Averaged control

We analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter.First we consider the problem of controllability for linear finite-dimensional systems and show that a necessary and sufficient condition for averaged controllability is an averaged rank condition, in the spirit of the classical rank condition for linear control systems, but involving averaged momenta of any order of the matrices generating the dynamics and representing the control action.We also describe some open problems and directions of possible research, in particular on the average controllability of evolution partial differential equations. In this context we analyze also the averaged version of a classical optimal control problem for a parameter dependent elliptic equation and derive the corresponding optimality system.     

A review of hierarchical facility location models

In this study, we review the hierarchical facility location models. Although there have been a number of review papers on hierarchical facility problems, a comprehensive treatment of models has not been provided since the mid-80s. This review fills the gap in the literature. We first classify the hierarchical facility problems according to the features of systems studied, which are based on flow pattern, service availability at each level of the hierarchy, and spatial configuration of services in addition to the objectives to locate facilities. We then investigate the applications, mixed integer programming models, and solution methods presented for the problem. With an overview of the selected works, we consolidate the main results in the literature.     

一类高阶线性系统的分层控制

近年来, 一种基于系统层次结构的分层控制方法发展了起来, 它主要针对的是高阶复杂系统. 为了分析和控制这类系统, 我们首先根据需要构建一个合适的低阶抽象系统, 然后在此基础上分析和设计原始系统控制律, 即所谓的接口函数. 本文将此方法用于一类高阶线性系统的稳定控制问题, 并得到了相应的控制律. 最后, 算例部分的仿真结果说明了这种方法的有效性.     

Positive state controllability of positive linear systems

Controllability of positive systems by positive inputs arises naturally in applications where both external and internal variables must remain positive for all time. In many applications, particularly in population biology, the need for positive inputs is often overly restrictive. Relaxing this requirement, the notion of positive state controllability of positive systems is introduced. A connection between positive state controllability and positive input controllability of a related system is established and used to obtain Kalman-like controllability criteria. In doing so we aim to encourage further study in this underdeveloped area.     

Controllability of product systems

For nonlinear continuous-time control systems we introduce the notion of controllability with selectable time, which is a little bit stronger than the usual controllability notion. For a large class of nonlinear systems on compact manifolds, controllability with selectable time is equivalent to controllability together with strong accessibility. It turns out that the controllability of products of independent control systems is related to this new controllability notion. The main result states that a smooth control affine product system is controllable if and only if all factors are controllable and at most one factor is not controllable with selectable time, provided the accessibility algebra of the product system has full rank.     

Control of nondeterministic discrete-event systems for bisimulation equivalence

Most prior work on supervisory control of discrete event systems is for achieving deterministic specifications, expressed as formal languages. In this paper we study supervisory control for achieving nondeterministic specifications. Such specifications are useful when designing a system at a higher level of abstraction so that lower level details of system and its specification are omitted to obtain higher level models that may be nondeterministic. Nondeterministic specifications are also meaningful when the system to be controlled has a nondeterministic model due to the lack of information (caused for example by partial observation or unmodeled dynamics). Language equivalence is not an adequate notion of behavioral equivalence for nondeterministic systems, and instead we use the finest known notion of equivalence, namely the bisimulation equivalence. Choice of bisimulation equivalence is also supported by the fact that bisimulation equivalence specification is equivalent to a specification in the temporal logic of /spl mu/-calculus that subsumes the complete branching-time logic CTL*. Given nondeterministic models of system and its specification, we study the design of a supervisor (possibly nondeterministic) such that the controlled system is bisimilar to the specification. We obtain a small model theorem showing that a supervisor exists if and only if it exists over a certain finite state space, namely the power set of Cartesian product of system and specification state spaces. Also, the notion of state-controllability is introduced as part of a necessary and sufficient condition for the existence of a supervisor. In the special case of deterministic systems, we provide an existence condition that can be verified polynomially in both system and specification states, when the existence condition holds.     

SYSTEM TRANSFORMATIONS AND ADAPTIVE SYSTEMS

The purpose of this paper is to formulate the concept of system transformation and the concept of adaptive system in the framework of general systems theory, and to characterize both concepts as well as mutual relationships between them from a qualitative viewpoint.

We define a system transformation as a mapping on the class of all systems under consideration in a general and unified manner, and especially consider the variety of system behavior under parallel, cascade, and feedback transformation for linear functional time systems. We introduce the notion of open system in terms of system transformation. We then formulate class controllability and adaptability of an open system under system transformation, and characterize them in terms of basic system properties. In particular, we obtain a necessary and sufficient condition under which an open system is adaptive.     

Using Control Theory to Achieve Service Level Objectives In Performance Management

A widely used approach to achieving service level objectives for a software system (e.g., an email server) is to add a controller that manipulates the target system's tuning parameters. We describe a methodology for designing such controllers for software systems that builds on classical control theory. The classical approach proceeds in two steps: system identification and controller design. In system identification, we construct mathematical models of the target system. Traditionally, this has been based on a first-principles approach, using detailed knowledge of the target system. Such models can be complex and difficult to build, validate, use, and maintain. In our methodology, a statistical (ARMA) model is fit to historical measurements of the target being controlled. These models are easier to obtain and use and allow us to apply control-theoretic design techniques to a larger class of systems. When applied to a Lotus Notes groupware server, we obtain model-fits with R² no lower than 75% and as high as 98%. In controller design, an analysis of the models leads to a controller that will achieve the service level objectives. We report on an analysis of a closed-loop system using an integral control law with Lotus Notes as the target. The objective is to maintain a reference queue length. Using root-locus analysis from control theory, we are able to predict the occurrence (or absence) of controller-induced oscillations in the system's response. Such oscillations are undesirable since they increase variability, thereby resulting in a failure to meet the service level objective. We implement this controller for a real Lotus Notes system, and observe a remarkable correspondence between the behavior of the real system and the predictions of the analysis. This indicates that the control theoretic analysis is sufficient to select controller parameters that meet the desired goals, and the need for simulations is reduced.     

Necessary and sufficient conditions for quadratic controllability of a class of uncertain systems

We introduce a controllability notion for uncertain systems, namely, quadratic controllability. For a specific class of norm bounded uncertain systems, we show that this notion is equivalent to controllability of a nominal system and the satisfaction of a certain structural condition by the uncertainty. For systems in which the uncertain parameters affect all control inputs, this structural condition is simply the familiar matching condition commonly encountered in the literature on robust and adaptive control of uncertain systems.     

On strong controllability for planar affine nonlinear systems

Different to linear systems, a controllable nonlinear system does not generally imply that it is strongly controllable. This paper will investigate the strong controllability of planar affine nonlinear systems and obtain its necessary and sufficient condition by introducing the variation function of the control curve. These conditions are imposed on the system structure only. In addition, we also point out that, for a class of polynomial systems, their strong controllability is equivalent to their controllability. Finally, some examples are given to show the application of our results.     

Multiple fuzzy model-based temperature predictive control for HVAC systems

In this paper, a multiple model predictive control (MMPC) strategy based on Takagi–Sugeno (T–S) fuzzy models for temperature control of air-handling unit (AHU) in heating, ventilating, and air-conditioning (HVAC) systems is presented. The overall control system is constructed by a hierarchical two-level structure. The higher level is a fuzzy partition based on AHU operating range to schedule the fuzzy weights of local models in lower level, while the lower level is composed of a set of T–S models based on the relation of manipulated inputs and system outputs correspond to the higher level. Following this divide-and-conquer strategy, the complex nonlinear AHU system is divided into a set of T–S models through a fuzzy satisfactory clustering (FSC) methodology and the global system is a fuzzy integrated linear varying parameter (LPV) model. A hierarchical MMPC strategy is developed using parallel distribution compensation (PDC) method, in which different predictive controllers are designed for different T–S fuzzy rules and the global controller output is integrated by the local controller outputs through their fuzzy weights. Simulation and real process testing results show that the proposed MMPC approach is effective in HVAC system control applications.     

State equation, controllability, and maximal matchings of petri nets

Petri nets are a versatile modeling device for studying the structure and control of concurrent systems. Petri nets and related graph models have been used for modeling a wide variety of systems from computers to social systems. In order to introduce this interesting modeling device to the researcher in control theory, this paper discusses Petri nets in the context of the state equation for a linear discrete-time system. The controllability concept of dynamic systems is applied to Petri nets for the first time. It is also shown that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.     

Pinning control and controllability of complex dynamical networks

In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output (SISO) or multi-input multi-output (MIMO) dynamical systems, and could be non-identical and nonlinear in general but will be specified to be identical linear time-invariant (LTI) systems here in the study of network controllability. Both state and structural controllability problems will be discussed, illustrating how the network topology, node-system dynamics, external control inputs and inner dynamical interactions altogether affect the controllability of a general complex network of LTI systems, with necessary and sufficient conditions presented for both SISO and MIMO settings. To that end, the controllability of a special temporally switching directed network of linear time-varying (LTV) node systems will be addressed, leaving some more general networks and challenging issues to the end for research outlook.     

分布式入侵检测模型研究

提出了分布级别的概念对分布式入侵检测系统进行分类，并引入信息抽象级别对入侵检测中审计数据所经历的逻辑抽象层次进行表述．在对现有的层次检测模型和协作检测模型的优点和缺陷进行详细分析之后，提出了一种用于分布式入侵检测系统的层次化协作模型(HCM)，并完成了相应的原型系统．该模型可以有效地综合两种现有模型的优点，在保证结点可控性和检测效率的同时提高系统的容错性和协作能力．     

On the receding horizon hierarchical optimal control of manufacturing systems

This paper concerns the development of a hierarchical framework for the integrated planning and scheduling of a class of manufacturing systems. In this framework, dynamic optimization plays an important role in order to define control strategies that, by taking into account the dynamic nature of these systems, minimize customized cost functionals subject to state and control constraints. The proposed architecture is composed of a set of hierarchical levels where a two-way information flow, assuming the form of a state feedback control, is obtained through a receding horizon control scheme. The averaging effect of the receding horizon control scheme enables this deterministic approach to handle random and unexpected events at all levels of the hierarchy. At a given level, production targets to the subsystems immediately below are defined by solving appropriate optimal control problems. Efficient iterative algorithms based on optimality conditions are used to yield control strategies in the form of production rates for the various subsystems. At the lower level, this control strategy is further refined in such a way that all sequences of operations are fully specified. The minimum cost sensitivity information provided in the optimal control formulation supports a mechanism, based on the notion of a critical machine, which plays an important role in the exploitation of the available flexibility. Finally, an important point to note is that our approach is particularly suited to further integration of the production system into a larger supply chain management framework, which is well supported by recent developments in hybrid systems theory.     

基于等级PRES+的嵌入式系统的建模与实现

为了有效的描绘规模较大的系统,需要一个分层机制,使模型可以有条理地构建.它由简单的单元组件构成,使得设计师在每个描述级上都可以很容易理解.提出并定义了用于形式化描述嵌入式系统建模的petri网的分层概念,显示了一个规模较大系统中的小部件如何使用层次的概念进行转换.该方法使得复杂的嵌入式系统描述更加模块化,具有可重用性,提高了嵌入式系统建模和分析的效率.通过一个实例表明了该方法的可行性.     

Aggregation of a class of interconnected, linear dynamical systems

In this paper, we introduce the notion of a “meaningful” average of a collection of dynamical systems as distinct from an “ensemble” average. Such a notion is useful for the study of a variety of dynamical systems such as traffic flow, power systems, and econometric systems. We also address the associated issue of the existence and computation of such an average for a class of interconnected, linear, time invariant dynamical systems. Such an “average” dynamical system is not only attractive from a computational perspective, but also represents the average behavior of the interconnected dynamical systems. The problem of analysis and control of heirarchical, large scale control systems can be simplified by approximating the lower level dynamics of such systems with such an average dynamical system.     

Hierarchical Control of Linear Systems from the Abstraction Feedback Gain

In this paper, the problem of hierarchical control for a class of linear systems is addressed. Given a large‐scale linear system, we obtain a stabilizing feedback gain for it from that of an abstract system. And then, we employ this feedback gain to design a new interface between the original system and the abstraction. Furthermore, the synthesis of the new interface can be allowed by a new simulation function characterized by a low‐order matrix associated to the abstraction. Finally, an example is given to illustrate the proposed approach.     

Key hierarchies for hierarchical access control in secure group communications

The problem of hierarchical access control in secure group communications has elicited much interest in the literatures. However, most of the researches to date on hierarchical access control pay more attention to the particular encryption techniques, but considered little about the features of key hierarchies. In hierarchical access control systems, keys are usually organized hierarchically. We analyze the user-based, resource-based and unified key hierarchies in this paper. The first two hierarchies are established from the access matrix. By unifying these two hierarchies, we get the unified key hierarchy. Furthermore, we introduce the explicit accessible set and the explicit dominating set to describe the key distributions for these hierarchies, and prove that the unified key hierarchy can be formed from the explicit dominating sets in the user-based key hierarchy or the explicit accessible sets in the resource-based key hierarchy. To evaluate the efficiency of the described key hierarchies, we combine these hierarchies with the existing key assignment models and analyze their storage and rekey overheads. These overheads can be derived from the access matrix, and the derivation procedure is described. The conclusions of this paper can help to establish a suitable key hierarchy so as to make the key assignment scheme more efficient in practical applications.     

Consistent abstractions of affine control systems

In this paper, we consider the problem of constructing abstractions of affine control systems that preserve reachability properties, and, in particular, local accessibility. In this framework, showing local accessibility of the higher level, abstracted model is equivalent to showing local accessibility of the, more detailed, lower level model. Given an affine control system and a smooth surjective map, we present a canonical construction for extracting an affine control system describing the trajectories of the abstracted variables. We then obtain conditions on the abstraction maps that render the original and abstracted system equivalent from a local accessibility point of view. Such consistent hierarchies of accessibility preserving abstractions of nonlinear control systems are then considered for various classes of affine control systems including linear, bilinear, drift free, and strict feedback systems