A controllability theory for nonlinear systems

A Lyapunov-like approach to the controllability of nonlinear dynamic systems is presented. A theory is developed which yields sufficient conditions for complete controllability for some classes of nonlinear systems; feedback controllers which drive the systems to desired terminal conditions, at a specified final time, are also obtained. Well-known controllability conditions for linear dynamic systems are derived using this general controllability theory. Elliptical regions are found which contain (bound) the trajectories of a class of systems controlled according to these methods. These regions are used in synthesizing controllers for nonlinear systems and for a class of state-variable inequality constrained problems. An uncontrollability theorem, based also upon Lyapunov-like notions, is presented; this yields sufficiency conditions for uncontrollability for some types of nonlinear systems. Relationships of the theories to other nonlinear controllability approaches are indicated.     

Dynamic equations in descriptor form

This paper studies a general form of sets of equations that is often the product of problem formulation in large-scale systems, especially when the equations are expressed in terms of the natural describing variables of the system. Such equations represent a broad class of time-evolutionary phenomena, and include as special cases ordinary static equations of arbitrary dimension, ordinary state-space equations, combinations of static and dynamic equations, and noncausal systems. The main thrust of the paper is to show (for sets of linear equations) that familiar concepts of dynamic system theory can be extended to this more general class, although sometimes with significant modification. Two new (and essentially dual) concepts, that of solvable and conditionable sets of equations, are found to be fundamental to the study of equations of this form. The notion of initial conditions, although not directly related to a state, is used as a general solution method for equations of this type. In addition a set of necessary and sufficient conditions for a set of dynamic equations to contain an embedded state-space representation is derived.     

Trust management and trust theory revision

A theory of trust for a given system consists of a set of rules that describe trust of agents in the system. In a certain logical framework, the theory is generally established based on the initial trust of agents in the security mechanisms of the system. Such a theory provides a foundation for reasoning about agent beliefs as well as security properties that the system may satisfy. However, trust changes dynamically. When agents lose their trust or gain new trust in a dynamic environment, the theory established based on the initial trust of agents in the system must be revised, otherwise it can no longer be used for any security purpose. This paper investigates the factors influencing trust of agents and discusses how to revise theories of trust in dynamic environments. A methodology for revising and managing theories of trust for multiagent systems is proposed. This methodology includes a method for modeling trust changes, a method for expressing theory changes, and a technique for obtaining a new theory based on a given trust change. The proposed approach is very general and can be applied to obtain an evolving theory of trust for agent-based systems.     

Observer theory in optimal control for systems with time delay†

An observer theory for estimating the state variables of deterministic linear time-invariant dynamic forced system is presented. The variation in the cost performance when some of the state variables are estimated by using a linear observer system is evaluated.     

A stability theory for constrained dynamic systems withapplications to electric power systems

This paper develops a stability theory for constrained dynamic systems which are defined as dynamic systems whose state trajectories are restricted to a particular set within the state space called the feasible operating region. This theory is based on a generalization of the concepts introduced by Venkatasubramanian et al. (1992), for the differential algebraic equation (DAE) stability problem. Our stability problem formulation includes a large class of constrained systems. It is particularly well suited for representing systems with inequality constraints. Also, with this modeling framework, we can develop an approximate model for a DAE system that may be defined arbitrarily close to the original system. The main theoretical result of this paper is a characterization of the boundary of the restricted asymptotic stability region. Specifically, we show that the quasistability boundary includes trajectories that are tangent to the boundary of the feasible operating region. Our primary application of these results is analyzing the electric power system stability following the occurrence of a network fault     

Controllability and the theory of economic policy: a structural approach

Tinbergen's policy rule states that we must have at least as many policy instruments as the number of target variables if we wish to realize an arbitrarily fixed set of policy targets. We explore the structural characterization of the controllability of economic systems described by a set of static or dynamic equations. First, an economic system is represented as a directed graph, where the nodes stand for economic variables, while the arcs indicate the relations among these variables. Then, the main result is as follows: a static economic system is structurally controllable if and only if there exists a set of disjoint paths on the graph representation or the system which connect the set of instruments to each target. Similar graph-theoretic characterization of structural controllability is obtained for dynamic systems. Conditions for structural output controllability and structural perfect controllability are also discussed.     

Optimal nonzero set point regulation via fixed-order dynamiccompensation

Standard LQG (linear quadratic Gaussian) theory is generalized to a regulation problem involving specified nonzero setpoints for the state and control variables and nonzero-mean disturbances. For generality, the results are obtained for the problem of fixed-order (i.e. not necessarily full order) dynamic compensation. When the state control, and disturbance offsets are set to zero and the compensator order is set equal to the plant dimension. The standard LQG result is recovered. These results provide the dynamic counterpart for the nonzero set point regulation results obtained by D.S. Bernstein and W.M. Haddad (1987) by means of static controllers     

Observer theory for distributed-parameter systems

This paper examines the problem of the approximate reconstruction of the unknown state variables in distributed-parameter systems. New results on the observer theory for important classes of linear and non-linear operator, partial differential, and partial differential-integral equations in describing distributed-parameter systems are presented. The specific developments employ the recent results on Lyapunov stability theory, along with the theory of linear and non-linear semigroup operators, and their infinitesimal generators. The questions of observability, stability of the state reconstruction error dynamics associated with the proposed observer structure are discussed. The theoretical results are illustrated with some applications to problems of the kinetic lumping of complex distributed-parameter chemical reaction systems, as well as the observer design for linear and non-linear distributed-parameter diffusion systems.     

基于流演算理论的动态访问控制模型研究

访问控制模型为系统的信息安全提供了一个理论框架,其目的是保护系统资源不被非法用户盗用,防止合法用户对受保护信息进行非法使用。然而,现有的访问控制模型大部分属于静态授权模型,不能方便地描述大规模、异构的分布式网络系统中授权过程的动态变化。为了解决上述不足,在充分研究流演算理论的基础上,提出了一个基于流演算理论的访问控制模型(FCDAC)。FCDAC将动态世界中的所有授权过程都看作是动作的结果,通过动作来实现状态的变化,并且在系统中只需描述动作的前提条件公理和状态更新公理就可容易地实现权限的变化。最后,通过一个教务管理实例验证上述理论,结果表明FCDAC是可行的。     

系统运动空间与系统映射论的初步探讨

在研究系统运动的动力和表象问题时,提出了系统运动空间和系统映射论的思想。由于它们在前期研究中解释了一些系统哲学问题,因此论文详细给出了它们及关联概念的定义。利用这些概念研究了自然系统和人工系统的特征,及它们之间的关系。研究表明:自然系统是因素全集到数据全集的映射;而人工系统是可测相关数据到可调节因素的映射。研究解释了人工系统得到的实验数据永远与自然系统产生的数据存在误差;人工系统的功能只是自然系统功能的一部分;人工系统只能无限趋近于自然系统而无法达到的原因。系统运动空间和系统映射论可以解决一些系统层面的问题,并拟在系统可靠性研究领域进行实现,但进一步问题有待研究。     

Truth Maintenance in Blackboard Environment

Constraint satisfaction and search problems generally fall into the class of problems for which a direct algorithmic solution does not exist. The solution of these problems requires the examination of state spaces. A problem solver (inference engine) alone is not able to organize and maintain state space consistently. For this purpose a so-called truth maintenance system is required. Our truth maintenance system (MEKON) organizes data within a data abstraction called a context . Each context corresponds to one problem state and contains currently believed data. The truth maintenance system provides believed data retrieval, belief revision, contradiction handling and non-monotonicity handling, the features that help a problem solver to examine state spaces. MEKON represents an ATMS-like system implemented within BEST (Blackboard-based Expert System Toolkit). However, some special MEKON features such as state variables, context sensitive generation of assumptions and explicit context generation, that are not present in standard ATMSs, facilitate not only the solution of constraint satisfaction problems, but also the solution of search problems (not provided by standard ATMSs). Being deeply integrated with Prolog/Rex, BEST's knowledge representation language, and BEST's inference engine, MEKON provides a simple and efficient means for the examination of state spaces. Facts, hypotheses (assumptions), and concepts (frames) are used to describe a problem state, contexts are used to represent points in the state spaces, while rules are used to perform state transitions. MEKON is the only truth maintenacne system that provides truth maintenance capabilities on local blackboards thus enabling the solution of complex problems which include different kinds of real constraint satisfaction and search problems concerning diagnosis, allocation tasks, classification tasks, planning or scenario making.     

Compensator design for multivariable linear systems

The problem of the specification of the order and structure of a linear dynamic compensator in order to obtain arbitrary pole placement in a closed-loop linear system comprised of the compensator in cascade with a linear plant is discussed. A significant application of the theory is to the design of optimal systems in those cases where not all the state variables of the plant can be measured. These results permit a completely algorithmized approach to the design of compensators for linear systems.     

Application of linear optimal control and filtering theory to the Saturn V launch vehicle

The application of linear optimal control and least square filtering theory to the design of a control system for the Saturn V launch vehicle is described. System performance is evaluated on the basis of the ratio of the standard deviations of structural load, engine deflection, and lateral velocity drift to their design limits. An optimal linear control is derived from a quadratic performance index in ratios of these critical variables to their design limits. It is shown that this essentially eliminates trial and error search for suitable quadratic index weighting coefficients. It is also shown that the standard deviations are only slightly degraded when feedback gains on actuator states and bending and slosh modes are eliminated, leaving feedback gains on only the three rigid-body states and feed-forward gains on the wind-induced angle of attack and wind-shear velocity. A new method of reducing the state estimation filter dimension to yield suboptimal estimation of the three rigid-body states and two wind model states is applied and shown to cause only a slight additional increase in the standard deviations of the critical system variables.     

Disturbance decoupling for a class of nonlinear MIMO systems by static measurement feedback

In this paper, the disturbance decoupling problem for a square-invertible nonlinear system is stated and solved by static feedback of measured variables only, in contrast with standard solutions which assume that the full state is available for feedback. The results are valid for left-invertible systems as well.     

Radial basis function neural network for approximation andestimation of nonlinear stochastic dynamic systems

This paper presents a means to approximate the dynamic and static equations of stochastic nonlinear systems and to estimate state variables based on radial basis function neural network (RBFNN). After a nonparametric approximate model of the system is constructed from a priori experiments or simulations, a suboptimal filter is designed based on the upper bound error in approximating the original unknown plant with nonlinear state and output equations. The procedures for both training and state estimation are described along with discussions on approximation error. Nonlinear systems with linear output equations are considered as a special case of the general formulation. Finally, applications of the proposed RBFNN to the state estimation of highly nonlinear systems are presented to demonstrate the performance and effectiveness of the method.     

An approach to a singular optimal control problem for non-linear systems using differential form theory

By applying differential form theory, we consider the singular control problem for non-linear systems with control variables appearing linearly in both the system dynamics and the performance index. First, we derive necessary conditions of singular optimality for a single-input system, including the relation to the Euler-Poisson equation and to the generalized Legendre-Clebsch condition. Defining the degree of singularity, we develop necessary conditions satisfied by the singular trajectory embedded in a reduced space. For a time-invariant system, we clarify the relation between the dynamic and the related static optimality. Second, we derive necessary conditions for singular optimality for a multi-input system where the dimension of the control vector is equal to that of the state space. We show that the Shima-Sawaragi condition for the optimality of boundary controls and the generalized Legendre-Clebsch condition are obtained from these conditions. The results are also applied to the analysis of a time-invariant system.     

面向Android应用程序的代码保护方法研究

近年来,Android操作系统快速发展,逐渐成为移动设备最常用的操作系统之一.与此同时,Android系统的安全问题也日益明显.由于Android系统自身的安全体系不够健全以及Android应用代码保护方法缺失,大量Android应用面临逆向工程、盗版、恶意代码植入等威胁.文章针对Android应用所面临的这些安全问题进行分析,并指出问题存在的原因.在此基础上,设计了一个完整的Android应用程序代码保护方法,该方法由PC端处理模块、Android端处理模块以及Android代码开发规范构成.为使该方法更具可操作性,文章还给出了一些关键技术的实现,包括基于AES算法的加密保护、伪加密、加壳、代码混淆以及特殊编码规则等.文章提出的面向Android应用程序的代码保护方法借鉴了传统的保护方法,结合Android系统的自身特性,采用文件加密、代码混淆、反动态调试、完整性校验以及加壳等技术,从对抗静态攻击和对抗动态调试两个方面提高了应用抗攻击的能力.因此,该方法不仅具有一定的理论意义,还具有一定的实际应用价值.     

Digital parameter-adaptive control of an air-conditioning plant

Two parameter-adaptive (self-tuning) control algorithms for multivariable systems are described. The algorithms are designed on the basis of linear input-output system models by the combination of recursive parameter estimation and control algorithms: a parameter-adaptive deadbeat controller and a parameter-adaptive optimal state controller. These controllers are applied to a two-input two-output air-conditioning pilot plant, which consists of an air heater and an air humidifier and whose output variables are the temperature and the relative humidity of the air measured at the air outlet. The air-conditioning plant is a nonlinear system and its linearized static and dynamic behaviour is strongly dependent on the operating point characterized mainly by the output variables and by the air flow rate through the plant. The results of the real-time control experiments indicate that it is possible to use the self-tuning features of the parameter-adaptive controllers to stabilize the controlled system after a short adaption phase and to achieve at least a satisfactory control performance for time varying air flow rates and for time varying setpoints of the output variables.     

Topology theory on rough sets.

For further studying the theories and applications of rough sets (RS), this paper proposes a new theory on RS, which mainly includes topological space, topological properties, homeomorphism, and its properties on RS by some new definitions and theorems given. The relationship between partition and countable open covering is discussed, and some applications based on the topological rough space and its topological properties are introduced. Moreover, some perspectives for future research are given. Throughout this paper, the advancements of the new theory on RS and topological algebra not only represent an important theoretical value but also exhibit significant applications of RS and topology.     

Using the bottom clause and mode declarations in FOL theory revision from examples

Theory revision systems are designed to improve the accuracy of an initial theory, producing more accurate and comprehensible theories than purely inductive methods. Such systems search for points where examples are misclassified and modify them using revision operators. This includes trying to add antecedents to clauses usually following a top-down approach, considering all the literals of the knowledge base. Such an approach leads to a huge search space which dominates the cost of the revision process. ILP Mode Directed Inverse Entailment systems restrict the search for antecedents to the literals of the bottom clause. In this work the bottom clause and mode declarations are introduced in a first-order logic theory revision system aiming to improve the efficiency of the antecedent addition operation and, consequently, also of the whole revision process. Experimental results compared to revision system FORTE show that the revision process is on average 55 times faster, generating more comprehensible theories and still not significantly decreasing the accuracies obtained by the original revision process. Moreover, the results show that when the initial theory is approximately correct, it is more efficient to revise it than learn from scratch, obtaining significantly better accuracies. They also show that using the proposed theory revision system to induce theories from scratch is faster and generates more compact theories than when the theory is induced using a traditional ILP system, obtaining competitive accuracies. This is an extended and revised version of the ILP 2008 paper (Duboc et al. 2008).