Stochastic stability analysis for joint process driven and networked hybrid systems

The stochastic stability and impulsive noise disturbance attenuation in a class of joint process driven and networked hybrid systems with coupling delays (JPDNHSwD) has been investigated. In particular, there are two separable processes monitoring the networked hybrid systems. One drives inherent network structures and properties, the other induces random variations in the control law. Continuous dynamics and control laws in networked subsystems and couplings among subsystems change as events occur stochastically in a spatio-temporal fashion. When an event occurs, the continuous state variables may jump from one value to another. Using the stochastic Lyapunov functional approach, sufficient conditions on the existence of a remote time-delay feedback controller which ensures stochastic stability for this class of JPDNHSwD are obtained. The derived conditions are expressed in terms of solutions of LMIs. An illustrative example of a dynamical network driven by two Markovian processes is used to demonstrate the satisfactory control performance.     

First-order hybrid Petri nets. An application to distributed manufacturing systems

In this paper we consider Hybrid Petri Nets (HPNs), a particular formalism that combines fluid and discrete event dynamics. We first provide a survey of the main HPN models that have been presented in the literature in the last decades. Then, we focus on a particular HPN model, namely the First-Order Hybrid Petri Net (FOHPN) model, whose continuous dynamics are piece-wise constant. Here the problem of designing an optimal controller simply requires solving on-line an appropriate linear integer programming problem. In this paper we show how FOHPNs can efficiently represent the concurrent activities of Distributed Manufacturing Systems (DMS), and some interesting optimization problems are also solved via numerical simulation.     

The reliability analysis of probabilistic and interval hybrid structural system

The aim of this paper is to evaluate the reliability of probabilistic and interval hybrid structural system. The hybrid structural system includes two kinds of uncertain parameters—probabilistic parameters and interval parameters. Based on the interval reliability model and probabilistic operation, a new probabilistic and interval hybrid reliability model is proposed. Firstly, we use the interval reliability model to analyze the performance function, and then sum up reliability of all regions divided by the failure plane. Based on the presented optimal criterion enumerating the main failure modes of hybrid structural system and the relationship of failure modes, the reliability of structure system can be obtained. By means of the numerical examples, the hybrid reliability model and the traditional probabilistic reliability model are critically contrasted. The results indicate the presented reliability model is more suitable for analysis and design of these structural systems and it can ensure the security of system well, and it only needs less uncertain information.     

概率方法在纺织产品质量检验中的应用

本文用统计分析方法分析了针织厂原产品质量检验方案 ,指出了其不合理性 ;从该厂的实际出发 ,针对三种不同批量建立了新的检验方案。实际证明 ,新方案既可以确保产品出厂质量 (限定在AQL值内 ) ,又可以对生产质量水平起到监督的作用     

Sonar array element location: A hybrid expert systems application

The design of many engineering systems, including sonar systems, has evolved (thanks in part to methods of operational research such as mathematical programming and simulation) from an almost strictly art form into a relatively scientific endeavor. Today we see, more and more, the use of, in particular, mathematical programming methods for the development of ‘optimally’ designed engineering hardware. Unfortunately, such designs are ‘optimal’ only under the unrealistic assumption of an error free model and the ability to develop a corresponding perfect design. That is, they fail to take into regard the often severe impact of the limitations of real world design tolerances. And this failure is becoming increasing more important as we begin to address modern day systems with their substantially increased size, sophistication and sensitivity.In this paper, we discuss the problem, with specific focus on the task of the development of sonar arrays. We present a hybrid methodology, combining expert systems with heuristic programming, that permits the engineer to incorporate the results of the mathematical programming solution while still using real world, imperfect components. And we present results as obtained on actual hardware.     

A model for stochastic hybrid systems with application to communication networks

We propose a model for stochastic hybrid systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuous-time Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for piecewise-deterministic Markov process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state.As an application, we construct a stochastic model for on-off TCP flows that considers both the congestion-avoidance and slow-start modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finite-dimensional model. This model shows that, for transfer-size distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms.     

A framework for the probabilistic analysis of hierarchical planning systems

As we have argued in previous papers, multi-level decision problems can often be modeled as multi-stage stochastic programs, and hierarchical planning systems designed for their solution, when viewed as stochastic programming heuristics, can be subjected to analytical performance evaluation. The present paper gives a general formulation of such stochastic programs and provides a framework for the design and analysis of heuristics for their solution. The various ways to measure the performance of such heuristics are reviewed, and some relations between these measures are derived. Our concepts are illustrated on a simple two-level planning problem of a general nature and on a more complicated two-level scheduling problem.     

Identification and adaptive control: An application to flight control systems

This paper presents the first results obtained in the application of stochastic control theory to flight control problems. It involves identification and adaptive control of an aircraft which operates over a wide range of environmental conditions that affect its dynamic characteristics. The bulk of the paper deals with theidentification problem of estimating stability derivatives in the presence of turbulence. Simulation results are presented both for identification and control (windgust alleviation and desired response to pilot input). While no practical implementation is reported, the implications for such implementation appear to be promising.The author is indebted to Mr. K. Iliff for all the simulation results using the IBM 360-91 at UCLA. The many helpful discussions with Dr. H. Rediess are gratefully acknowledged. Thanks are also due to Mr. Jiri Ruzicka for lending a helping hand throughout.     

A unified approach to controllability analysis for hybrid control systems

A unified approach is proposed for controllability analysis of a class of hybrid control systems, employing the controllability concept defined in [M. Tittus, B. Egardt, Control design for integrator hybrid systems, IEEE Transactions on Automatic Control 43 (4) (1998) 491–500; J.H. van Schuppen, A Sufficient Condition for Controllability of a Class of Hybrid Systems, in: LNCS, vol. 1386, Springer, 1998, pp. 374–383; Z. Yang, M. Verhaegen, Y.J. Wang, Z.J. Chen, Hybrid controllability of linear switched systems, in: Proceedings of 37th Control and Decision Conference, Tampa, FL, USA, December 1998, pp. 3920–3925]. The unified approach comprises global reachability analysis at the discrete event system level, local reachability analysis at the continuous-time dynamical system level and a merging of the results of these two methods using a discrete-path search algorithm. The proposed method is demonstrated useful for controllability analysis of complex hybrid control systems. The method is illustrated by analyzing the controllability of a linear switched system.     

Incremental stability analysis of stochastic hybrid systems

In this paper, we study the incremental stability of stochastic hybrid systems, based on the contraction theory, and derive sufficient conditions of global stability for such systems. As a special case, the conditions to ensure the second moment exponential stability which is also called exponential stability in the mean square of stochastic hybrid systems are obtained. The theoretical results in this paper extend previous works from deterministic or stochastic systems to general stochastic hybrid systems, which can be applied to qualitative and quantitative analysis of many physical and biological phenomena. An illustrative example is given to show the effectiveness of our results.     

An application of quasivariational inequalities to linear control systems

Starting from a recent result on generalized quasivariational inequalities, we derive a general theorem concerning the qualitative properties of the fixed-point set of certain multifunctions. Then, we apply our result to the problem of the existence of periodic solutions for a linear control system with the property that the final value lies on the relative boundary of the corresponding attainable set.This research was presented during the 19th Course of the International School of Mathematics G. Stampacchia, Variational Inequalities and Network Equilibrium Problems, Erice, Italy, June 1994.     

Cost and probabilistic analysis of series systems with mixed standby components

This paper deals with the reliability and availability characteristics of four different series system configurations with mixed standby (include cold standby and warm standby) components. The failure times of the primary and warm standby components are assumed to be exponentially distributed with parameters λ and , respectively. The repair time distribution of each server is also exponentially distributed with parameter μ. We derive the mean time-to-failure, MTTF, and the steady-state availability, A_T(∞), for four configurations and perform comparisons. For all four configurations, comparisons are done for specific values of distribution parameters and of the cost of the components. Finally, the configurations are ranked based on: MTTF, A_T(∞), and cost/benefit where benefit is either MTTF or A_T(∞).     

An optimal compactness theorem and application to elliptic-parabolic systems

We give a new optimal compactness criterion which insures that time dependent bounded sequences in suitable Hilbert spaces contain convergent subsequences. Our proof is related to PDE techniques. We then give an abstract application of the result.     

An application of a hybrid approach to modeling a flexible manufacturing system

Both analytic and simulation models were used to analyze the capabilities and requirements of an automated circuit card manufacturing system. Analytic models were used to determine the sensitivity of the measures of effectiveness (MOEs) to various design parameters. This analysis gave approximate results and bounded the range of input parameters for the simulation model. A detailed simulation model was required for use during both the design and production phases of the project. This simulation model incorporated only those variables to which the MOEs are most sensitive, and provided additional features to observe system behavior. The benefits and appropriate uses for each class of models are discussed.     

A small-gain approach to networked control systems with asynchronous communication

The aim of this work is to give a procedure to compute an ISS Lyapunov function (ISS - input-to-state stability) for a large-scale networked control system (NCS) in which sensors, controllers and actuators are connected via multiple communication networks that operate asynchronously, [1]. The main idea is that the NCS is modeled as an interconnection of controlled subsystems and (hybrid) error systems, for which local ISS Lyapunov functions can be derived from the underlying medium access control (MAC) protocol systematically. The application of a small-gain result leads to the construction of an ISS Lyapunov function for the whole NCS. In particularly, maximally allowable transfer intervals (MATIs) and maximally allowable delays (MADs) for each communication network can be computed that are directly related to the ISS gains and convergence rates. In this respect, tradeoffs between the quality-of-control (QoC) of the whole NCS and the quality-of-service (QoS) of the communication networks become explicit. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An MCDM approach to production analysis: An application to irrigated farms in Southern Spain

The analysis of the decision-making process in agricultural enterprises is approached with the development of a methodology based upon two stages: firstly we enlarge our knowledge of the system under study by performing grouping operation - cluster analysis - of the farm enterprises. The result of this stage is to classify farms according to crop pattern, which is the basis for the second stage of analysis: the system is studied by solving a weighted goal programming to approach the weights given by different farmers to the objectives of the decision process. This methodology is applied to two nearby but different irrigation units in Southern Spain, and we found that there was an important degree of heterogeneity in production plans explained by differences in objective weights.     

An innovative unification process for probabilistic hesitant fuzzy elements and its application to decision making

Fuzzy Optimization and Decision Making - The probabilistic hesitant fuzzy element (PHFE) is a worthwhile extension of hesitant fuzzy element (HFE) which is a means of allowing the decision makers...