Network-Based Robust Passive Control for Fuzzy Systems With Randomly Occurring Uncertainties

This paper is concerned with the problem of robust passive control for uncertain systems with mode-dependent time delays and Markovian jump parameters. The time delay varies in an interval and depends on the mode of operation. The problem aims at designing a new state feedback controller which guarantees the passivity of the close-loop system for all admissible uncertainties. In terms of a linear matrix inequality (LMI) and Lyapunov function, the passive stability criteria are formulated. A numerical example illustrates the effectiveness of the method is given.

Robust observer-based passive control for uncertain singular time-delay systems subject to actuator saturation

This paper concerns the robust passive control problem for linear systems with norm-bounded time-varying uncertainties in all the system matrices. Our objective is to design a feedback controller such that the closed-loop system is both quadratically stable and strictly passive for all admissible uncertainties. It is shown that such a problem is equivalent to a scaled strictly positive real control problem for a certain linear time-invariant system in which no uncertainty occurs. Therefore, a complete solution can be obtained by using the existing results of standard positive real control.

The classical CUSUM (C) chart is designed by assuming that the size of the shift in the process, in which a quick detection is important, is known a priori. However, this assumption is often violated in practice, as the actual shift size is rarely known even though it may vary within a certain interval. The adaptive C (AC) chart gives better protection against process shifts in a certain interval than the classical C chart. In this paper, we propose a new weighted AC (WAC) chart with the variable sample size and sampling interval (VSSI) feature, which encompasses the fixed sampling rate (FSR), variable sample size (VSS) and variable sampling interval (VSI) based WAC charts. The Monte Carlo simulations are adopted in the run-length computations of the considered charts, where the newly developed (VSS and VSSI based) charts outperform the existing (FSR and VSI) WAC charts when detecting small shifts in the process mean. An illustrative example shows the implementation of the existing and proposed WAC charts.

The Pareto distribution has been widely used to model data in numerous areas including actuarial science, climatology, economics, finance, and reliability. The exponential weighted moving average (EWMA) chart with variable sample size and sampling interval (VSSI) is quicker than EWMA chart, EWMA chart with variable sample size (VSS), and EWMA chart with variable sampling interval (VSI) in detecting the mean shifts of a normal process. In this study, we present an EWMA‐VSSI chart to monitor the Pareto data with estimated parameters. The average time to signal (ATS) is computed by using the Markov chain approach. The results indicate that the proposed chart performs better than the other EWMA charts with fixed sample size, VSS, and VSI in terms of ATS. The design parameters of the proposed control charts are given in order to expedite the use of the chart by practitioners. Two examples are used to illustrate the application of the proposed control charts.

ABSTRACTThis paper is concerned with the problem of observer-based reliable passive control for uncertain Takagi–Sugeno (T–S) fuzzy systems with time-delay and actuator faults. By employing Lyapunov stability theory, fault treatment method and linear matrix inequalities (LMIs), a sufficient condition on the existence of an observer-based reliable passive controller is given. Further, the LMI conditions are proposed for the observer-based reliable passive controller design. The gain of reliable controller and observer can be obtained by solving the proposed LMIs. Using the reliable passive controller, the closed-loop system is not only internally stable but also strictly passive even though some actuator components fail and system state fails to be measured completely. Finally, a truck-trailer system example is given to verify the effectiveness and advantages of the designed approach.

Finite-horizon reliable control with randomly occurring uncertainties and nonlinearities subject to output quantization

On the design of variable sample size and sampling intervals [formula omitted] charts under non-normality

The paper establishes the analytical grounds of the uniform superiority of a variable sampling interval (VSI) Shewhart control chart over the conventional fixed sampling interval (FSI) control chart, with respect to the zero-time performance, for a wide class of process distributions. We provide a sufficient condition on the distribution of a control chart statistic, and propose a criterion to determine the control limits and the regions in the in-control area of the VSI chart, corresponding to the different sampling intervals used by it. The condition and the criterion together ensure the uniform zero-time superiority of the VSI chart over the matched FSI chart, in detecting a process shift of any magnitude. It is shown that normal, Student's t and Laplace distributions satisfy the sufficient condition. In addition, chi-square, F and beta distributions satisfy it, provided that these are not extremely skewed. Further, it is illustrated that the superiority of the VSI feature is not trivial and cannot be assured if the sufficient condition is not satisfied or the control limits and the regions are not determined according to the proposed criterion. An application of the result to confirm the superiority of the VSI feature is demonstrated for the control chart for individual observations used to monitor a milk-pouch filling process.

The problem of robust velocity and height control is dealt with for hypersonic vehicles subject to high nonlinearity and uncertainties. Robust linear controller design for nonlinear systems suffers from the problem of conservation because the nonlinear dynamics are considered as uncertainties. In this paper, a feedback linearization controller is firstly applied to achieve dynamic decoupling of the velocity and height channels. Robust controllers are then designed for each channel to achieve the desired tracking and restrain the effects of parametric uncertainties, external disturbances, and nonlinear dynamics, which cannot be accurately counteracted by the feedback linearization technique. This method can guarantee the robust stability and robust tracking properties of the closed-loop control system. Moreover, the conservation of the robust controller design can be reduced because the nonlinear information of the dynamic system is used. Simulation results are given to show the advantages of the proposed robust nonlinear control method compared with its linear counterpart.

Controlling over-adjusted process means and variances using VSI cause selecting control charts

The deployment of statistical process control (SPC) in service process is a prominent global phenomenon in recent years. In this paper, we proposed the optimal variable sample size and sampling interval (VSSI) mean square error (MSE) control chart to monitor the difference between the process mean and the target value and the process variation shifts, and its performance is measured by the average time to signal (ATS). From data analyses, we found the optimal VSSI MSE chart that performs better than the specific VSSI and optimal variable sampling interval (VSI) and fixed sample size and sampling interval (FSSI) MSE chart. An example was given to illustrate this new proposed approach.

This paper improves the sensitivity of the existing run sum chart for shifts in the coefficient of variation by proposing two types of adaptive schemes, i.e. the variable sample size and sampling interval (VSSI) and variable parameter (VP) schemes. The VSSI run sum chart varies the sample size and sampling interval , while the VP run sum chart varies not only n and h but also the size of each region of the run sum chart. The operations, as well as formulae and algorithms to optimize the charts’ performance, are developed. Subsequently, tables of optimal charting parameters are obtained. The VP run sum chart is shown to outperform the VSSI run sum chart. The proposed charts are also shown to outperform the variable sampling interval (VSI) run sum, variable sample size (VSS) run sum, and the VSSI, VSS and VSI charts, as well as the VSS and VSI EWMA charts for moderate and large shift sizes. Implementation on an actual industrial example shows the sensitivity of the proposed charts towards small shifts.

This study investigates the statistical properties of the adaptive Hotelling's T 2 charts with run rules in which the sample size and sampling interval are allowed to vary according on the current and past sampling points. The adaptive charts include variable sample size (VSS), variable sampling interval (VSI), and variable sample size and sampling interval (VSSI) charts. The adaptive Hotelling's T 2 charts with run rules are compared with the fixed sampling rate Hotelling's T 2 chart with run rules. The numerical results show that the VSS, VSI, and VSSI features improve the performance of the Hotelling's T 2 chart with run rules.

We consider the robust (H???) control problem for linear time-invariant systems over unreliable communication channels that are subject to packet losses from sensors to the controller and from the controller to the actuators. Moreover, the acknowledgments of control packet transmissions are also sent over reverse unreliable communication channels, which is known as the quasi-TCP model. The robust control problem is formulated within a stochastic zero-sum dynamic game framework, from which we obtain an H??? controller that minimizes the worst-case cost function in the presence of an adversary in the dynamical system. We characterize a set of existence conditions of the H??? controller in terms of the disturbance attenuation parameter ?? and packet loss rates. For the least disturbance attenuation scenario (as ?? ??? 8), we show that the H??? control system converges to the corresponding LQG system. We also show that the H??? controller for the TCP- and UDP-cases can be arrived at as appropriate limits of the solution for the quasi-TCP problem. Numerical examples are presented to illustrate the theoretical results.