Stabilization of networked control systems with nonuniform random sampling periods

In this paper, a new linear delayed delta operator switched system model is proposed to describe networked control systems with packets dropout and network‐induced delays. The plant is a continuous‐time system, which is sampled by time‐varying random sampling periods. A general delta domain Lyapunov stability criterion is given for delta operator switched systems with time delays. Sufficient conditions for asymptotic stability of closed‐loop networked control systems with both packets dropout and network‐induced delays are presented in terms of linear matrix inequalities (LMIs). A verification theorem is given to show the solvability of the stabilization conditions by solving a class of finite LMIs. Both the case of data packets arrive instantly and the case of invariant sampling periods in delta operator systems are given, respectively. Three numerical examples are given to illustrate the effectiveness and potential of the developed techniques. Copyright © 2010 John Wiley & Sons, Ltd.     

Model predictive control of distributed networked control systems with quantization and switching topology

This work is concerned with the robust model predictive control (MPC) for a class of distributed networked control systems (NCSs), in which the input quantization and switching topology are both considered. By utilizing the sector bound approach, the NCSs with quantization are converted into the linear systems with sector bound uncertainties. The topology switching is governed by a switching signal and the dynamic behavior is modeled as a switched control system. A new robust MPC design technique is derived to minimize the upper bound of a weighted quadratic performance index. Moreover, the conditions of both the recursive feasibility of the MPC design and the stability of the resulting closed‐loop system are developed. Finally, simulation results are presented to verify the effectiveness of the proposed MPC design.     

Improved closed‐loop stability for fixed‐point controller realizations using the delta operator

A stable discrete‐time control system may achieve a lower than predicted performance or even become unstable when the discrete‐time control law is implemented with a fixed‐point digital control processor due to the finite word length (FWL) effects, which depends on the control law state‐space realization and the discrete‐time operator (e.g., the delta operator or the forward‐shift operator) used to represent the control law. To improve the closed‐loop stability (and as a byproduct, performance) when the control law is implemented, a state‐space approach that selects the control law realization to optimize a stability‐related objective function is developed using the delta operator. Analytical and numerical comparison of the fixed‐point performance of delta control laws with the performance of the corresponding forward‐shift control laws quantifies the improved closed‐loop stability of the delta realizations over those of the corresponding forward‐shift realizations. It is also shown that there exists a simple mapping between the optimal FWL forward‐shift control law realizations and the optimal FWL delta control law realizations. The results are illustrated by delta and forward‐shift control law realizations of a discrete‐time H_∞ control law designed for a teleoperation motion‐scaling system. Copyright © 2001 John Wiley & Sons, Ltd.     

A periodic approach for input‐delay problems: Application to network controlled systems affected by polytopic uncertainties

This paper deals with robust stability and stabilization of linear discrete‐time systems subject to uncertainties and network constraints. In network control systems, the control loop is closed over a network, which induces additional dynamics to the original control loop such as delays, sampling, and quantization among many others. This paper focuses on networked induced delays due to unreliable network for which packet losses may occur. An equivalent periodic‐like representation of the resulting system is proposed. This allows first to revisit existing results in this framework and second to take model uncertainties into account by analyzing the closed‐loop model by means of a recent method based on robust control for discrete‐time time‐varying systems. Stability analysis and dynamic state‐feedback stabilization are characterized via new conditions, whose conservatism is extensively discussed. Effectiveness of the proposed methodology is illustrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Quantized sliding mode control in delta operator framework

This paper is concerned with quantized sliding mode control in the unified delta operator system framework. To solve the quantization measurement saturating problem, a dynamic quantization strategy including discrete on‐line open‐loop zooming‐out and closed‐loop zooming‐in policies is presented. By analyzing the sign relation between the traditional linear switching function and the quantized linear switching function, a novel quantized sliding mode control method is proposed, and both the amplitude of the control gain and the value of the quantization measurement saturating parameter are reduced compared with previous results. Some simulation results are presented to verify the effectiveness of the proposed method.     

Stabilization of fuzzy systems with quantization and packet dropout

The discrete‐time and continuous‐time fuzzy systems with quantization and packet dropout are considered in this paper. The quantizer used here is a uniform one with arbitrary quantization regions, and the packet dropout process is modeled as a time‐homogenous Markov process. Because of the properties of packet dropout process, the fuzzy systems considered here are seen as Markov jump fuzzy systems, and the theories of Markov jump system are used to discuss the mean square stability of the closed‐loop systems. On the basis of the zoom strategy and Lyapunov theory, for the given failure rate and recovery rate, sufficient conditions are given for the closed‐loop fuzzy systems to be mean square stable, and the feedback controllers are designed to ensure the stability of fuzzy systems. A single link direct joint driven manipulator model is presented to show the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd.     

Model predictive control for networked control systems

This paper investigates the problem of model predictive control for a class of networked control systems. Both sensor‐to‐controller and controller‐to‐actuator delays are considered and described by Markovian chains. The resulting closed‐loop systems are written as jump linear systems with two modes. The control scheme is characterized as a constrained delay‐dependent optimization problem of the worst‐case quadratic cost over an infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the stochastic stability of the closed‐loop system. Copyright © 2008 John Wiley & Sons, Ltd.     

Asymptotic Stability and Finite‐Time Stability of Networked Control Systems: Analysis and Synthesis

This paper focuses on the problems of asymptotic stability and finite‐time stability (FTS) analysis, along with the state feedback controller design for networked control systems (NCSs) with consideration of both network‐induced delay and packet dropout. The closed‐loop NCS is modeled as a discrete‐time linear system with a time‐varying, bounded state delay. Sufficient conditions for the asymptotic stability and the FTS of the closed‐loop NCS are provided, respectively. Based on the stability analysis results, a mixed controller design method, which guarantees the asymptotic stability of the closed‐loop NCS in the usual case and the FTS of the closed‐loop NCS in the unusual case (that is, in some particular time intervals, large state delay occurs), is presented. A numerical example is provided to illustrate the effectiveness of the proposed mixed controller design method.     

Insensitive output feedback H ∞ control of delta operator systems with insensitivity to sampling time jitter

The insensitive multi‐objective H _∞ control synthesis problem via dynamic output feedback for linear delta operator systems with insensitivity to sampling time jitter is investigated in the case of small sampling times. The delta‐domain model instead of the standard shift‐domain model is used to avoid the inherent numerical ill‐condition resulting from using the latter model at high sampling rates. Parameter sensitivity function of the transfer function with respect to sampling time is defined to mitigate the effect of sampling time jitter because it may cause significant degradation of the overall system performance. It is worth pointing out that a novel bounded real lemma for delta operator allowing extra degree of freedom for multi‐objective control design is presented by using the well‐known projection lemma. Then, from this new lemma, a two‐step design procedure based on LMI is presented to design insensitive dynamic output feedback controllers such that the resulting closed‐loop system is asymptotically stable and meets the requirement of sensitivity specification. A numerical example is also presented to show the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Sliding mode fault‐tolerant control of uncertain system: A delta operator approach

This paper is concerned with the sliding mode control of uncertain nonlinear systems against actuator faults and external disturbances based on delta operator approach. The nonlinearity, actuator fault, and external disturbance are considered in this study, and the bounds of Euclidean norms of the nonlinearity and the specific lower and upper bounds of the actuator faults and the disturbances are unknown knowledge. Our attention is mainly focused on designing a sliding mode fault‐tolerant controller to compensate the effects from the nonlinearity, unknown actuator fault, and external disturbance. Based on Lyapunov stability theory, a novel‐adaptive fault‐tolerant sliding mode control law is deigned such that the resulting closed loop delta operator system is finite‐time convergence and the actuator faults can be tolerated, simultaneously. Finally, simulation results are provided to verify the effectiveness of the proposed control design scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Sampled‐data control of networked nonlinear systems with variable delays and drops

This paper investigates the stabilization problem of the nonlinear networked control systems (NCSs) with drops and variable delays. The NCS is modeled as a sampled‐data system. For such a sampled‐data NCS, the stability properties are studied for delay that can be both shorter and longer than one sampling period, respectively. The exponential stability conditions are derived in terms of the parameters of the plant and time delay. On the other hand, a model‐based control scheme based on an approximate discrete‐time model of the plant is presented to guarantee the stability of the closed‐loop system subject to variable time delays and packet losses. The performance of the proposed control schemes are examined through numerical simulations of an automated rendezvous and docking of spacecraft system. Moreover, the simulations show that by employing the model‐based controller, a higher closed‐loop control performance can be achieved. Copyright © 2013 John Wiley & Sons, Ltd.     

网络控制系统动态量化H∞控制

基于线性矩阵不等式技术,采用状态反馈控制,考虑同时带有网络诱导随机丢包 和量化的H∞控制问题。考虑信号经网络从传感器到控制器和从控制器到执行器的传输中存在 通信诱导随机丢包,并采用动态量化器量化信号。设计H∞控制器的同时,提出量化的控制策 略,使得闭环系统在量化器的量化范围条件下指数均方稳定且具有指定的H∞性能指标。通过 数值仿真例子表明设计方法的有效性。     

BIBO stability and stabilization of networked control systems with short time‐varying delays

This paper presents a robust control approach to solve the stability and stabilization problems for networked control systems (NCSs) with short time‐varying delays. A new discrete‐time linear uncertain system model is proposed to describe the NCS, and the uncertainty of the network‐induced delay is transformed into the uncertainty of the system matrix. Based on the obtained uncertain system model, a sufficient BIBO stability condition for the closed‐loop NCS is derived by applying the small gain theorem. The obtained stability condition establishes a quantitative relation between the BIBO stability of the closed‐loop NCS and two delay parameters, namely, the delay upper bound and the delay variation range bound. Moreover, design procedures for the state feedback stabilizing controllers are also presented. An illustrative example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Boundary control of linear stochastic reaction‐diffusion systems

This paper considers the boundary control problem for linear stochastic reaction‐diffusion systems with Neumann boundary conditions. First, when the full‐domain system states are accessible, a boundary control is designed, and a sufficient condition is established to ensure the mean‐square exponential stability of the resulting closed‐loop system. Next, when the full‐domain system states are not available, an observer‐based control is proposed such that the underlying closed‐loop system is stable. Furthermore, observer‐based controller is designed for the systems with an H_∞ performance. Simulation examples are given to demonstrate the effectiveness and potential of the new design techniques.     

Networked predictive control for Hammerstein systems

This paper is concerned with the problems of design and stability analysis of networked predictive control for Hammerstein systems. The Hammerstein nonlinearity is removed (or partially removed) by inverting it. By predicting the future control sequence, the random network‐induced delay and data dropout are compensated actively. The stability of the closed‐loop system is analyzed by applying the switched Lyapunov function approach. Simulation results are presented to illustrate the validity of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Decentralized control and communication

In this paper, the past and current issues involved in the design of decentralized networked control systems are reviewed. The basic models of interconnected systems described as continuous-time linear time-invariant systems in the time domain serve as a framework for the inclusion of communication channels in the decentralized feedback loop. The I/O-oriented models and the interaction oriented models with disjoint subsystems and interactions are distinguished. The overview is focused on packet dropouts, transmission delays, and quantization effects which are included in the time-driven design of feedback loop components. Single- and multiple-packet transmissions are considered in this contents. The design of decentralized state feedback gain matrices with delayed feedback uses the methodology of sampled-data feedback design for continuous-time systems, while the decentralized H_∞ quantizer design is based on the static output controller. The Liapunov stability approach results in computationally efficient decentralized control design strategies described by using linear matrix inequalities.     

Robust exponential stability of uncertain stochastic systems with probabilistic time‐varying delays

This paper is concerned with the problem of delay‐distribution–dependent robust exponential stability for uncertain stochastic systems with probabilistic time‐varying delays. Firstly, inspired by a class of networked systems with quantization and packet losses, we study the stabilization problem for a class of network‐based uncertain stochastic systems with probabilistic time‐varying delays. Secondly, an equivalent model of the resulting closed‐loop network‐based uncertain stochastic system is constructed. Different from the previous works, the proposed equivalent system model enables the controller design of the network‐based uncertain stochastic systems to enjoy the advantage of probability distribution characteristic of packet losses. Thirdly, by applying the Lyapunov‐Krasovskii functional approach and the stochastic stability theory, delay‐distribution–dependent robust exponential mean‐square stability criteria are derived, and the sufficient conditions for the design of the delay‐distribution–dependent controller are then proposed to guarantee the stability of the resulting system. Finally, a case study is given to show the effectiveness of the results derived. Moreover, the allowable upper bound of consecutive packet losses will be larger in the case that the probability distribution characteristic of packet losses is taken into consideration.     

Adaptive finite‐time control for nonlinear teleoperation systems with asymmetric time‐varying delays

This paper addresses the adaptive finite‐time control problem of nonlinear teleoperation system in the presence of asymmetric time‐varying delays. To achieve the finite‐time position tracking, a novel adaptive finite‐time coordination algorithm based on subsystem decomposition is developed. By introducing a switching‐technique‐based error filtering into our design framework, the complete closed‐loop master (slave) teleoperation system is modeled as a special class of switched system, which is composed of two subsystems. To analyze such system, a finite‐time state‐independent input‐to‐output stability criterion is first developed for some normal switched nonlinear delayed systems. Then based on the classical Lyapunov–Krasovskii method, the stability of complete closed‐loop systems is obtained. It is shown that the proposed scheme can make the position errors converge into a deterministic domain in finite time when the robots continuously contact with human operator and/or the environment in the presence of asymmetric time‐varying delays. Finally, the simulation results are given to demonstrate the effectiveness. Copyright © 2015 John Wiley & Sons, Ltd.     

Multi‐tasking optimal control of networked control systems: A delta operator approach

In this paper, the multi‐tasking optimal control problem is addressed in the delta‐domain for a class of networked control systems (NCSs) with external disturbances. A delta‐domain model is proposed to describe the NCSs with random packet dropouts and long‐time delay, and the so‐called ε‐Nash equilibrium is employed to quantify the impacts from the disturbances on the underlying NCSs. The multi‐tasking optimal control strategies are developed and the upper bound for the ε‐Nash equilibrium is provided explicitly. Some simulation results on the two‐area load frequency control system are given to show the validity and applicability of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Stabilization of Uncertain Systems With Markovian Modes of Time Delay and Quantization Density

This work studies the stabilization of a class of control systems that use communication networks as signal transmission medium. The lateral motion of independently actuated four-wheel vehicle is modeled as an uncertain-linear system. Time delay and quantization density are modeled as Markov chains. The networked control systems (NCSs) with plants being lateral motion are first transformed to switched linear systems with uncertain parameters. Sufficient and necessary conditions for the stochastic stability of closed-loop networked control systems are then established. By solving the matrix inequalities, this work presents an output-feedback controller that depends on the modes of time delay and quantization density. The controller performance is illustrated via a vehicular lateral motion system.