Interval analysis and dioid: application to robust controller design for timed event graphs

This paper deals with feedback controller synthesis for timed event graphs, where the number of initial tokens and time delays are only known to belong to intervals. We discuss here the existence and the computation of a robust controller set for uncertain systems that can be described by parametric models, the unknown parameters of which are assumed to vary between known bounds. Each controller is computed in order to guarantee that the closed-loop system behavior is greater than the lower bound of a reference model set and is lower than the upper bound of this set. The synthesis presented here is mainly based on dioid, interval analysis and residuation theory.     

Control of Petri nets subject to strict temporal constraints using Max-Plus algebra

In this paper, we treat the control problem of timed discrete event systems under temporal constraints. This type of constraint is very frequent in production systems, transportation network and in networked automation systems. Precisely, we are interested in the validation of strict temporal constraints imposed on the paths in a timed event graph (TEG) by using Max-Plus algebra. Not all the transitions of the considered TEG model are controllable, i.e. only the input transitions are controllable. An analytical approach for computing state feedback controllers is developed. Sufficient condition is given for the existence of causal control laws satisfying the temporal constraints. In the first, a TEG with observable transitions is considered. Then, the proposed approach is extended to the partially observable TEG. The synthesised feedback can be interpreted by places of control connected to the TEG to guarantee the respect of the time constraints. The proposed method is illustrated in the assembly system example.     

Event‐switched control design with guaranteed performances

In this paper, a new event‐switched control method is presented for controlling discrete‐time linear systems subject to bounded disturbances. The main advantage of the proposed method is that the nominal performance of the controlled system with periodic control updates is kept in a framework that do not require to periodically update the control law. The feedback control loop can be opened as long a state‐dependent event condition is satisfied. This condition is obtained using set theory approaches. In particular, the concept of robustly positively invariant sets is used to calculate the nominal performance and the event condition. The simulation presented in this paper confirms the efficiency of the present approach. A reduction of the numerical complexity of the approach is also proposed. Copyright © 2016 John Wiley & Sons, Ltd.     

Stable and Real-Time Scheduling of a Class of Hybrid Dynamic Systems

Based on some practical engineering problems arising from process control and space-structure control, this paper studies a class of hybrid dynamic systems in which N plants are controlled by a central controller in sharing time manner, where the plants are described by differential equations and the controller works according to the mechanism of discrete events. An event feedback strategy is suggested to be a scheduling policy such that one and only one plant among N plants is chosen to be controlled at any time. Some conditions of asymptotical and exponential stability are then given and an exponential upper bound of states norm is also estimated for the event feedback scheduling strategy. An algorithm based on event feedback strategy is presented to determine the control laws of the plants to meet the given performance. An example follows to illustrate the application and effect of the results.     

Grid automata and supervisory control of dense real-time discrete event systems

We present a generalization of the classical supervisory control theory for discrete event systems to a setting of dense real-time systems modeled by Alur and Dill timed automata. The main problem involved is that in general the state space of a timed automaton is (uncountably) infinite. The solution is to reduce the dense time transition system to an appropriate finite discrete subautomaton, the grid automaton, which contains enough information to deal with the timed supervisory control problem (TSCP). The plant and the specifications region graphs are sampled for a granularity defined in a way that each state has an outgoing transition labeled with the same time amount. We redefine the controllability concept in the context of grid automata, and we provide necessary and sufficient solvability conditions under which the optimal solution to centralized supervisory control problems in timed discrete event systems under full observation can be obtained. The enhanced setting admits subsystem composition and the concept of forcible event. A simple example illustrates how the new method can be used to solve the TSCP.     

A New Class of Supervisors for Timed Discrete Event Systems Under Partial Observation

Brandin and Wonham have developed a supervisory control framework for timed discrete event systems (TDESs) in order to deal with not only logical specifications but also temporal specifications. Lin and Wonham have extended this framework to the partial observation case, and presented necessary and sufficient conditions for the existence of a nonblocking supervisor under partial observation. In this paper, we define a new class of supervisors for TDESs under partial observation. We then present necessary and sufficient conditions for the existence of a nonblocking supervisor defined in this paper. These existence conditions of our supervisor are weaker than those of Lin and Wonham's supervisor. Note, however, that the price that must be paid to weaken the existence conditions is the higher computational cost. Moreover, given a closed regular language, we study computation of a sublanguage that satisfies the existence conditions of our supervisor. We present an algorithm for computing such a sublanguage larger than the supremal closed, controllable, and normal sublanguage.     

Dynamic self‐triggered output‐feedback control for nonlinear stochastic systems with time delays

In this paper, the dynamic self‐triggered output‐feedback control problem is investigated for a class of nonlinear stochastic systems with time delays. To reduce the network resource consumption, the dynamic event‐triggered mechanism is implemented in the sensor‐to‐controller channel. Criteria are first established for the closed‐loop system to be stochastically input‐to‐state stable under the event‐triggered mechanism. Furthermore, sufficient conditions are given under which the closed‐loop system with dynamic event‐triggered mechanism is almost surely stable, and the output‐feedback controller as well as the dynamic event‐triggered mechanism are co‐designed. Moreover, a dynamic self‐triggered mechanism is proposed such that the nonlinear stochastic system with the designed output‐feedback controller is stochastically input‐to‐state stable and the Zeno phenomenon is excluded. Finally, a numerical example is provided to illustrate the effectiveness of proposed dynamic self‐triggered output‐feedback control scheme.     

Nonblocking supervisory control of timed discrete event systems under communication delays: The existence conditions

This paper addresses the problem of nonblocking supervisory control of timed discrete event systems under communication delays based on the framework proposed by Brandin and Wonham. For such a system, a supervisory control command could be applied to the system after some time-delay limited by a finite bound corresponding to the maximal number of tick occurrences, and some uncontrollable events may unexpectedly occur within this time-delay. This paper presents the necessary and sufficient conditions for the existence of a nonblocking supervisor that can achieve a given language specification in consideration of such delayed communications.     

基于参数自适应延时反馈的混沌系统控制及应用

针对延迟反馈法参数较难确定的问题,给出了一种自适应调节反馈系数方法来控制非线性Lorenz混沌系统的方案.数值仿真结果表明,选择适当的延迟时间和反馈系数能够控制系统的不稳定周期轨道、消除混沌,并能使系统从失稳状态进入稳定状态.由于不需要外加参考信号,可以在混沌态的任意时刻施加控制,所以该方法简单易行.同时将以上控制效果应用于动画的控制中,对指定动画角色行为进行控制,使其可以运动到混沌的轨道上或者某一个特殊的轨迹上.     

A design methodology for distributed control systems to optimize performance in the presence of time delays

When a control system is implemented in a distributed fashion, with multiple processors communicating over a network, both the communication delays associated with the network and the computation delays associated with the processing time can degrade the system's performance. In this case, the performance of the system may depend not only on the performance of the individual components but also on their interaction and cooperation. The approach taken in this paper assumes that the control has been designed without taking into account the network architecture. A theoretical framework is presented which allows the effect of time delays on the mechanical performance of the system to be precisely modelled, and these models are used to determine the optimal network architecture for the given control system. A design example of a two-axis contouring system is presented.     

离散事件系统的无死锁模块化状态反馈控制

本文讨论离散事件系统的无死锁模块化状态反馈问题。首先我们定义自动机的交与并运算，然后通过引入自动机对的Ｄ－不变关系，我们证明当控制目标是两个谓词的交时，模块化状态反馈控制器是无死锁的充要条件是各子控制器是无死锁的且相应的控制器满足Ｄ－不变关系。我们证明了一个给定的自动机对于另一自动机的Ｄ－不变子自动机类有最大元存大，并由此给出一个综合算法。     

Consensus of multi‐agent systems with time‐varying topology: An event‐based dynamic feedback scheme

The event‐based control strategy is an effective methodology for reducing the controller update and communication over the network. In this paper, the event‐based consensus of multi‐agent systems with linear dynamics and time‐varying topology is studied. For each agent, a state‐dependent threshold with an exponentially decaying bound is presented to determine the event times, and a new event‐based dynamic feedback scheme is proposed. It is shown that the controller update for each agent is only dependent on its own event times, which reduces significantly the controller update or computation for each agent. Moreover, based on the event‐based dynamic feedback scheme and the event triggering function presented in this paper, the continuous communication among neighboring agents is avoided, and the Zeno‐behavior of the closed‐loop systems is excluded. A numerical example is given to illustrate the effectiveness of theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Supervisory control for real-time scheduling of periodic and sporadic tasks with resource constraints

In the framework of supervisory control of timed discrete event systems, this paper addresses the design problem of a real-time scheduler that meets stringent time constraints of periodic tasks and sporadic tasks which exclusively access shared resources. For this purpose, we present the timed discrete event models of execution of periodic tasks and sporadic tasks and resource access for shared resources. Based on these models, we present the notion of deadlock-free and schedulable languages that contain only deadline-meeting sequences which do not reach deadlock states. In addition, we present the method of systematically computing the largest deadlock-free and schedulable language, and it is also shown that schedulability analysis can be done using this language. We further show that the real-time scheduler achieving the largest deadlock-free and schedulable language is optimal in the sense that there are no other schedulers to achieve schedulable cases more than those achieved by the optimal scheduler.     

具有参数不确定性的非线性系统的鲁棒输出跟踪

研究具有非线性参数化的非线性系统的输出跟踪问题.采用时变状态反馈控制律, 指数镇定输出跟踪误差,并保证非线性系统的所有状态是有界的.为了实现时变状态反馈控 制律,设计高增益鲁棒观测器观测构造该控制律所需要的状态,使得整个闭环系统的输出能 渐近跟踪期望输出,且该闭环系统中所有信号都是有界的.     

Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable （While some switching models are probably unstabilizable）, an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.     

基于Internet的力反馈技术研究

论述了基于Internet的力反馈技术及其相关技术的发展和研究意义，综合机器人遥操作控制领域的理论方法，结合多媒体技术的最新发展，构建了一种基于事件的系统结构及其设计方法．基于该方法，分析了系统的可靠性、稳定性及力媒体传输的透明性，并设计了一个基于Internet的力反馈技术的系统实例．     

Distributed output feedback MPC with randomly occurring actuator saturation and packet loss

In this paper, a distributed output feedback model predictive control (OFMPC) algorithm is presented for the polytopic uncertain system subject to randomly occurring actuator saturation and packet loss. Compared with the intensively applied state feedback control in MPC, the OFMPC is more feasible to the real world because the system states are often unmeasurable. With taking both actuator saturation and packet loss into account, the presented OFMPC algorithm is more practical. Moreover, by splitting the controller inputs into two independent parts, the presented dynamic output feedback control (DOFC) strategy provides more freedom to the controller design. With the global system decomposed into some subsystems, the computation complexity is reduced, thus the online designing time can be saved. By defining the estimation error function and forming an augmented system to handle the DOFC and by transforming the nonlinear feedback law into a convex hull of linear feedback laws, the distributed controllers are obtained by solving a linear matrix inequality (LMI) optimization problem. Finally, some simulation examples are employed to show the effectiveness of the techniques proposed in this paper. Copyright © 2015 John Wiley & Sons, Ltd.     

Fourier-Neural-Network-Based Learning Control for a Class of Nonlinear Systems With Flexible Components

This paper considers an output feedback learning control for a class of uncertain nonlinear systems with flexible components. The distinct time delay caused by system flexibility leads to the phase lag phenomenon and low system bandwidth. Therefore, the tracking problem of such systems is very difficult and challenging. To improve the tracking performance of such systems, an iterative learning control scheme using the Fourier neural network (FNN) is presented in this paper. This scheme uses only local output information for feedback. FNN employs orthogonal complex Fourier exponentials as its activation functions and the physical meaning of its hidden-layer neurons is clear. The FNN-based learning controller introduced here relies on the frequency-domain method, which converts the tracking problem in the time domain into a number of regulation problems in the frequency domain. A novel phase compensation method is introduced to deal with the phase lag phenomenon, so that the bandwidth of the closed-loop system is increased. Experiments on a belt-driven positioning table are conducted to show the effectiveness of the proposed controller.     

Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable (While some switching models are probably unstabilizable), an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.     

Output feedback adaptive control of a class of nonlinear discrete-time systems with unknown control directions

In this paper, output feedback adaptive control is investigated for a class of nonlinear systems in output-feedback form with unknown control gains. To construct output feedback control, the system is transformed into the form of the NARMA (nonlinear-auto-regressive-moving-average) model, based on which future output prediction is carried out. With employment of the predicted future output, a constructive output feedback adaptive control is given with the discrete Nussbaum gain exploited to overcome the difficulty due to unknown control directions. Under the global Lipschitz condition of the system functions, the boundedness of all the closed-loop signals and asymptotical output tracking are achieved by the proposed control. Simulation results are presented to show the effectiveness of the proposed approach.