improved impulsive system approach

This paper presents a novel impulsive system approach to input-to-state stability (ISS) analysis of networked control systems (NCSs) with time-varying sampling intervals and delays. This approach is based upon the new idea that an NCS can be viewed as an interconnected hybrid system composed of an impulsive subsystem and an input delay subsystem. A new type of time-varying discontinuous Lyapunov-Krasovskii functional, which makes full use of the information on the piecewise-constant input and the bounds of the network delays, is introduced to analyze the ISS property of NCSs. Linear matrix inequality based sufficient conditions are derived for ISS of NCSs with respect to external disturbances. When applied to the approximate tracking problem for NCSs, the derived ISS result provides bounds on the steady-state tracking error. Numerical examples are provided to show the efficiency of the proposed approach.     

Stable neural controller design for unknown nonlinear systems using backstepping

We propose, from an adaptive control perspective, a neural controller for a class of unknown, minimum phase, feedback linearizable nonlinear system with known relative degree. The control scheme is based on the backstepping design technique in conjunction with a linearly parametrized neural-network structure. The resulting controller, however, moves the complex mechanics involved in a typical backstepping design from off-line to online. With appropriate choice of the network size and neural basis functions, the same controller can be trained online to control different nonlinear plants with the same relative degree, with semi-global stability as shown by the simple Lyapunov analysis. Meanwhile, the controller also preserves some of the performance properties of the standard backstepping controllers. Simulation results are shown to demonstrate these properties and to compare the neural controller with a standard backstepping controller.     

Input-to-state stability and interconnections of discontinuous dynamical systems

In this paper we will extend the input-to-state stability (ISS) framework to continuous-time discontinuous dynamical systems (DDS) adopting piecewise smooth ISS Lyapunov functions. The main motivation for investigating piecewise smooth ISS Lyapunov functions is the success of piecewise smooth Lyapunov functions in the stability analysis of hybrid systems. This paper proposes an extension of the well-known Filippov’s solution concept, that is appropriate for ‘open’ systems so as to allow interconnections of DDS. It is proven that the existence of a piecewise smooth ISS Lyapunov function for a DDS implies ISS. In addition, a (small gain) ISS interconnection theorem is derived for two DDS that both admit a piecewise smooth ISS Lyapunov function. This result is constructive in the sense that an explicit ISS Lyapunov function for the interconnected system is given. It is shown how these results can be applied to construct piecewise quadratic ISS Lyapunov functions for piecewise linear systems (including sliding motions) via linear matrix inequalities.     

Predictive observer‐based control for networked control systems with network‐induced delay and packet dropout

This paper addresses the stability analysis and synthesis problems for a class of networked control systems (NCSs) under effects of both network‐induced delay and packet dropout. The motivation comes from the increasing NCS applications where the full state vector is not available. To handle the concerned problems, two predictive observer‐based controllers are constructed. The first one is a memoryless controller with the predictive observer collocated with the plant. The second one, with the predictive observer colocated with the controller, uses the last effective plant information as well as the knowledge of the plant dynamics. The stability conditions of NCSs are derived via both network‐condition‐dependent Lyapunov function and common quadric Lyapunov function. The corresponding controller design problems are also solved based upon the obtained stability conditions. Simulation and experimental results are given to demonstrate the effectiveness of the proposed approaches. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stability validation of a constrained model predictive networked control system with future input buffering

This paper addresses the stability of a newly-developed control strategy for networked control systems (NCS). This control strategy hones the potential of constrained model predictive control (MPC) by buffering the predicted control sequence at the actuator in anticipation of typical data transmission errors associated with NCS. Closed-loop stability in the sense of Lyapunov is guaranteed for the controller in the linear case, by bounding the projected receding horizon costs by lower- and upper-bounding terms using a predetermined terminal cost. A stability theorem is developed, which provides a suboptimal measure for the controller in real time, and is sufficient to estimate the worst-case transmission delay that can be handled by the developed control buffering strategy. The stability conditions, as governed by the theorem, are validated through real-time implementation on an electro-hydraulic servo system of an industrial processing machine, through an Ethernet network.     

一类非线性网络控制系统镇定的新方法

研究了一类非线性网络控制系统(Networked control systems, NCSs)的镇定问题. 在一般的网络环境中, 通过平行分布补偿技术, 将非线性NCS建模为包含一个稳定子系统和一个可能不稳定子系统的模糊时滞切换系统. 利用分段Lyapunov泛函方法和平均驻留时间方法, 得到了非线性NCS指数稳定的充分条件, 并以线性矩阵不等式(Linear matrix inequality, LMI) 形式给出了模糊控制器的设计方法. 最后通过数值例子说明了所给方法的有效性.     

Changing supply rates for input-output to state stable discrete-time nonlinear systems with applications

We present results on changing supply rates for input-output to state stable discrete-time nonlinear systems. Our results can be used to combine two Lyapunov functions, none of which can be used to verify that the system has a certain property, into a new composite Lyapunov function from which the property of interest can be concluded. The results are stated for parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used to design a controller for a sampled-data system. We present several applications of our results: (i) a LaSalle criterion for input to state stability (ISS) of discrete-time systems; (ii) constructing ISS Lyapunov functions for time-varying discrete-time cascaded systems; (iii) testing ISS of discrete-time systems using positive semidefinite Lyapunov functions; (iv) observer-based input to state stabilization of discrete-time systems. Our results are exploited in a case study of a two-link manipulator and some simulation results that illustrate advantages of our approach are presented.     

Lyapunov functions for time-varying systems satisfying generalized conditions of Matrosov theorem

The classical Matrosov theorem concludes uniform asymptotic stability of time-varying systems via a weak Lyapunov function (positive definite, decrescent, with negative semi-definite derivative along solutions) and another auxiliary function with derivative that is strictly nonzero where the derivative of the Lyapunov function is zero (Mastrosov in J Appl Math Mech 26:1337–1353, 1962). Recently, several generalizations of the classical Matrosov theorem have been reported in Loria et al. (IEEE Trans Autom Control 50:183–198, 2005). None of these results provides a construction of a strong Lyapunov function (positive definite, decrescent, with negative definite derivative along solutions) which is a very useful analysis and controller design tool for nonlinear systems. Inspired by generalized Matrosov conditions in Loria et al. (IEEE Trans Autom Control 50:183–198, 2005), we provide a construction of a strong Lyapunov function via an appropriate weak Lyapunov function and a set of Lyapunov-like functions whose derivatives along solutions of the system satisfy inequalities that have a particular triangular structure. Our results will be very useful in a range of situations where strong Lyapunov functions are needed, such as robustness analysis and Lyapunov function-based controller redesign. We illustrate our results by constructing a strong Lyapunov function for a simple Euler-Lagrange system controlled by an adaptive controller and use this result to determine an ISS controller.     

Stabilization of Networked Stochastic Time-Delay Fuzzy Systems With Data Dropout

This paper deals with the problem of stabilization for networked stochastic systems with transmitted data dropout. The plant in the networked control system (NCS) under consideration is a discrete stochastic time-delay nonlinear system represented by a Takagi-Sugeno fuzzy model. Exponential stability criteria of the NCS are developed by using a common quadratic Lyapunov function and a fuzzy Lyapunov function, respectively. A stabilization controller with convergence rate constraint can be designed by solving a set of linear matrix inequalities that is numerically feasible with commercially available software. Three numerical examples are presented to demonstrate the effectiveness of the proposed methods.     

Adaptive predictive functional control for networked control systems with random delays

Nowadays, more and more field devices are connected to the central controller through a serial communication network such as fieldbus or industrial Ethernet. Some of these serial communication networks like controller area network (CAN) or industrial Ethernet will introduce random transfer delays into the networked control systems (NCS), which causes control performance degradation and even system instability. To address this problem, the adaptive predictive functional control algorithm is derived by applying the concept of predictive functional control to a discrete state space model with variable delay. The method of estimating the network-induced delay is also proposed to facilitate the control algorithm implementing. Then, an NCS simulation research based on TrueTime simulator is carried out to validate the proposed control algorithm. The numerical simulations show that the proposed adaptive predictive functional control algorithm is effective for NCS with random delays.     

Fault tolerant control for networked control systems with packet loss and time delay

In this paper, a fault tolerant control with the consideration of actuator fault for a networked control system (NCS) with packet loss is addressed. The NCS with data packet loss can be described as a switched system model. Packet loss dependent Lyapunov function is used and a fault tolerant controller is proposed respectively for arbitrary packet loss process and Markovian packet loss process. Considering a controlled plant with external energy-bounded disturbance, a robust H _∞ fault tolerant controller is designed for the NCS. These results are also expanded to the NCS with packet loss and networked-induced delay. Numerical examples are given to illustrate the effectiveness of the proposed design method.