Receding Horizon Control for a Class of Discrete-Event Systems With Real-Time Constraints

We consider discrete-event systems (DES) involving the control of tasks with real-time constraints. When future event time information is limited, we propose a receding horizon (RH) controller in which only some future information is available within a time window. Analyzing sample paths obtained under this scheme and comparing them to optimal sample paths (obtained when all event times are known), we derive a number of attractive properties of the RH controller, including: the fact that it still guarantees all real-time constraints; there are segments of its sample path over which all controls are still optimal; the error relative to the optimal task departure times is decreasing under certain conditions. Simulation results are included to verify the properties of the controller and show that its performance can be near-optimal even if the RH window size is relatively small     

Supervisory control of fuzzy discrete event systems: a formal approach.

Fuzzy discrete event systems (DESs) were proposed recently by Lin and Ying [19], which may better cope with the real-world problems of fuzziness, impreciseness, and subjectivity such as those in biomedicine. As a continuation of [19], in this paper, we further develop fuzzy DESs by dealing with supervisory control of fuzzy DESs. More specifically: 1) we reformulate the parallel composition of crisp DESs, and then define the parallel composition of fuzzy DESs that is equivalent to that in [19]. Max-product and max-min automata for modeling fuzzy DESs are considered, 2) we deal with a number of fundamental problems regarding supervisory control of fuzzy DESs, particularly demonstrate controllability theorem and nonblocking controllability theorem of fuzzy DESs, and thus, present the conditions for the existence of supervisors in fuzzy DESs; 3) we analyze the complexity for presenting a uniform criterion to test the fuzzy controllability condition of fuzzy DESs modeled by max-product automata; in particular, we present in detail a general computing method for checking whether or not the fuzzy controllability condition holds, if max-min automata are used to model fuzzy DESs, and by means of this method we can search for all possible fuzzy states reachable from initial fuzzy state in max-min automata. Also, we introduce the fuzzy n-controllability condition for some practical problems, and 4) a number of examples serving to illustrate the applications of the derived results and methods are described; some basic properties related to supervisory control of fuzzy DESs are investigated. To conclude, some related issues are raised for further consideration.     

A receding–horizon approach to the nonlinear H∞ control problem

The receding–horizon (RH) methodology is extended to the design of a robust controller of H_∞ type for nonlinear systems. Using the nonlinear analogue of the Fake H_∞ algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input–output map of the closed-loop system obtained with the RH control law has a bounded L₂-gain. Robustness properties of the nonlinear H_∞ control law in face of dynamic input uncertainty are considered.     

Neural Network Implementation of Nonlinear Receding-Horizon Control

The Receding Horizon (RH) approach is an effective way to derive control algorithms for nonlinear systems with stabilising properties also in the presence of state and control constraints. However, RH methods imply a heavy computational burden for on-line optimisation, therefore they are not suitable for the control of ‘fast’ systems, for example mechanical ones, which call for the use of short sampling periods. The aim of this paper is to show through an experimental study how a Nonlinear RH (NRH) control law can be computed off-line, and subsequently approximated by means of a neural net-work, which is effectively used for the on-line implementation. The proposed design procedure is applied to synthesise a neural NRH controller for a seesaw equipment. The experimental results reported here demonstrate the feasibility of the method.     

Perturbation analysis of feedback-controlled stochastic flow systems

Stochastic flow systems arise naturally or as abstractions of discrete-event systems (DESs), referred to as stochastic flow models (SFMs). In this paper, we consider such systems operating with a feedback control mechanism, building on earlier work that has studied such SFMs without any feedback. Using infinitesimal perturbation analysis, we derive gradient estimators for loss and workload related performance metrics with respect to threshold parameters used for buffer control. These estimators are shown to be unbiased. They are also shown to depend only on data observable from a sample path of the actual DES. This renders them computable in on-line environments and easily implementable for control and performance optimization purposes. In the case of linear feedback, we further show that the estimators are nonparametric. Finally, we illustrate the use of these estimators in network control by combining them with standard gradient-based stochastic optimization schemes and providing several simulation-based examples.     

Hammerstein-Wiener nonlinear model based predictive control for relative QoS performance and resource management of software systems

Runtime management of Quality of Service (QoS) performance and resource provisioning is a vital issue in shared resource software environments. A useful performance management technique for such software systems is the relative guarantee feedback control scheme. The existing approaches for this class of control systems are mainly based on off-line linear or on-line model identification and control techniques, which tend to have performance issues in the presence of nonlinearities induced by this scheme. Instead of using such modeling techniques, this paper proposes a new approach for QoS performance management and resource provisioning by using an off-line identification of Hammerstein and Wiener nonlinear block structural model. Using the characteristic structure of the nonlinear model, a predictive feedback controller based on a gain schedule technique is incorporated in the design to achieve the performance objectives. The proposed approach is validated using experiments based on a prototype, demonstrating superior runtime QoS performance management and resource provisioning in a complex software system.     

Two formal methods for the synthesis of discrete event systems

The design of discrete event systems (DES) is based mainly on either analysis or synthesis approaches. In the synthesis approach, the design process starts from high level requirements which are then automatically refined to obtain lower abstraction levels. In this paper, we begin by introducing the two design approaches and defining the synthesis problem in DESs, and in protocols in particular. Then, we survey and assess some existing protocol synthesis methods. Then, we present two novel formal and systematic methods we have developed for the synthesis of DESs. The first method is used for the design of distributed systems which must satisfy some temporal constraints. The second method takes into account concepts such as controllability and observability, which are used in the control theory of DESs. Finally, we conclude and propose some future works.     

Diagnosability of Fuzzy Discrete-Event Systems: A Fuzzy Approach

In order to more effectively cope with the real-world problems of vagueness, fuzzy discrete-event systems (FDESs) were proposed by Lin and Ying recently. Then we and Cao and Ying investigated the supervisory control of FDESs independently. In this paper, we are concerned with another important issue of FDESs, the failure diagnosis. More specifically: (1) we propose a ldquofuzzy diagnosabilityrdquo approach by introducing a fuzzy diagnosability function to characterize the diagnosability degree, which takes values in the interval [0,1] rather than { 0,1}; (2) based on the observability of events, we formalize the construction of the diagnosers that are used to perform fuzzy diagnosis; (3) a number of basic properties of the diagnosers are investigated. In particular, we present a necessary and sufficient condition for failure diagnosis of FDESs. Our results generalize the important consequences of the diagnosability for crisp discrete-event systems (DESs) introduced by Sampath et al. The newly proposed approach allows us to deal with the problem of diagnosability for both crisp DESs and FDESs; (4) in addition, a method for checking the fuzzy diagnosability for FDESs is proposed. Also, some examples are provided to illustrate the application of the diagnosability of FDESs.     

基于递归神经网络的移动域控制方法

构造一种线性差分式Hopfield网络（LDHNN），其稳定状态可使能量函数达到唯一极小值，利用该网络稳定性与其能量函数收敛特性的关系，提出了基于LDHNN的移动域控制方法，LDHNN的理论设计表明，网络的稳态输出即为移动域LQ控制问题的解，当系统满足一定条件时，基于LDHNN的移动域LQ控制能保证闭环最优控制系统的渐近稳定性．数字仿真取得了与理论分析一致的实验结果。     

Controlled Markov chains with safety upper bound

In this note, we introduce and study the notion of safety control of stochastic discrete-event systems (DESs), modeled as controlled Markov chains. For nonstochastic DESs modeled by state machines or automata, safety is specified as a set of forbidden states, or equivalently by a binary valued vector that imposes an upper bound on the set of states permitted to be visited. We generalize this notion of safety to the setting of stochastic DESs by specifying it as an unit-interval valued vector that imposes an upper bound on the state probability distribution vector. Under the assumption of complete state observation, we identify: 1) the set of all state feedback controllers that satisfy the safety requirement for any given safe initial state probability distribution, and 2) the set of all safe initial state probability distributions for a given state feedback controller.     

Flexible diagnosis of discrete-event systems by similarity-based reasoning techniques

Diagnosis of discrete-event systems (DESs) may be improved by knowledge-compilation techniques, where a large amount of model-based reasoning is anticipated off-line, by simulating the behavior of the system and generating suitable data structures (compiled knowledge) embedding diagnostic information. This knowledge is exploited on-line, based on the observation of the system behavior, so as to generate the set of candidate diagnoses (problem solution). This paper makes a step forward: the solution of a diagnostic problem is supported by the solution of another problem, provided the two problems are somewhat similar. Reuse of model-based reasoning is thus achieved by exploiting the diagnostic knowledge yielded for solving previous problems. The technique still works when the available knowledge does not fit the extent of the system, but only a partition of it, that is, when solutions are available for subsystems only. In this case, the fragmented knowledge is exploited in a modular way, where redundant computation is avoided. Similarity-based diagnosis is meant for large-scale DESs, where the degree of similarity among subsystems is high and stringent time constraints on the diagnosis response is a first-class requirement.     

Control of discrete event systems modeled as hierarchical statemachines

Discrete-event systems (DESs) are systems in which state changes take place in response to events that occur discretely, asynchronously, and often nondeterministically. A class of DESs modeled as hierarchical state machines (HSMs), a special case of the statecharts formalism introduced recently, is considered. An efficient algorithm is provided for solving reachability problems in the HSM framework. It utilizes the hierarchical structure of HSMs. This efficient solution is used extensively in control applications, where controllers achieving a desired behavior are synthesized online     

Robust and fault-tolerant supervisory control of discrete event systems with partial observation and model uncertainty

This paper proposes the notions of faults and failures in discrete event systems (DESs) with partial observation. They are associated with controllability and an observability property. The proposed notions are used to address the notion of tolerable fault event sequences which represents fault-tolerant behaviour of systems as a desired specification. A robust and fault-tolerant supervisor is a controller which is robust to model uncertainty and guarantees fault-tolerant behaviour of a system. In this paper we present necessary and sufficient conditions for the existence of a robust and fault-tolerant supervisor. The developed conditions capture the concepts of controllability and observability which are cores in the control of DESs with partial observation     

终端约束滚动时域控制的次优性分析

讨论了有终端约束的滚动时域控制相对于传统最优控制的次优性问题．首先考虑一 般形式的非线性系统,通过分析有限时域滚动优化的特点,得到了滚动时域控制次优性的上 界;然后将结果进一步应用于线性系统,得到一个量化的评价指标．     

Stochastic model predictive control for constrained discrete-time Markovian switching systems

In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the SMPC law under very weak assumptions. In the special but important case of constrained MJLS we present an algorithm for computing explicitly the SMPC control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization.     

Stable iterative adaptive dynamic programming algorithm with approximation errors for discrete-time nonlinear systems

In this paper, a novel iterative adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. When the iterative control law and iterative performance index function in each iteration cannot be accurately obtained, it is shown that the iterative controls can make the performance index function converge to within a finite error bound of the optimal performance index function. Stability properties are presented to show that the system can be stabilized under the iterative control law which makes the present iterative ADP algorithm feasible for implementation both on-line and off-line. Neural networks are used to approximate the iterative performance index function and compute the iterative control policy, respectively, to implement the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.     

一种非线性优化控制方法及其在鱼雷控制中的应用

提出了一种带优化修正函数的非线性ＰＩＤ控制器设计方法,通过对控制器参数离线寻优,并对修正函数在线优化调整,可用它设计出性能优良且易于工程实现的控制器,然后用地为某型鱼雷非线性系统设计了弹道深义控制器并在各种人水条件下进行了仿真研究,仿真表明,所设计的鱼雷非线笥弹道深度控制系统具有良好的动、静态特性,且对鱼雷人水条件的变化具有较强的适应性。     

Near optimal decentralised control with a pre-specified degree of stability

In this paper we develop a method for computing near optimal decentralised control with a pre-specified degree of stability for large scale, linear, interconnected dynamical systems. All the calculations in the new method are performed off-line using a three level hierarchical structure. We provide a condition the satisfaction of which ensures that the system has a pre-specified degree of stability. We also show that the control developed using the new method is more stable than the optimal decentralised control obtained by neglecting all interactions between the subsystems.     

具有多项式时间复杂性的离散事件系统安全诊断

离散事件系统的故障诊断能将已发生的不可观故障事件及时诊断出来,但往往容易忽略故障诊断期间系统的安全性.为解决这一问题,提出了一种具有多项式时间复杂性的安全故障诊断方法.先对离散事件系统的安全可诊断性进行了形式化,再通过构造一个非法语言识别器对系统被禁止操作序列进行识别,并在此基础上构建了一个对系统实施安全诊断的安全验证器,得到了一个关于离散事件系统安全可诊断性的充分必要条件,实现了对系统的安全故障诊断.同时,通过对安全验证器的构建与安全可诊断性的判定的复杂性分析,得到了该安全故障诊断方法可在多项式时间内实现等结论.