LMI approach to reliable H_∞ control of linear systems

The reliable design problem for linear systems is concerned with. A more practical model of actuator faults than outage is considered. An LMI approach of designing reliable controller is presented for the case of actuator faults that can be modeled by a scaling factor. The resulting control systems are reliable in that they provide guaranteed asymptotic stability and H∞ performance when some control component （actuator） faults occur. A numerical example is also given to illustrate the design procedure and their effectiveness. Furthermore, the optimal standard controller and the optimal reliable controller are compared to show the necessity of reliable control.

Robust reliable guaranteed cost control for uncertain singular systems with time-delay

The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.

Model-Based Fault Tolerant Control for Hybrid Dynamic Systems with Sensor Faults

A model-based fault tolerant control approach for hybrid linear dynamic systems is proposed in this paper. The proposed method, taking advantage of reliable control, can maintain the performance of the faulty system during the time delay of fault detection and diagnosis (FDD) and fault accommodation (FA), which can be regarded as the first line of defence against sensor faults. Simulation results of a three-tank system with sensor fault are given to show the efficiency of the method.

Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay

To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.

Robust reliable H-infinity control for nonlinear uncertain stochastic time-delay systems with Markovian jumping parameters

This paper deals with the problems of robust reliable exponential stabilization and robust stochastic stabilization with H-infinity performance for a class of nonlinear uncertain time-delay stochastic systems with Markovian jumping parameters. The time delays are assumed to be dependent on the system modes. Delay-dependent conditions for the solvability of these problems are obtained via parameter-dependent Lyapunov functionals. Furthermore, it is shown that the desired state feedback controller can be designed by solving a set of linear matrix inequalities. Finally, the simulation is provided to demonstrate the effectiveness of the proposed methods.

Robust reliable H_∞ control for discrete-time Markov jump linear systems with actuator failures

The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures, The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities （LMIs）. A numerical example is also given to illustrate the design procedures and their effectiveness.

Robust H-infinity reliable control for a class of nonlinear uncertain neutral delay systems

This paper focuses on the robust H-infinity reliable control for a class of nonlinear neutral delay systems with uncertainties and actuator failures. We design a state feedback controller in terms of linear matrix inequality(LMI)such that the plant satisfies robust H-infinity performance for all admissible uncertainties, and actuator failures among a prespecified subset of actuators. An example is also given to illustrate the effectiveness of the proposed approach.

Suboptimal reliable guaranteed cost control for continuous-time systems with multi-criterion constraints

The suboptimal reliable guaranteed cost control （RGCC） with multi-criterion constraints is investigated for a class of uncertain continuous-time systems with sensor faults. A fauk model in sensors, which considers outage or partial degradation of sensors, is adopted. The influence of the disturbance on the quadratic stability of the closed-loop systems is analyzed. The reliable state-feedback controller is developed by a linear matrix inequalities （LMIs） approach, to minimize the upper bound of a quadratic cost fimction under the conditions that all the closed-loop poles be placed in a specified disk, and that the prescribed level of H∞ disturbance attenuation and the upper bound constraints of control inputs＇ magnitudes be guaranteed. Thus, with the above muki-criterion constraints, the resulting closed-loop system can provide satisfactory stability, transient property, a disturbance rejection level and minimized quadratic cost performance despite possible sensor faults.

Dynamic estimation and reliability control of quality assurance for bored piles

A systematic method was proposed to estimate the occurrence probability of defective piles(OPDP) from a site according to quality assurance inspection. The OPDP was firstly suggested as the criterion to weight the performance of a pile foundation. Its prior distribution and updating distribution were deduced to follow Beta distributions. To calibrate the OPDP, a dynamic estimation model was established according to the relationships between prior mean and variance and updating mean and variance. Finally, a reliability-control method dealing with uncertainties arising from quality assurance inspection was formalized to judge whether all the bored piles from a site can be accepted. It is exemplified that the OPDP can be substantially improved when more definite prior information and sampling formation become available. For the example studied herein, the Bayesian estimator of updating variance for OPDP is reduced from 0.0037 to 0.0014 for the first inspection, from 0.0014 to 0.0009 for the second inspection, and with less uncertainty by incorporating experience information.

Robust H_∞ reliable control for uncertain singular systems with state delay

The problem of robust and H∞ reliable control for a class of uncertain singular systems with state time-delay is concerned. The problem we address is to design a state feedback controller such that the resulting close-loop systems is regular, impulse free and stable for all admissible uncertainties as well as actuator faults among a prespecified subset. A linear matrix inequality （LMI） design approach is proposed to solve the problem addressed with Hoo norm bound constraint on disturbance attenuation. Finally, a numerical example is provided to demonstrate the application of the proposed method.

Robust reliable H_∞ control for a class of uncertain time-delay systems

This paper deals with the problem of robust reliable H∞ control for a class of uncertain nonlinear systems with time-varying delays and actuator failures. The uncertainties in the system are norm-bounded and time-varying. Based on Lyapunov methods, a sufficient condition on quadratic stabilization independent of delay is obtained. With the help of LMIs (linear matrix inequalities) approaches, a linear state feedback controller is designed to quadratically stabilize the given systems with a H∞ performance constraint of disturbance attenuation for all admissible uncertainties and all actuator failures occurred within the prespecified subset. A numerical example is given to demonstrate the effect of the proposed design approach.

Reliable Memory Feedback Design for a Class of Nonlinear Fuzzy Systems with Time-varying Delay

This paper is concerned with the robust reliable memory controller design for a class of fuzzy uncertain systems with timevarying delay. The system under consideration is more general than those in other existent works. The controller, which is dependent on the magnitudes and derivative of the delay, is proposed in terms of linear matrix inequality （LMI）. The closed-loop system is asymptotically stable for all admissible uncertainties as well as actuator faults. A numerical example is presented for illustration.

A Family of Reliable H_∞ State-Feedback Controllers for Nonlinear Systems with Strictly Redundant Actuators: the Full Information Case

The paper is concerned with the reliable H ∞ state feedback control and controller parameterization problem for nonlinear systems with strictly redundant actuators. Based on Hamilton Jacobi inequality, the sufficient condition is presented such that the reliable control problem is resolved, and a family of controllers is given such that the resulting closed loop systems are asymptotically stable and their L 2 gain is limitable not only when all actuators are operational but also when any one,but only one of actuators experiences an outage. The results of this paper provide a deep insight into the synthesis of the reliable nonlinear H ∞ state feedback.

Software Reliability Experimentation and Control

This paper classifies software researches as theoretical researches, experimental researches, and engineering researches, and is mainly concerned with the experimental researches with focus on software reliability experimentation and control. The state-of-the-art of experimental or empirical studies is reviewed. A new experimentation methodology is proposed, which is largely theory discovering oriented. Several unexpected results of experimental studies are presented to justify the importance of software reliability experimentation and control. Finally, a few topics that deserve future investigation are identified.

Reliable Control for Nonlinear Systems with Stochastic Actuators Fault and Random Delays Through a T-S Fuzzy Model Approach

This paper considers the reliable control design for T-S fuzzy systems with probabilistic actuators faults and random time-varying delays. The faults of each actuator occurs randomly and its failure rates are governed by a set of unrelated random variables satisfying certain probabilistic distribution. In terms of the probabilistic failures of each actuator and time-varying random delays, new fault model is proposed. Based on the new fuzzy model, reliable controller is designed and sufficient conditions for the exponentially mean square stability （EMSS） of T-S fuzzy systems are derived by using Lyapunov functional method and linear matrix inequality （LMI） technique. It should be noted that the obtained criteria depend on not only the size of the delay, but also the probability distribution of it. Finally, a numerical example is given to show the effectiveness of the proposed method.

Reliable control of discrete-time linear systems with actuator failure

A sufficient condition is given for robust stability of a discrete linear system in which an arbitrary portion of input channel is permanently attenuated or disconnected due to actuator fault.The partial disconnection/attenuation of the control input,is modelled as uncertainty and dealt with via a robust control method.The proposed method enables one to design a controller in such a way that the closed loop system remains stable when any combination of input signals is disconnected if the open loop system is stable and fulfils some additional properties.It is shown that the linear quadratic regulator can guarantee reliable closed loop with some specific choices for weighting matrices.The result is extended to unstable systems by assuming additional constraints on the failed actuators.Compared to previously established results,the proposed conditions are easier to verify and applicable to a wider class of systems.An example is also included.

Fault-distribution-dependent reliable control for time-varying delay system

This paper considers the problem of reliable control for continuous-time systems with interval time-varying delay. By introducing a random matrix, a new practical actuator fault model is established. Using the Lyapunov-Krasovskii approach, a sufficient condition for the existence of reliable controller is expressed by a linear matrix inequality（LMI）. An illustrative example is exploited to show the effectiveness, of the proposed design procedures.

Non-fragile reliable control for positive Markovian jump systems based on event-triggered mechanism

This paper is concerned with the non-fragile reliable control of positive Markovian jump systems with actuator saturation based on event-triggered mechanism.First,an event-triggering condition is given in the form of 1-norm.Using a stochastic co-positive Lyapunov function,a design approach is proposed for the non-fragile controller gain and the corresponding auxiliary feedback gain.Under the designed controller,the closed-loop system is positive and stochastically stable even if actuator faults occur.A cone is constructed as the invariant set of the systems.All conditions are solvable in terms of linear programming.Finally,two examples are provided to verify the effectiveness of the obtained results.

An Enhanced LMI Approach for Mixed H2/H∞ Flight Tracking Control

The coupling between the Lyapunov variables and system matrices makes the problem of mixed H2/H∞ flight tracking controller design non-convex. With the aid of enhanced linear matrix inequality （LMI） approach, the non-convex optimization problem is transformed into convex LMI representations. The proposed coupling is eliminated by introducing slack variables. Moreover, a necessary and sufficient condition is derived for the mixed H2/H∞ flight tracking controller which not only stabilizes the controlled system but also satisfies the mixed H2/H∞ performance index in normal case and fault cases. The new enhanced LMI representations provide additional degrees of freedom to solve the non-convex optimization problem, and reduce the conservativeness of the controller design. Simulation results of the aero-data model in a research environment （ADMIRE） model show the advantages of the enhanced LMI approach.