Optimal guaranteed cost stabilization of networked systems with bounded random packet losses

This paper is concerned with the optimal guaranteed cost stabilizing controller design problem for a class of networked control systems (NCSs) with random packet losses. The number of consecutive packet losses is assumed to be upper bounded, and the closed‐loop NCS is described as a discrete‐time stochastic delay system with a time‐varying input delay and a stochastic parameter. A sufficient condition is derived for the closed‐loop NCS to be exponentially stable and achieve an optimal guaranteed cost performance level. The relationships among the exponential decay rate, the guaranteed cost performance level, and two parameters characterizing the random packet losses, namely, the packet loss probability and the maximal number of consecutive packet losses, are simultaneously established in the obtained condition. Furthermore, design procedures for the state feedback stabilizing controllers are also presented. Finally, an illustrative example is given to show the effectiveness of the proposed results. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust guaranteed cost control of discrete‐time networked control systems

This paper is concerned with the robust guaranteed cost control problem for networked control systems (NCSs). The plant considered is an uncertain linear discrete‐time system, where the communication limitations include packet‐loss and signal transmission delay. Our purpose is to design a robust state‐feedback guaranteed cost controller such that the resulting closed‐loop system is robustly stable, and a specified quadratic cost function is upper bound for all admissible uncertainties under such communication limitations. A model of NCSs is established which contains two additive delay components, one being a known constant, and the other unknown constant. By introducing a novel Lyapunov‐Krasoviskii function with the idea of delay partitioning, new sufficient conditions for the existence of guaranteed cost controllers are proposed. Numerical examples are provided to demonstrate the usefulness of the developed theory. Copyright © 2010 John Wiley & Sons, Ltd.     

H∞ output tracking control over networked control systems with Markovian jumping parameters

The problem of H_∞ output tracking control over networked control systems (NCSs) with communication limits and environmental disturbances is studied in this paper. A wide range of time‐varying stochastic problem arising in networked tracking control system is reduced to a standard convex optimization problem involving linear matrix inequalities (LMIs). The closed‐loop hybrid NCS is modeled as a Markov jump linear system in which random time delays and packet dropouts are described as two stochastic Markov chains. Gridding approach is introduced to guarantee the finite value of the sequences of transmission delays from sensor to actuator. Sufficient conditions for the stochastic stabilization of the hybrid NCS tracking system are derived by the LMI‐based approach through the computation of the optimal H_∞ performance. The mode‐dependent robust H_∞ output tracking controller is obtained by the optimal iteration method. Numerical examples are given to demonstrate the effectiveness of the proposed robust output tracking controller for NCS. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust reliable control for discrete‐time‐delay systems with stochastic nonlinearities and multiplicative noises

This paper is concerned with the reliable control problem against actuator failures for a class of uncertain discrete‐time stochastic nonlinear time‐delay systems. The failures of actuators are quantified by a variable varying in a given interval. The stochastic nonlinearities described by statistical means cover several well‐studied nonlinear functions as special cases. The time‐varying delay is unknown with given lower and upper bounds. The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. Attention is focused on the analysis and design of a stable controller such that, for all possible actuator failures, stochastic nonlinearities and disturbances, time delays and admissible parameter uncertainties, the closed‐loop system is exponentially mean‐square stable. A linear matrix inequality approach is developed to solve the addressed problem. A numerical example is given to demonstrate the effectiveness of the proposed design approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal linear quadratic Gaussian control for discrete time-varying system with simultaneous input delay and state/control-dependent noises

This article focuses on the problem of linear quadratic Gaussian (LQG) control for discrete time-varying system with input delay and state/control-dependent noises. When the state variables can be exactly observed, first, we obtain the maximum principle by applying the method of variation. Second, a nonhomogeneous relationship between the state and the costate is developed in virtue of the obtained maximum principle and the mathematical induction. It is noted that the nonhomogeneous relationship is the solution to the forward and backward stochastic difference equations (FBSDEs). Finally, based on the solution to the FBSDEs, a necessary and sufficient condition for the optimal LQG control is derived in terms of coupled Riccati equations. Moreover, the analytical expression of the optimal controller is presented. The derived results are applied in networked control systems with packet dropout. Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.     

Dynamic output feedback of networked control systems with partially known Markov chain packet dropouts

In this paper, a class of networked control systems with output feedback control and H _∞ performance is discussed. It considers packet dropouts in both measurement (S/C) and actuation (C/A) channels. Markovian chain principle is used in modeling the packet dropouts in S/C and C/A channels. The time scale adopted in these two independent homogeneous Markov chain is linear with the physical time. The model also takes into consideration the late arriving packets. The effect of interaction between packet dropouts in both channels on the stability of system, when the networks of both (S/C) and (C/A) channels overlap is also examined. Sufficient condition for the existence of H _∞ output feedback controller is presented and it is shown that it is dependent on the upper bounds of the number of consecutive packet dropouts. The developed stability analysis and control scheme is also investigated with partially known transition probability matrices. Finally, a numerical example has been given to show the effectiveness of developed method. Copyright © 2013 John Wiley & Sons, Ltd.     

State estimation for a networked control system with packet delay,packet dropouts,and uncertain observation in S-E and C-A channels

In this work, a minimum variance estimator is designed for a networked system with inherent network imperfections in both sensor to estimator (S-E) and controller to actuator (C-A) channels simultaneously. The channels are affected by packet delays, dropouts, and uncertain observations. These effects are modeled using five Bernoulli distributed random variables. Correlation of noise at neighboring time caused by random delay is avoided by introducing two additional variables in the augmented stochastic model. The developed augmented stochastic model can handle network imperfections in both the S-E and C-A channels simultaneously. A minimum variance recursive linear estimator is designed using an innovation approach and projection theorem. Furthermore, sufficient condition is presented for the existence of steady state property of the proposed estimator. Simulation studies are carried out for the proposed estimator using a numerical example and a single link robot arm. Finally, performance comparison with other popular filters shows the effectiveness of the designed estimator.     

Robust fault detection for networked control systems with packet dropouts: An average dwell time method

The problem of fault detection for networked control systems with respect to packet dropouts is investigated in this paper based on average dwell time method. For the cases that there may be sensor stuck failure and packet dropouts, the networked control systems are modeled as discrete time switched systems. Subsequently, a novel fault detection scheme, which is valid to detect the failures with small magnitudes even the outage ones, is proposed by making the generated residuals sensitive to servo inputs in faulty cases and robust against it in normal case. By utilizing the average dwell time method, new sufficient conditions, which include some existing results, for characterizing the sensitivity performance and the attenuation performance are presented in terms of linear matrix inequalities. Meanwhile, the relation between the packet dropout rate and the system performance is established. Finally, an application of a linearized aircraft is given to demonstrate the effectiveness of the proposed results. Copyright © 2014 John Wiley & Sons, Ltd.     

Delay‐dependent robust H ∞ control for uncertain singular time‐delay system with Markovian jumping parameters

The problem of robust H _∞ control for a class of uncertain singular time‐delay systems with Markovian jumping parameters is addressed in this paper. The considered Markovian jump singular systems involve constant time delay and norm‐bounded uncertainties. On the basis of LMI approach, a delay‐dependent condition is proposed, which ensures the nominal Markovian jump singular system to be regular, impulse‐free and stochastically stable. From the delay‐dependent condition, a sufficient condition leading to the existence of a state feedback controller that guarantees the robust admissibility and the H _∞ performance is also given. A numerical example is given to demonstrate the applicability of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal dropout policies for networked control systems

By realizing the feedback paths over communication networks, we get a class of networked control systems (NCSs), where the network's quality‐of‐service (QoS) is commonly characterized by the average dropout rate of feedback data packets. The control performance of an NCS however, is determined not only by the average dropout rate but also by the dropout pattern of feedback data packets. This paper provides a systematic way to determine the optimal dropout pattern (policy) under a given average dropout rate, where the performance is measured by the output signal power under an exogenous white noise. By modeling the finite‐memory dropout policies with the general Markov chain, this paper formulates the optimal dropout policy design into the optimization of parameters of a dropout Markov chain. That optimization is first solved by an augmented Lagrangian gradient method, which may be stuck at local optima because of the problem's non‐convexity. To compensate this weakness, we apply the branch‐and‐bound method to the optimization whose constraints are bilinear. The branch‐and‐bound method can approach the global optimal solution with any desired tolerance in finite steps. The obtained optimal dropout policy may be interpreted as a network's QoS constraint whose enforcement provides a hard guarantee on the control system's performance. An example is used to illustrate the effectiveness of the achieved results. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust H∞ control of stochastic time‐delay jumping systems with nonlinear disturbances

This paper deals with the problems of robust stabilization and H_∞ control for a class of uncertain stochastic jumping systems with nonlinear disturbances and time delays. The uncertain parameters are assumed to be norm‐bounded and mode dependent, and the time delays enter into the state matrix, the stochastic perturbation term, as well as the state feedback. The stochastic robust stabilization problem addressed in this paper is to design a state feedback controller with input delay such that, for all admissible uncertainties and the nonlinear disturbances, the closed‐loop system is robustly, stochastically, exponentially stable in the mean square. Moreover, the purpose of the robust H_∞ control problem is to guarantee a specified H_∞ performance index, while still achieving the mean‐square exponential stability requirement for the closed‐loop system. By resorting to the Itô's differential formula and the Lyapunov stability theory, sufficient conditions are derived, respectively, for the robust stabilization and the robust H_∞ control problems. It is shown that the addressed problems can be solved if a set of linear matrix inequalities (LMIs) are feasible. A numerical example is employed to illustrate the usefulness of the proposed LMI‐based design methods. Copyright © 2006 John Wiley & Sons, Ltd.     

Observer‐based H∞ control for uncertain singular time‐delay systems with actuator saturation

In this paper, the observer‐based H_∞ control problem for uncertain singular time‐delay systems with actuator saturation is concerned. First, a delay‐dependent linear matrix inequality (LMI) condition is obtained which, guarantees that the uncertain singular time‐delay systems with actuator saturation are regular, impulse free, and asymptotically stable with H_∞ performance condition. Then, with this condition, the estimation of stability region and the design method of observer‐based H_∞ controller are given by solving LMIs and convex optimization problem. Finally, some numerical examples are provided to demonstrate the merit of the obtained results. Copyright © 2015 John Wiley & Sons, Ltd.     

Dissipative control for singular Markovian jump systems with time delay

This paper focuses on the problem of dissipative control for continuous‐time singular time‐delayed systems with Markovian jump parameters. Different from usually mode‐dependent or mode‐independent controller design methods, a partially mode‐dependent dissipative controller is firstly proposed via using a mode‐dependent Lyapunov function. The stochastic property of the mode available to a controller operation is taken into consideration in the corresponding controller design. Moreover, the existence of the established controller is given in terms of strict linear matrix inequalities. Finally, numerical examples are used to demonstrate the effectiveness of the given theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Delay‐dependent H∞ control for singular Markovian jump systems with time delay

The problem of delay‐dependent H_∞ control is considered for singular Markovian jump systems with time delay. The aim of the problem is to design a state feedback controller, which guarantees that the resultant closed‐loop system is not only regular, impulse free and stochastically stable, but also satisfies a prescribed H_∞ performance level for all delays no larger than a given upper bound in terms of linear matrix inequality (LMI) approach. A strict LMI condition is developed to guarantee the existence of the desired state feedback controller. An explicit expression for the desired controller is also given. Numerical examples show the effectiveness of the proposed methods. Copyright © 2008 John Wiley & Sons, Ltd.     

Secondary delay‐partition approach on robust performance analysis for uncertain time‐varying Lurie nonlinear control system

This paper investigates the problem of robust performance analysis for Lurie nonlinear control system with parameter uncertainties and interval time‐varying delays. Based on an augmented Lyapunov‐Krasovskii functional including multiple integral terms, new delay‐dependent robust stability criteria are derived by proposing a novel secondary delay‐partition approach. Moreover, to obtain less conservative stability conditions, an optimized integral inequality is developed by introducing an adjustable parameter ? ₁. Finally, 5 numerical simulation examples are given to illustrate the effectiveness and advantages of the proposed results.     

Delay‐dependent output feedback L1 control for positive Markovian jump systems with mode‐dependent time‐varying delays and partly known transition rates

The paper deals with the problem of delay‐dependent output feedback L₁ control for positive Markovian jump systems with mode‐dependent time‐varying delays and partly known transition rates. First, by constructing an appropriate co‐positive type Lyapunov function, sufficient conditions for stochastic stability and L₁‐gain performance of the open‐loop system are developed. Then, an effective method is proposed to construct the output feedback controller. These sufficient criteria are derived in the form of linear programming. A key point of this paper is to extend the special requirement of completely known transition rates to more general form that covers completely known and completely unknown transition rates as two special cases. Finally, a numerical example is given to illustrate the validity of the main results. Copyright © 2016 John Wiley & Sons, Ltd.     

Mixed H2/H∞ control for a class of nonlinear discrete‐time networked control systems with random delays and stochastic packet dropouts

The paper studies the problem of mixed H₂/H_∞ control for a class of nonlinear discrete‐time networked control systems. By using the indicator function method, random network‐induced delays and stochastic packet dropouts are taken into account in a unified framework in the designed mixed H₂/H_∞ controller. In the presences of random transmission delays, stochastic packet dropouts and all admissible disturbances, the resulting closed‐loop system is stochastically stable in mean square and attains the prescribed H₂ and H_∞ performances. The designed mixed H₂/H_∞ controller can be obtained by solving a set of feasible linear matrix inequalities. Finally, a numerical example is provided to show the usefulness and effectiveness of the developed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Quantized event-triggered H∞ control of linear networked systems with time-varying delays and packet losses

This paper studies the event-triggered (ET) H_∞ control of linear networked systems based on static output-feedback. An emulation-based stabilization of the networked system is investigated under the constraints such as (i) quantizations, (ii) network-induced delays, (iii) external disturbances, and (iv) packet losses. In particular, output measurement and control input quantizations, lower and upper bounds of the network-induced delays, bounded external disturbances, and packet losses are carefully taken into account. The process of stability analysis has three steps. In the first step, a quantized ET control is defined, and then three sector-bound methods for logarithmic quantization are formulated. In the second step, the ET-mechanism is described with an input delay model. Based on the model, for two approaches, namely, switching-ET and periodic-ET, the criteria for the exponential stability and L₂ -gain analysis of perturbed networked system are established, respectively. In the third step, a constraint for packet loss effect is provided. In summary, the stability analysis is based on linear matrix inequalities (LMIs) through a Lyapunov-Krasovskii functional method. Finally, the simulation results are given to evaluate the validation of the analysis using two benchmark examples.     

Design of ℋ︁∞ fuzzy controllers for nonlinear systems with random data dropouts

The problem of ??_∞ control of nonlinear networked control systems subject to random data dropout is concerned in this paper. The random data dropout, because of the limited bandwidth of the network channels, could exist in the communication channels both from the sensor to the controller and from the controller to the actuator simultaneously. The nonlinear plant is represented by the well‐known Takagi–Sugeno fuzzy model and the random data dropout is expressed by the Bernoulli random binary distribution. In the presence of random data dropout, two control schemes, state feedback and static output feedback, are proposed to design ??_∞ controllers such that the closed‐loop system is stochastically stable and preserves a guaranteed ??_∞ performance. The addressed controller design problem is transformed to an auxiliary convex optimization problem, which can be solved by a linear matrix inequality approach. Three examples are provided to illustrate the applicability and less conservativeness of the developed theoretical results. It is easy to see that our approach is simple but our results are much less conservative than the recently published results. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal control for discrete‐time singular stochastic systems with input delay

The finite‐horizon linear quadratic regulation problem is considered in this paper for the discrete‐time singular systems with multiplicative noises and time delay in the input. Firstly, the extremum principle is discussed, and a stationary condition is derived for the singular stochastic system. Then, based on the relationships established between the state and the costate variables, the stationary condition is also shown to be a sufficient criterion assuring the existence of the solution for the stochastic control problem. The optimal controller is designed as a linear function of the current state and the past inputs information, which can be recursively calculated by effective algorithms. With the designed optimal controllers, the explicit expression is also derived for the minimal value of the performance index. One numerical example is provided in the end of the paper to illustrate the effectiveness of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.