Timed Petri Nets in Hybrid Systems: Stability and Supervisory Control

In this paper, timed Petri nets are used to model and control hybrid systems. Petri nets are used instead of finite automata primarily because of the advantages they offer in dealing with concurrency and complexity issues. A brief overview of existing results on hybrid systems that are based on Petri nets is first presented. A class of timed Petri nets named programmable timed Petri nets (PTPN) is then used to model hybrid systems. Using the PTPN, the stability and supervisory control of hybrid systems are addressed and efficient algorithms are introduced. In particular, we present sufficient conditions for the uniform ultimate boundness of hybrid systems composed of multiple linear time invariant plants which are switched between using a logical rule described by a Petri net. This paper also examines the supervisory control of a hybrid system in which the continuous state is transfered to a region of the state space in a way that respects safety specifications on the plant's discrete and continuous dynamics.     

TREE-LIKE HIERARCHY OF SYSTEMS

In this paper the concepts of tree-like hierarchy of systems and linked hierarchy of systems are introduced. The concepts can be seen as generalizations of those of time systems and linked time systems, respectively; moreover, the concepts can be used to establish models of social organizations and of the development of a cultural entity. Some open questions are posed.     

Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models

This paper introduces a new approach for nonlinear and non-stationary (time-varying) system identification based on time-varying nonlinear autoregressive moving average with exogenous variable (TV-NARMAX) models. The challenging model structure selection and parameter tracking problems are solved by combining a multiwavelet basis function expansion of the time-varying parameters with an orthogonal least squares algorithm. Numerical examples demonstrate that the proposed approach can track rapid time-varying effects in nonlinear systems more accurately than the standard recursive algorithms. Based on the identified time domain model, a new frequency domain analysis approach is introduced based on a time-varying generalised frequency response function (TV-GFRF) concept, which enables the analysis of nonlinear, non-stationary systems in the frequency domain. Features in the TV-GFRFs which depend on the TV-NARMAX model structure and time-varying parameters are investigated. It is shown that the high-dimensional frequency features can be visualised in a low-dimensional time–frequency space.     

具有随机丢包的关联系统的分散控制

研究了在子系统之间信息传输存在随机丢包现象时关联大系统的性能分析及控制器设计问题. 通过引入空间变量及空间移动算子, 将关联系统建模成具有Markovian跳变参数的关于离散时间变量和空间变量的多维系统, 结合跳变系统有界实引理, 得到使整个关联系统均方稳定并满足一定性能指标的解析条件. 然后基于线性矩阵不等式变换给出确保关联大系统鲁棒均方稳定性的一种分散输出反馈控制器的设计方法. 最后通过一组多机器人直线编队的例子说明本文算法的正确性和有效性.     

Model reduction based on limited‐time interval impulse response Gramians

In this paper, three new Gramians are introduced namely ‐ limited‐time interval impulse response Gramians (LTIRG), generalized limited‐time Gramians (GLTG) and generalized limited‐time impulse response Gramians (GLTIRG). GLTG and GLTIRG are applicable to both unstable systems and also to systems which have eigenvalues of opposite polarities and equal magnitude. The concept of these Gramians is utilized to develop model reduction algorithms for linear time‐invariant continuous‐time single‐input single‐output (SISO) systems. In the cases of GLTIRG and GLTG based model reduction, the standard time‐limited Gramians are generalized to be applied to unstable systems by transforming the original system into a new system which requires the solution of two Riccati equations. Two numerical examples are included to illustrate the proposed methods. The results are also compared with standard techniques.     

Diagnosability of fuzzy discrete event systems

In this paper, discrete event systems (DESs) are reformulated as fuzzy discrete event systems (FDESs) and fuzzy discrete event dynamical systems (FDEDSs). These frameworks include fuzzy states, events and IF-THEN rules. In these frameworks, all events occur at the same time with different membership degrees. Fuzzy states and events have been introduced to describe uncertainties that occur often in practical problems, such as fault diagnosis applications. To measure a diagnoser’s fault discrimination ability, a fuzzy diagnosability degree is proposed. If the diagnosability of the degree of the system yields one a diagnoser can be implemented to identify all possible fault types related to a system. For any degree less than one, researchers should not devote their time to distinguish all possible fault types correctly. Thus, two different diagnosability definitions FDEDS and FDES are introduced. Due to the specialized fuzzy rule-base embedded in the FDEDS, it is capable of representing a class of non-linear dynamic system. Computationally speaking, the framework of diagnosability of the FDEDS is structurally similar to the framework of diagnosability of a non-linear system. The crisp DES diagnosability has been turned into the term fuzzy diagnosability for the FDES. The newly proposed diagnosability definition allows us to define a degree of diagnosability in a class of non-linear systems. In addition, a simple fuzzy diagnosability checking method is introduced and some numerical examples are provided to illustrate this theoretical development. Finally, the potential applications of the proposed method are discussed.     

Necessary and sufficient condition for average consensus of networked multi-agent systems with heterogeneous time delays

This paper deals with an average-consensus problem of networked multi-agent systems with heterogeneous time delays. First, a necessary and sufficient condition is derived for multi-agent systems to achieve average consensus. This condition is represented in the form of an algebraic condition by using the delay-transition and the delay-weighted Laplacians. Second, a performance criterion is introduced to evaluate multi-agent systems that do not achieve average consensus. The criterion is represented in terms of the norms with respect to the above Laplacians. These results imply that the introduced Laplacians play important roles in analysing multi-agent systems with heterogeneous time delays. The validity of the analysis results is demonstrated by simulations with six-agent systems.     

一类时滞非线性控制系统的输出调节

研究了一类单输出时滞线性系统的输出调节问题,首先通过精确线性化方法将其转化为一类特殊线性时滞系统对非线系统的跟踪总是,然后通过积分变换转化为无时滞的线性系统对非线性系统的跟踪,新的精确线性化结果保证了经过积分变换后的系统仍然可控,同时,提出了可解性的概念解决了线性系统对非线性系统的跟踪问题,得到了时滞非线性系统输出调节问题的局部和全局的结果,该结果对外部系统假设较弱。     

Iterative Learning Control for uncertain systems: Robust monotonic convergence analysis

In this paper, we present a novel Robust Monotonic Convergence (RMC) analysis approach for finite time interval Iterative Learning Control (ILC) for uncertain systems. For that purpose, a finite time interval model for uncertain systems is introduced. This model is subsequently used in an RMC analysis based on μ analysis. As a result, we can handle additive and multiplicative uncertainty models in the RMC problem formulation, analyze RMC of linear time invariant MIMO systems controlled by any linear trial invariant ILC controller, and formulate additional straightforward RMC conditions for ILC controlled systems. To illustrate the derived results, we analyze the RMC properties of linear quadratic (LQ) norm optimal ILC.     

Linear time-variable systems: Stability of reduced models

The notion of a ‘uniformly balanced’ realization for time-variable systems has been previously introduced. This representation is characterized by the fact that its controllability and observability grammians are equal and diagonal. Such a framework has many remarkable properties and leads to a setting where the subsystems can be taken as reduced model for time-variable systems. It turns out that once the stability of a subsystem is guaranteed, then the subsystem preserves many of the properties of the original system. In this paper, the stability of subsystems is fully explored.     

Stability analysis for networked control systems based on event-time-driven mode

This article studies the problem of stability analysis for a class of networked control systems (NCS), whose control gain is assumed to be known. A switched delay system model is obtained based on the event-time-driven scheme. To solve the stability problem of the new NCS model, a new approach based on the Lyapunov functional exponential estimation method is introduced. By using this method, sufficient conditions are developed to guarantee exponential stability of the considered system. The results obtained may be less conservative than the existing ones from the perspective of maximum allowable transfer interval because the unavailable time is considered in this article. An example is given to show the effectiveness of the proposed method.     

μ-Dependent model reduction for uncertain discrete-time switched linear systems with average dwell time

In this article, the model reduction problem for a class of discrete-time polytopic uncertain switched linear systems with average dwell time switching is investigated. The stability criterion for general discrete-time switched systems is first explored, and a μ-dependent approach is then introduced for the considered systems to the model reduction solution. A reduced-order model is constructed and its corresponding existence conditions are derived via LMI formulation. The admissible switching signals and the desired reduced model matrices are accordingly obtained from such conditions such that the resulting model error system is robustly exponentially stable and has an exponential H _∞ performance. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results.     

On Near‐controllability of Discrete‐time Upper‐triangular Bilinear Systems with Applications to Controllability

Near‐controllability is defined for those systems that are uncontrollable but have a large controllable region. It is a property of nonlinear control systems introduced recently, and it has been demonstrated on two classes of discrete‐time bilinear systems. This paper studies near‐controllability of discrete‐time upper‐triangular bilinear systems, which are uncontrollable and are more general than the two classes mentioned. A necessary and sufficient condition for the systems in dimension two to be nearly controllable is presented, which covers the existing results. For the systems with high dimensions, necessary conditions and sufficient conditions of near‐controllability are provided, which generalize the existing results. In particular, the obtained near‐controllability results are applied to controllability of discrete‐time bilinear systems. An example also is given to demonstrate the effectiveness, which shows that the controllability problems of discrete‐time bilinear systems can be solved by near‐controllability.     

Energy-shaping for Hamiltonian control systems with time delay

This paper investigates the asymptotical stabilization of Hamiltonian control systems with time delay. First, Hamiltonian control systems with time delay are proposed. Second, a two-to-one (TTO) principle is introduced that two different Hamiltonian functions are simultaneously energy-shaping by one desired energy function. Third, a novel matching equation is built via the TTO principle for the Hamiltonian control systems with time delay, which generates an effective control law for the Hamiltonian control systems with time delay. Finally, a numerical example shows the effectiveness of proposed method.     

Self-organization in the commons: An empirically-tested model

A appropriate bottom-up rule system can support the sustainability of common-pool resources such as forests and fisheries. The process that leads to the developments of such institutional settings requires the considerations of multiple social, physical, and institutional factors over long time horizons. In this paper, we present the SONICOM model as a general exploratory model of CPR systems. The model can be configured to represent different CPR systems in order to explore what kind of institutional settings result in stable systems, i.e. situations where the resource and the appropriators are in a state of well-being. We use a large-N-dataset of CPR management institutions to validate the model. The results show numerous correlations between various parameters of the system such as rule compliance, social influence and resource growth rate which help explaining the process of institutional emergence as well as unveiling the conditions under which systems are stable.     

Evolving information systems: meeting the ever-changing environment

Abstract. To meet the demands of organizations and their ever-changing environment, information systems are required which are able to evolve to the same extent as organizations do. Such a system has to support changes in all time-and application-dependent aspects. In this paper, requirements and a conceptual framework for evolving information systems are presented. This framework includes an architecture for such systems and a revision of the traditional notion of update. Based on this evolutionary notion of update (recording, correction and forgetting) a state transition-oriented model on three levels of abstraction (event level, recording level, correction level) is introduced. Examples are provided to illustrate the conceptual framework for evolving information systems.     

一种网络控制系统的随机通信逻辑设计与分析

针对网络控制系统的带宽约束问题,提出一种基于系统状态的状态依赖泊松过程决定的随机通信逻辑,并将其应用于一般结构的状态反馈网络控制系统．介绍了具有通信逻辑的网络控制系统的结构,建立了具有随机通信逻辑的网络控制系统模型．利用随机稳定性理论和带时倚强度泊松过程相关原理,进一步证明了系统保持均方渐近稳定的充分条件．最后通过仿真算例验证了结论的有效性．     

基于延时预测的模型状态反馈网络控制方法

网络延时的存在不仅会使控制系统的动、静态性能变差,还可能会破坏系统的稳定性,造成既有控制方法的失效。针对带有随机延时的网络控制系统,提出了一种基于网络延时实时预测和系统状态逼近的控制方法。首先,建立无延时的理想控制系统模型作为标准控制系统模型;其次,应用基于隐马尔可夫模型(HMMs)的延时预测算法预测网络延时,该方法能够实时自适应学习,以适应网络负载情况的变化,得到更符合实际情况的延时预测值;最后,根据网络延时的预测值、实际网络控制系统与标准控制系统模型的状态之差,来调整控制信号,从而使实际网络控制系统的状态与标准控制系统模型接近、甚至相等,达到期望的控制效果。数字仿真结果表明,这一方法是可行的,能够获得更加快速的动态性能和稳定的静态性能。     

Variable Structure Predefined‐Time Stabilization of Second‐Order Systems

A controller that stabilizes second‐order vector systems in predefined‐time is introduced in this paper. That is, for second‐order systems a controller is designed such that the trajectories reach the origin in a time defined in advance. The proposed controller is a variable structure controller that first drive the system trajectories to a linear manifold in predefined time and then drives the system trajectories to a non‐smooth manifold with the predefined‐time stability property, in predefined time also; this is done in order to avoid the differentiability problem that inherently appears when stabilizing high‐order systems in finite time under the block control principle technique. The proposal is applied to the predefined‐time exact tracking of fully actuated mechanical systems. As an example, the proposed solution is applied to a two‐link planar manipulator, and numerical simulations are conducted to show its performance.