A Lightweight Model Predictive Controller For Repetitive Discrete Event Systems

A lightweight model predictive controller for a class of discrete event systems is developed. The target is first in first out (FIFO) systems, in which the precedence relations are represented by a directed acyclic graph. Using max‐plus algebra, a system's behavior can be described by a set of linear equations referred to as the state space representation. Using this representation, we address the problem of adjusting system parameters and determining optimal control inputs for given reference signals. To determine system parameters, we formulate and solve an optimization problem using a branch‐and‐bound method, by which the number of constraints is reduced. Then, the optimal control inputs are determined. Since this part is often the bottleneck in online control, we propose two methods for the efficient computation thereof. The first method is beneficial for systems with sparse adjacency matrices and small‐scale systems with a greater prediction horizon. In contrast, the second approach is beneficial for larger‐scale systems with a smaller prediction horizon. The effectiveness of the proposed framework is verified through numerical simulations.     

Optimal Nonblocking Directed Control of Discrete Event Systems

For the control of discrete event systems, the notion of directed control refines that of supervisory control. A directed controller is one that selects at most one controllable event to be enabled at any state (without disabling any uncontrollable event), which is in fact how a discrete event control is implemented. In contrast, a supervisory controller computes a maximal allowable set of controllable events at each state, leaving undecided exactly which controllable event should be enabled. In previous works, we developed a framework for the computation of optimal directed controllers and a polynomial synthesis algorithm for acyclic plants. In this paper, we present a novel synthesis approach for general plants, i.e., plants with or without cycles, thus providing a complete solution to the optimal directed control problem. The complexity of the approach remains polynomial in the size of plant.      

无限时间长时延网络控制系统的随机最优控制

考虑二次性能指标下线性网络控制系统的随机最优控制问题,建立了控制器为事件驱动时长时延线性网络控制系统的数学模型,证明了在无限时间情况下离散随机黎卡提代数方程解的存在性,设计出无限时间情况下线性网络控制系统的随机最优控制器,得到相应的最优性能指标的表达形式,并证明了相应的随机最优控制器可使网络控制系统均方指数稳定.最后以网络控制下的倒立摆为对象进行仿真研究,仿真结果表明该方法的正确性和有效性.     

Event-Triggered Optimal Adaptive Control Algorithm for Continuous-Time Nonlinear Systems

This paper proposes a novel optimal adaptive eventtriggered control algorithm for nonlinear continuous-time systems. The goal is to reduce the controller updates, by sampling the state only when an event is triggered to maintain stability and optimality. The online algorithm is implemented based on an actor/critic neural network structure. A critic neural network is used to approximate the cost and an actor neural network is used to approximate the optimal event-triggered controller. Since in the algorithm proposed there are dynamics that exhibit continuous evolutions described by ordinary differential equations and instantaneous jumps or impulses, we will use an impulsive system approach. A Lyapunov stability proof ensures that the closed-loop system is asymptotically stable. Finally, we illustrate the effectiveness of the proposed solution compared to a timetriggered controller.      

A First Step Towards Adaptive Control for Linear Systems in Max Algebra

Alinear system theory has been developed for discrete event systemssubject to synchronization. We are interested in the just intime control of such systems in presence of a possible mismatchbetween the system and its model. Taking such mismatch into accountin controller synthesis prevents us from using the usual openloop control structure. The approach we propose to synthesizethe controller is inspired by the principle of the indirect adaptivecontrol well known in conventional system theory. Its designleads to solve an optimal tracking problem under an equalityconstraint. Preliminary results about the estimation of modelsare presented.     

Intelligent Control Paradigm for Dynamic Discrete Event System Simulation

Simulation based control of discrete event systems has been a potential approach to support decision-making in the manufacturing scenario. In this paper, a knowledge intensive simulation modelling approach for a discrete even system is investigated. Based on the proposed simulation model, a robust control mechanism is presented that is believed to add significant value to discrete event dynamic system. The algorithm utilises neural network feedforward control plus robust proportional derivative feedback control to achieve control performance and output stability. The novel simulation approach, as well as the proposed controller, is implemented in an Extend TM environment and the effectiveness and usefulness of the proposed controller are verified, industrially, in the hard disk drive assembly process, a significant component of the Singapore manufacturing economy.     

具有控制约束的网络控制系统的鲁棒H_∞控制

针对具有控制约束的网络控制系统(Networked Control Systems,NCS)的特点,建立了具有外部扰动的网络控制系统模型,对其H∞性能加以分析和研究,并验证所取得的理论成果.假设具有控制约束的网络控制系统的H∞控制器与执行器均为事件驱动,传感器为时间驱动,且网络诱导时延小于传感器的采样周期,然后将此类网络控制系统的广义被控对象建模为一类线性离散系统,运用Lyapunov函数和线性矩阵不等式(LMI),导出闭环系统渐近稳定且满足给定H∞性能指标的充分条件,并给出了控制器的具体求法.得到了系统的H∞控制器存在条件及具体方法,通过设计该控制器,使具有外部扰动的网络控制系统的性能有很大的改善,通过Matlab仿真证明该控制器行之有效.     

Online optimal control of nonlinear discrete-time systems using approximate dynamic programming

In this paper,the optimal control of a class of general affine nonlinear discrete-time(DT) systems is undertaken by solving the Hamilton Jacobi-Bellman(HJB) equation online and forward in time.The proposed approach,referred normally as adaptive or approximate dynamic programming(ADP),uses online approximators(OLAs) to solve the infinite horizon optimal regulation and tracking control problems for affine nonlinear DT systems in the presence of unknown internal dynamics.Both the regulation and tracking contro...     

Decision making in fuzzy discrete event systems

The primary goal of the study presented in this paper is to develop a novel and comprehensive approach to decision making using fuzzy discrete event systems (FDES) and to apply such an approach to real-world problems. At the theoretical front, we develop a new control architecture of FDES as a way of decision making, which includes a FDES decision model, a fuzzy objective generator for generating optimal control objectives, and a control scheme using both disablement and enforcement. We develop an online approach to dealing with the optimal control problem efficiently. As an application, we apply the approach to HIV/AIDS treatment planning, a technical challenge since AIDS is one of the most complex diseases to treat. We build a FDES decision model for HIV/AIDS treatment based on expert’s knowledge, treatment guidelines, clinic trials, patient database statistics, and other available information. Our preliminary retrospective evaluation shows that the approach is capable of generating optimal control objectives for real patients in our AIDS clinic database and is able to apply our online approach to deciding an optimal treatment regimen for each patient. In the process, we have developed methods to resolve the following two new theoretical issues that have not been addressed in the literature: (1) the optimal control problem has state dependent performance index and hence it is not monotonic, (2) the state space of a FDES is infinite.     

具有执行器故障的Delta算子系统D稳定H_∞鲁棒容错控制

研究Delta算子描述的不确定线性系统在区域极点约束和H∞范数界约束下的鲁棒容错控制问题。利用线性矩阵不等式（LMI）理论,给出了在执行器失效情况下Delta算子不确定系统在区域极点约束下的鲁棒H∞容错控制存在的充分条件,并可通过求解LMI得到鲁棒容错控制器的设计。所得结果可将连续系统和离散系统的有关结果统一到Delta算子框架中。数值算例验证了该方法的可行性。     

Event‐triggered optimal tracking control of nonlinear systems

We propose a novel event‐triggered optimal tracking control algorithm for nonlinear systems with an infinite horizon discounted cost. The problem is formulated by appropriately augmenting the system and the reference dynamics and then using ideas from reinforcement learning to provide a solution. Namely, a critic network is used to estimate the optimal cost while an actor network is used to approximate the optimal event‐triggered controller. Because the actor network updates only when an event occurs, we shall use a zero‐order hold along with appropriate tuning laws to encounter for this behavior. Because we have dynamics that evolve in continuous and discrete time, we write the closed‐loop system as an impulsive model and prove asymptotic stability of the equilibrium point and Zeno behavior exclusion. Simulation results of a helicopter, a one‐link rigid robot under gravitation field, and a controlled Van‐der‐Pol oscillator are presented to show the efficacy of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

离散时滞系统的近似最优扰动抑制

研究了状态变量合有时滞的离散系统在外部扰动下的最优控制问题．通过引入一个灵敏度参数,将原系统的最优扰动抑制问题转化为一族不含超前项和时滞项的两点边值问题,并由此导出了最优扰动抑制控制器的这代近似设计方法．得到的最优扰动抑制控制律由解析的前馈一反馈项和伴随向量级数和形式的补偿项组成,截取伴随向量级数的有限和得到原系统的次优扰动抑制控制律．数值仿真表明该近似最优控制器对外部持续扰动具有良好的鲁棒性。     

带状态约束的事件触发积分强化学习控制

为克服全状态对称约束以及控制策略频繁更新的局限,同时使得无限时间的代价函数最优,针对一类具有部分动力学未知的仿射非线性连续系统,提出一种带状态约束的事件触发积分强化学习的控制器设计方法。该方法是一种基于数据的在线策略迭代方法。引入系统转换将带有全状态约束的系统转化为不含约束的系统。基于事件触发机制以及积分强化学习算法,通过交替执行系统转换、策略评估、策略改进,最终系统在满足全状态约束的情况下,代价函数以及控制策略将分别收敛于最优值,并能降低控制策略的更新频率。此外,通过构建李亚普诺夫函数对系统以及评论神经网络权重误差的稳定性进行严格的分析。单连杆机械臂的仿真实验也进一步说明算法的可行性。     

离散时滞系统的最优滑模控制

针对离散线性时滞系统,设计了最优滑模面和最优离散变结构控制律.在设计最优滑模面的过程中,利用逐次逼近算法,将既含有时滞项又含有超前项的两点边值问题转化为不含时滞项和超前项的线性两点边值问题,并证明了其解序列一致收敛于原系统的最优滑模.进一步给出了原系统的变结构控制律.     

PID控制器参数调整的滚动优化算法

A novel supervised receding horizon optimal scheme is presented for discrete time systems in the process control. In the employing level, PID controller is used, while the receding horizon approach is applied to the optimized level. The considered problem is to optimize the employing level PID controller parameters through minimizing a generalized predictive control criterion. Compared with a fixed parameters PID controller, the proposed algorithm provides well performance over a range of operating condition.     

Receding Horizon Optimization Approach to PID Controller Parameters Auto-tuning

A novel supervised receding horizon optimal scheme is presented for discrete time systems in the process control.In the employing level,PID controller is used,while the receding horizon approach is applied to the optimized level.The considered problem is to optimize the employing level PID controller parameters through minimizing a generalized predictive control criterion.Compared with a fixed parameters PID controller,the proposed algorithm provides well performance over a range of operating condition.     

Robust Input Covariance Constraint Control for Uncertain Polytopic Systems

In this paper, the robust input covariance constraint (ICC) control problem with polytopic uncertainty is solved using convex optimization with linear matrix inequality (LMI) approach. The ICC control problem is an optimal control problem that optimizes the output performance subjected to multiple constraints on the input covariance matrices. This control problem has significant practical implications when hard constraints need to be satisfied on control actuators. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the robust ICC control problem for polytopic uncertain systems. Both continuous‐ and discrete‐time systems are considered. Parameter‐dependent and independent Lyapunov functions have been used for robust ICC controller synthesis. Numerical design examples are presented to illustrate the effectiveness of the proposed approach.     

Model-based periodic event-triggered stabilization for continuous-time stochastic nonlinear systems

In this paper, we investigate a model-based periodic event-triggered control framework for continuous-time stochastic nonlinear systems. In this framework, an auxiliary approximate discrete-time model of stochastic nonlinear systems is constructed in the controller module, which is utilized not only to design a discrete-time controller but also as a state predictor within trigger intervals. This discrete controller design approach, the strategy of state prediction, and the periodic detection strategy for the trigger rule not only provide a manner of more direct and easier implementation on the digital platform but also effectively reduce the communication load while a satisfactory control performance is maintained. Additionally, the mean-square exponentially stabilization for continuous-time stochastic nonlinear systems is achieved, in which a guideline for determining the maximum admissible sampling period is provided and the periodic event trigger rule is designed. The final numerical simulation also supports the effectiveness of our proposed framework.     

Model‐based event‐triggered predictive control for networked systems with communication delays compensation

This paper addresses the model‐based event‐triggered predictive control problem for networked control systems (NCSs). Firstly, we propose a discrete event‐triggered transmission scheme on the sensor node by introducing a quadratic event‐triggering function. Then, on the basis of the aforementioned scheme, a novel class of model‐based event‐triggered predictive control algorithms on the controller node is designed for compensating for the communication delays actively and achieving the desired control performance while using less network resources. Two cases, that is, the value of the communication delay of the first event‐triggered state is less or bigger than the sampling period, are considered separately for certain NCSs, regardless of the communication delays of the subsequent event‐triggered states. The codesign problems of the controller and event‐triggering parameter for the two cases are discussed by using the linear matrix inequality approach and the (switching) Lyapunov functional method. Furthermore, we extended our results to the NCSs with systems uncertainties. Finally, a practical ball and beam system is studied numerically to demonstrate the compensation effect for the communication delays with the proposed novel model‐based event‐triggered predictive control scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

A new event‐driven output‐based discrete‐time control for the sporadic MIMO tracking problem

This paper presents a new sporadic control approach to the tracking problem for MIMO closed‐loop systems. An LTI sampled data plant with unmeasurable state affected by external unknown disturbances is considered. The plant is interconnected to an event‐based digital dynamic output‐feedback controller via a network. Both the external reference and the unknown disturbance are assumed to be generated as the free output response of unstable LTI systems. The main feature of the new event‐driven communication logic (CL) is that it works without the strict requirement of a state vector available for measurement. The purpose of the CL is to reduce as much as possible the number of triggered messages along the feedback and feedforward paths with respect to periodic sampling, still preserving internal stability and without appreciably degrading the control system tracking capability. The proposed event‐driven CL is composed of a sensor CL (SCL) and of a controller CL (CCL). The SCL is based on the computation of a quadratic functional of the tracking error and of a corresponding suitably computed time‐varying threshold: a network message from the sensor to the controller is triggered only if the functional equals or exceeds the current value of the threshold. The CCL is directly driven by the SCL: the dynamic output controller sends a feedforward message to the plant only if it has received a message from the sensor at the previous sampled instant. Formulation of the controller in discrete‐time form facilitates its implementation and provides a minimum inter‐event time given by the sampling period. An example taken from the related literature shows the effectiveness of the new approach. The focus of this paper is on the stability and performance loss problems relative to the sporadic nature of the control law. Other topics such as network delay or packets dropout are not considered. Copyright © 2012 John Wiley & Sons, Ltd.