Showing papers in "International Journal of Systems Science in 2001"
TL;DR: A class of switching laws is proposed so that the entire switched system is exponentially stable with a desired stability margin and it is shown quantitatively that, when norms of the perturbations are small, the solutions of the switched systems converge to the origin exponentially under the same switching laws.
Abstract: We study the stability properties of switched systems consisting of both Hurwitz stable and unstable linear time-invariant subsystems using an average dwell time approach. We propose a class of switching laws so that the entire switched system is exponentially stable with a desired stability margin. In the switching laws, the average dwell time is required to be sufficiently large, and the total activation time ratio between Hurwitz stable subsystems and unstable subsystems is required to be no less than a specified constant. We also apply the result to perturbed switched systems where nonlinear vanishing or non-vanishing norm-bounded perturbations exist in the subsystems, and we show quantitatively that, when norms of the perturbations are small, the solutions of the switched systems converge to the origin exponentially under the same switching laws.
593 citations
TL;DR: In this article, an operational matrix of integration P based on Legendre wavelets is presented, and a general procedure for forming this matrix is given. Illustrative examples are included to demonstrate the validity and applicability of the matrix P.
Abstract: An operational matrix of integration P based on Legendre wavelets is presented. A general procedure for forming this matrix is given. Illustrative examples are included to demonstrate the validity and applicability of the matrix P.
233 citations
TL;DR: An inventory model with a varying rate of deterioration and partial backlogging rate under the condition of permissible delay in payments used in conjunction with the economic order quantity model is discussed.
Abstract: The paper deals with an inventory model with a varying rate of deterioration and partial backlogging rate under the condition of permissible delay in payments. The existing literature on the subject generally deal with situations where the payment of an order is made on the receipt of items by the inventory system and shortages are either completely backlogged or fully lost. In this paper, a varying deterioration rate of time and the condition of permissible delay in payments used in conjunction with the economic order quantity model are the focus of discussion. In addition, the shortages are neither completely backlogged nor completely lost assuming the backlogging rate to be inversely proportional to the waiting time for the next replenishment. Numerical examples are presented to illustrate the model.
216 citations
TL;DR: In this article, some sufficient criteria are derived for the global exponential stability of the equilibrium of Hopfield neural networks of the form Ci dui /dt.
Abstract: In this article, some sufficient criteria are derived for the global exponential stability of the equilibrium of Hopfield neural networks of the form Ci dui /dt
116 citations
TL;DR: In this article, a parametric observer-based approach for robust fault detection in multivariable linear systems with unknown disturbances is proposed, where the residual is generated through utilizing a Luenberger function observer.
Abstract: A new parametric observer-based approach for robust fault detection in multivariable linear systems with unknown disturbances is proposed. The residual is generated through utilizing a Luenberger function observer. By using a parametric solution to a class of generalized Sylvester matrix equations, a parametrization is proposed for the residual generator on the basis of a Luenberger function observer. By further properly constraining the design parameters provided in the Luenberger observer design, the effect of the unknown disturbance is decoupled from the residual signal. The proposed approach provides all the degrees of freedom and is demonstrated to be simple and effective.
105 citations
TL;DR: In this paper, a comprehensive list of commonly used models for friction is presented, and model-based and non-model-based adaptive friction controllers are developed with guaranteed closed-loop stability.
Abstract: In this paper, adaptive friction compensation is investigated using both model-based and neural network (non-model-based) parametrization techniques. After a comprehensive list of commonly used models for friction is presented, model-based and non-modelbased adaptive friction controllers are developed with guaranteed closed-loop stability. Intensive computer simulations are carried out to show the effectiveness of the proposed control techniques, and to illustrate the effects of certain system parameters on the performance of the closed-loop system. It is observed that as the friction models become complex and capture the dominate dynamic behaviours, higher feedback gains for model-based control can be used and the speed of adaptation can also be increased for better control performance. It is also found that neural networks are suitable candidate for friction modelling and adaptive controller design for friction compensation.
89 citations
TL;DR: An inventory model with negotiable back orders is first proposed, then another model where lead time is also subject to change is discussed, and Numerical examples are included to illustrate the procedures of the solution.
Abstract: For inventory problems with stock-out under probabilistic demands, most of the published data assumes that the average shortages are very small and thus are neglected. However, some of the stock-out in practice might be significant and is back ordered and filled as soon as an adequate size of replenishment arrives. Typically, a supplier will institute an emergency expediting order to obtain the item when a shortage occurs and a price discount can always be offered on the stock-out item in order to secure more back orders. In this article, an inventory model with negotiable back orders is first proposed, then another model where lead time is also subject to change is discussed. Numerical examples are included to illustrate the procedures of the solution.
79 citations
TL;DR: It is proposed that, for stereo vision applications in which real-world coordinates are to be evaluated, artificial neural networks be used to train the system such that the need for camera calibration is eliminated.
Abstract: Stereo-pair images obtained from two cameras can be used to compute three-dimensional (3D) world coordinates of a point using triangulation. However, to apply this method, camera calibration parameters for each camera need to be experimentally obtained. Camera calibration is a rigorous experimental procedure in which typically 12 parameters are to be evaluated for each camera. The general camera model is often such that the system becomes nonlinear and requires good initial estimates to converge to a solution. We propose that, for stereo vision applications in which real-world coordinates are to be evaluated, artificial neural networks be used to train the system such that the need for camera calibration is eliminated. The training set for our neural network consists of a variety of stereo-pair images and corresponding 3D world coordinates. We present the results obtained on our prototype mobile robot that employs two cameras as its sole sensors and navigates through simple regular obstacles in a high-con...
79 citations
TL;DR: Asymptotic properties of a conventional learning algorithm are examined for a class of non-linear systems with time delay in the presence of initial function errors and are shown to be effective in the improvement of tracking performance, in particular robustness and uniform convergence.
Abstract: Most of the available results on iterative learning control address trajectory tracking problem for systems without time delay. The role of the initial function in tracking performance of iterative learning control for systems with time delay is not yet fully understood. In this paper, asymptotic properties of a conventional learning algorithm are examined for a class of non-linear systems with time delay in the presence of initial function errors. It is shown that a non-zero initial function deviation can cause a lasting tracking error on the entire operation. Impulsive action is one method to eliminate such lasting tracking error but it is not a practical approach. As an alternative, an initial rectifying action is introduced in the learning algorithm. The initial rectifying action is ®nite and used over a speci®ed interval. It is shown to be eA ective in the improvement of tracking performance, in particular robustness and uniform convergence. The results are further extended to systems with multiple time delays. An example is given and computer simulations are presented to demonstrate the performance of the proposed approach.
68 citations
TL;DR: By combining the short-term predicted value by a Fourier series and a long-term estimated error by the Markov forecasting method, the approach can predict the future more accurately.
Abstract: In recent years the grey theorem has been successfully used in many prediction applications. The proposed Markov-Fourier grey model prediction approach uses a grey model to predict roughly the next datum from a set of most recent data. Then, a Fourier series is used to fit the residual error produced by the grey model. With the Fourier series obtained, the error produced by the grey model in the next step can be estimated. Such a Fourier residual correction approach can have a good performance. However, this approach only uses the most recent data without considering those previous data. In this paper, we further propose to adopt the Markov forecasting method to act as a longterm residual correction scheme. By combining the short-term predicted value by a Fourier series and a long-term estimated error by the Markov forecasting method, our approach can predict the future more accurately. Three time series are used in our demonstration. They are a smooth functional curve, a curve for the stock market and th...
55 citations
TL;DR: This paper studies the problem of non-fragile guaranteed cost control (GCC) state-feedback design for discrete-time uncertain linear systems and proposes a less conservative solution.
Abstract: This paper studies the problem of non-fragile guaranteed cost control (GCC) state-feedback design for discrete-time uncertain linear systems. The systems are assumed to have norm-bounded system uncertainties in both the state and the input matrices. The state-feedback gains are assumed to have norm-bounded controller uncertainties which can be either additive or multiplicative. The non-fragile GCC state-feedback designs, which are related to solutions of some matrix inequalities, guarantee the cost of the system to be within a certain bound for all these admissible uncertainties. Our proposed design approach of separating the controller uncertainty from the system uncertainty gives a less conservative solution. A numerical example is given to illustrate the design methods and the design benefits.
TL;DR: A single server queue with Poisson arrivals, two stages of heterogeneous service with different general (arbitrary) service time distributions and binomial schedule server vacations with deterministic (constant) vacation periods is analysed.
Abstract: We analyse a single server queue with Poisson arrivals, two stages of heterogeneous service with different general (arbitrary) service time distributions and binomial schedule server vacations with deterministic (constant) vacation periods. After first-stage service the server must provide the second stage service. However, after the second stage service, he may take a vacation or may decide to stay on in the system. For convenience, we designate our model as M/G 1, G 2/D/1 queue. We obtain steady state probability generating function of the queue length for various states of the server. Results for some particular cases of interest such as M/Ek 1 , Ek 2 /D/1, M/M 1, M 2/D/1, M/E k /D/1 and M/G 1, G 2/1 have been obtained from the main results and some known results including M/Ek /1 and M/G/1 have been derived as particular cases of our particular cases.
TL;DR: A new delay-dependent criterion is proposed to guarantee stability for a class of uncertain nonlinear neutral systems with a single time delay and the Lyapunov stability theorem and matrix inequalities are used to prove the main result.
Abstract: In this paper, asymptotic stability for a class of uncertain nonlinear neutral systems with a single time delay is considered. A new delay-dependent criterion is proposed to guarantee stability for such systems. The Lyapunov stability theorem and matrix inequalities are used to prove the main result. Finally, four numerical examples are given to demonstrate that our robust stability condition is less conservative than those reported in the control literature. The tolerable time-delay intervals that guarantee asymptotic stability of systems are larger than other results in those examples.
TL;DR: This paper investigates impulsive controllability and impulsive observability and proposes a new decomposition approach for singular systems and a new model reduction algorithm that will retain the impulsive nature of the original singular system via the Nehari approximation technique.
Abstract: In this paper, model reduction for singular systems will be investigated. First, a previous model reduction algorithm is presented and proved to be not appropriate in practice. Detailed examination of this existing algorithm will show that the difficulty of model reduction for singular systems is to retain its impulsive nature. Thus, based on this kind of acute observation, we investigate impulsive controllability and impulsive observability and propose a new decomposition approach for singular systems. Then a new model reduction algorithm will be proposed on the basis of this new decomposition via the Nehari approximation technique. This new model reduction algorithm will retain the impulsive nature of the original singular system. Finally, one example will be presented to illustrate the effectiveness of the proposed model reduction algorithm.
TL;DR: In this article, a mixed H 2 /H X controller design method for linear systems with time-varying delays in both state and control input is presented. And the sufficient conditions for the existence of controller and the upper bound of performance measure are presented using linear matrix inequality (LMI) technique.
Abstract: This paper describes the mixed H 2 /H X controller design method of linear systems with time-varying delays in both state and control input. More specifically, the proposed mixed H 2 /H X controller minimizes the H 2 performance measure when satisfying a prescribed H X norm bound on the closed loop system. The sufficient conditions for the existence of controller, the mixed H 2 /H X controller design method and the upper bound of performance measure are presented using the linear matrix inequality (LMI) technique. Also, all solutions including controller gain and the upper bound of performance measure are obtained simultaneously. Furthermore, the proposed controller design method can be easily extended into the problem of robust mixed H 2 /H X controller design method for parameter uncertain systems with time-varying delays in both state and control input.
TL;DR: In this paper, a back-propagation neural network is utilized to identify shifts in process parameter values from AR (1) time series models with varying values of the autocorrelation coefficient φ.
Abstract: Traditional statistical process control (SPC) techniques of control charting are not applicable in many process industries because data from these facilities are autocorrelated. Therefore the reduction in process variability obtained through the use of SPC techniques has not been realized in process industries. Techniques are needed to serve the same functions as SPC control charts, which are to identify shifts in correlated parameters. Neural networks are a potential tool for identifying shifts in correlated process parameters, as data independence is not an assumption of neural network theory. In this research, a back-propagation neural network is utilized to identify shifts in process parameter values from AR (1) time series models with varying values of the autocorrelation coefficient φ. To find the appropriate number of input nodes for use in a neural network model, the all-possible-regression selection procedure is applied. In addition, time series residual control charts are also developed for the ...
TL;DR: The study proposes a computer-aided approach to achieve a compromise for all the elements in the comparison matrix while implementing the Analytic Hierarchy Process to resolve the disparity of judgements within decisionmakers.
Abstract: The Analytic Hierarchy Process (AHP) has been widely utilized to solve multicriteria decision-making problems in synthesizing conflict opinions. Normally, AHP uses the geometric averaging approach to synthesize preference weights determined by decision-makers. This approach has been criticized by many researches since synthesis weight may not reach a consensus. To make the synthesis acceptable to all decision-makers, the study proposes a computer-aided approach to achieve a compromise for all the elements in the comparison matrix while implementing AHP. Accordingly, decision-makers can conveniently exchange trustful information, which is generated by the embedded genetic algorithm, sensitivity analysis and similarity measure of the judgements done by decision-makers. Consequently, the consensus of all the elements in the comparison matrix can be obtained through such an innovative approach to resolve the disparity of judgements within decisionmakers.
TL;DR: The basic concept used in this paper parallels the geometric process replacement policy N introduced by Lam in 1988, which generalizes and modifies Lam's 1988 work.
Abstract: This paper presents a new policy for determining the optimal replacement time of a deteriorating production system. The optimal replacement time is expressed in terms of the accumulated number of failures that the system has experienced. The provision of preventive maintenance is incorporated in the system model and the objective function is cost efficiency (i.e. the long-run average cost per unit working time). A numerical example is given in the paper. The basic concept used in this paper parallels the geometric process replacement policy N introduced by Lam in 1988. The work in this paper generalizes and modifies Lam's 1988 work.
TL;DR: In this paper, the authors study invariant and attracting sets of Hopfield neural networks with delay and obtain sufficient conditions of global asymptotic stability of the equilibrium point. And they provide an estimate of the existence range of attractors by using invariant sets.
Abstract: This paper studies invariant and attracting sets of Hopfield neural networks system with delay. Sufficient criteria are given for the invariant and attracting sets. In particular, we provide an estimate of the existence range of attractors by using invariant and attracting sets. Moreover, when the system has an equilibrium point, we obtain the sufficient conditions of global asymptotic stability of the equilibrium point. Several examples are also worked out to demonstrate the advantages of our results.
TL;DR: In this paper, a continuous review inventory model is presented in which they considered both the lead time and the order quantity as decision variables and developed an algorithmic procedure to find the optimal order quantity and optimal lead time; the effects of parameters are also studied.
Abstract: In recent papers by Ben-Daya and Raouf and by Ouyang et al. a continuous review inventory model is presented in which they considered both the lead time and the order quantity as decision variables. When the demands of the different customers do not have identical lead times, then we cannot use only a distribution (such as Ouyang et al. who used a normal distribution) to describe the demand of the lead time. Hence, we have extended the model of Ouyang et al. by considering the mixtures of normal distribution (see the book by Everitt and Hand). In addition, we also still assume that shortages are allowed. Moreover, the total amount of stock-out is considered as a mixture of back orders and lost sales during the stock-out period. Moreover, we also develop an algorithmic procedure to find the optimal order quantity and optimal lead time; the effects of parameters are also studied.
TL;DR: The proposed model following the control structure (MFC) may find a wide application in new intelligent controllers for robust control of parameter-varying plants such as electrothermal plants.
Abstract: The paper deals with the properties of a two-loop control system structure containing the model of a controlled plant and two PID controllers Special attention was paid to high robustness of the structure to perturbations of the controlled plant in relation to its nominal model and to good damping of the disturbances On the basis of theoretical and simulation results, the properties of the considered structure are compared with those of the classic, single-loop control structure The proposed model following the control structure (MFC) may find a wide application in new intelligent controllers for robust control of parameter-varying plants such as electrothermal plants
TL;DR: In this article, an order level inventory model is developed for a deteriorating item with a linear trend in demand, where the finite production rate is proportional to the time-dependent demand rate and the deterioration rate is time proportional.
Abstract: An order level inventory model is developed for a deteriorating item with a linear trend in demand. It is assumed that the finite production rate is proportional to the time-dependent demand rate and the deterioration rate is time proportional. The unit production cost is taken to be inversely related to the demand rate. The model is first solved allowing no shortage in inventory. The case of inventory shortage is discussed next. The results are illustrated with the help of numerical examples. The sensitivity of the solution to changes in the values of the parameters associated with the model is discussed.
TL;DR: A new algorithm for the numerical global solution of nonlinear and nonconvex, infinitely constrained problems is proposed, which is a partially elitist genetic algorithm that uses, at the lower level, an interval procedure to compute a penalty-based fitness function.
Abstract: Infinitely constrained (or semi-infinite) optimization can be successfully used to solve a significant variety of optimization-based engineering design problems. In this paper a new algorithm for the numerical global solution of nonlinear and nonconvex, infinitely constrained problems is proposed. At the upper level this hybrid algorithm is a partially elitist genetic algorithm that uses, at the lower level, an interval procedure to compute a penalty-based fitness function. The deterministic nature of the interval procedure, whose global convergence with certainty is established by using concepts of interval analysis, guarantees the feasibility of the estimated global solution provided by the hybrid algorithm. Computational results are reported for three test problems and the hybrid algorithm is applied to the optimal worst-case H2 design of a proportionalintegral-derivative (PID) controller for an uncertain nonminimum-phase plant.
TL;DR: In this article, a linear consecutive-k-out-of-n:F repairable system with one repair man is studied, where the working time and the repair time of the components in the system are both exponentially distributed, and each component after repair is "as good as new".
Abstract: In this paper, a linear consecutive-k-out-of-n: F repairable system with one repair man is studied. Assume that the working time and the repair time of the components in the system are both exponentially distributed, and each component after repair is 'as good as new'. By using the definition of generalized transition probability and the concept of key component, the state transition probabilities in the system are derived under a key component will have higher priority for repair. Some important reliability indices are also studied.
TL;DR: In this article, the authors present definitions and basic properties of uncertain variables and show how they may be applied to the analysis and decision making in static systems with unknown parameters in their mathematical models.
Abstract: This paper presents definitions and basic properties of uncertain variables and shows how they may be applied to the analysis and decision making in static systems with unknown parameters in their mathematical models. The unknown parameters are assumed to be uncertain variables described by certainty distributions given by an expert. Two versions of the uncertain variables are described. The uncertain variable in the first version may be considered as a special case of the fuzzy number with a specific interpretation. Two forms of systems are considered in the paper: a system described by a function (functional system) and a system described by a relation (relational system). In both cases the statements and general solutions of the analysis and decision problems are presented. Simple examples illustrating the application of the uncertain variables are included.
TL;DR: This paper addresses the problem of a manufacturing system that procures raw materials from suppliers in a lot and processes them to convert to finished products and proposes an ordering policy for raw materials to meet the requirements of a production facility.
Abstract: This paper addresses the problem of a manufacturing system that procures raw materials from suppliers in a lot and processes them to convert to finished products. It proposes an ordering policy for raw materials to meet the requirements of a production facility. In turn, this facility must deliver finished products demanded by outside
buyers at fixed interval points in time. First, a general cost model is developed considering both raw materials and finished products. Then this model is used to develop a
simple procedure to determine an optimal ordering policy for procurement of raw materials and also the manufacturing batch size to minimize the total cost for meeting the customer demand on time. The proposed procedure provides better results than the traditional separate policies. Numerical examples are also presented.
TL;DR: Simulation shows the effectiveness of the stabilizing method proposed in this paper, by constructing a Hamiltonian function as the total energy function for the fifth-order model and changing the system into a forced Hamiltonian system with dissipation.
Abstract: Using the Hamiltonian function approach, this paper proposes an energy-based stabilizing method for a fifth-order model of synchronous generators to keep the terminal machine voltage (output) remaining at a given expected value. By constructing a Hamiltonian function as the total energy function for the fifth-order model and changing the system into a forced Hamiltonian system with dissipation, an energy-based Lyapunov function is obtained. As the result, a suitable stabilizing controller is constructed for the system. Simulation shows the effectiveness of the stabilizing method proposed in this paper.
TL;DR: This paper proposes a new approach to extracting fuzzy rules from training examples by means of genetic-based premise learning and was applied to the well-known gas furnace data of Box and Jenkins to show its validity and to compare its performance with those of other works.
Abstract: The task of fuzzy modelling involves specification of rule antecedents and determination of their consequent counterparts. Rule premises appear here a critical issue since they determine the structure of a rule base. This paper proposes a new approach to extracting fuzzy rules from training examples by means of genetic-based premise learning. In order to construct a 'parsimonious' fuzzy model with high generalization ability, general premise structure allowing incomplete compositions of input variables as well as OR connectives of linguistic terms is considered. A genetic algorithm is utilized to optimize both the premise structure of rules and fuzzy set membership functions at the same time. Determination of rule conclusions is nested in the premise learning, where consequences of individual rules are determined under fixed preconditions. The proposed method was applied to the well-known gas furnace data of Box and Jenkins to show its validity and to compare its performance with those of other works.
TL;DR: In this paper, a robust reliable controller design for a class of uncertain nonlinear systems is proposed, and sufficient conditions for robust stability in the presence of possible actuator failure are given in terms of the linear matrix inequalities (LMIs) and the controller that stabilizes the system is computed using standard LMI techniques.
Abstract: This paper deals with the problem of robust reliable controller design for a class of uncertain nonlinear systems. The system under consideration is subject to time-varying multistate time delays, parameter uncertainties, nonlinearities and even failures in prescribed subsets of auctuators. The nonlinearities are assumed to satisfy boundedness conditions. The parameter uncertainties and multistate time delays are time varying and structured. A systematic approach using linear matrix inequalities (LMIs) is proposed to solve the design problem of this controller. Sufficient conditions for robust stability in the presence of possible actuator failure are given in terms of the LMIs and the controller that stabilizes the system is computed using standard LMI techniques.