Optimal non‐blocking decentralized supervisory control with unobservable controllable events

Paranormality is an observation property of a language, in which the occurrence of unobservable events never exits the closure of the language. In this paper, a synthesis method is proposed to construct a paranormal supervisor. We propose a method to construct a controllable language such that the occurrence of unobservable events does not exit the closure of the controllable language. Moreover, a new observation property, that is, Quasi Output Control Consistency (QOCC) is defined to construct the optimal (least restrictive) non‐blocking decentralized supervisory control in the presence of unobservable controllable events. Using QOCC and natural observer properties, we propose a method to construct a normal supervisor such that an arbitrary pair of lookalike strings are initiated and terminated with identical observable and uncontrollable events. It is assumed that one of these strings has unobservable controllable events. An OCC property is defined in the literature as a special case of QOCC property, where none of the lookalike strings has unobservable controllable events.     

对称离散事件系统事件重标记观测器性质研究

当离散事件系统(discrete-event systems,DES)由多组结构相同的组件构成时,则称离散事件系统具有对称性.为了化简对称离散事件系统的状态空间,本文提出事件重标记映射,将完成相同任务的事件标记为同一事件,将与控制无关的不可控事件设为不可观测事件,并将其标记为空字符擦除.为了确保事件重标记前后系统对应的最大监督控制器具有相同的控制效果,本文引入重标记观测器(relabeling observer property,ROP)的概念并给出判断被控对象对应的语言关于事件重标记映射是否具有重标记观测器性质的算法;然后运用重标记观测器性质证明事件重标记前后监督控制器控制效果的等价性,从而可用简化后的监督控制器实现与事件重标记操作前相同的控制任务.最后通过实例验证所提理论的正确性.     

Observer-based fault-tolerant control for a class of nonlinear networked control systems

This paper presents a fault-tolerant control (FTC) scheme for nonlinear systems which are connected in a networked control system. The nonlinear system is first transformed into two subsystems such that the unobservable part is affected by a fault and the observable part is unaffected. An observer is then designed which gives state estimates using a Luenberger observer and also estimates unknown parameter of the system; this helps in fault estimation. The FTC is applied in the presence of sampling due to the presence of a network in the loop. The controller gain is obtained using linear-quadratic regulator technique. The methodology is applied on a mechatronic system and the results show satisfactory performance.     

An optimal control approach to robust tracking of linear systems

In our early work, we show that one way to solve a robust control problem of an uncertain system is to translate the robust control problem into an optimal control problem. If the system is linear, then the optimal control problem becomes a linear quadratic regulator (LQR) problem, which can be solved by solving an algebraic Riccati equation. In this article, we extend the optimal control approach to robust tracking of linear systems. We assume that the control objective is not simply to drive the state to zero but rather to track a non-zero reference signal. We assume that the reference signal to be tracked is a polynomial function of time. We first investigated the tracking problem under the conditions that all state variables are available for feedback and show that the robust tracking problem can be solved by solving an algebraic Riccati equation. Because the state feedback is not always available in practice, we also investigated the output feedback. We show that if we place the poles of the observer sufficiently left of the imaginary axis, the robust tracking problem can be solved. As in the case of the state feedback, the observer and feedback can be obtained by solving two algebraic Riccati equations.     

Minimal-order observer and output-feedback stabilization control design of stochastic nonlinear systems

1IntroductionTheproblemofestimatingtheparametersofmultiplesinusoidsinnoisehasre-ceivedconsiderableattentioninthepastthirtyyears,andalotofalgorithmshavebeenestablishedtosolvetheproblem.Amongallofthealgorithms,themaximumlikelihood(ML)estimatorisaprominentone[1],andseveralalgorithms,suchasANP[2]andIMP[3,4]arerelatedtoML.ThedrawbackoftheMLestimatorisitshighcomputationalcomplexity,sothealternatingprojection(AP)algorithm[5]wasdevelopedtomakeitsrealtimerealizationpossible.Butthefundamentaldefic…     

改进非线性干扰观测器的机械臂自适应反演滑模控制

针对传统滑模和传统干扰观测器在机械臂关节位置跟踪中存在的控制输入抖振、需要测量加速度项、应用模型受限等问题,提出一种改进非线性干扰观测器的机械臂自适应反演滑模控制算法。首先,设计改进的非线性干扰观测器进行在线测试,在滑模控制律中加入干扰估计值对可观测的干扰进行补偿;然后选择合适的设计参数,使观测误差指数型收敛;其次,引入反演自适应控制律,对不可观测的干扰进行估计,进一步改善控制系统的跟踪性能;最后,利用李雅普诺夫函数验证了闭环系统的渐近稳定性,并将其应用于机械臂关节位置跟踪。实验结果表明,与传统滑模算法比较,所提控制算法不但加快了系统的响应速度,而且能有效地削弱系统抖振、避免测量加速度项并扩大应用模型使用范围。     

Modeling of a dynamic dual-input dual-output fast steeringmirror system

A modeling method is proposed for a dynamic fast steering mirror (FSM) system with dual inputs and dual outputs. A physical model of the FSM system is derived based on first principles, describing the dynamics and coupling between the inputs and outputs of the FSM system. The physical model is then represented in a state-space form. Unknown parameters in the state-space model are identified by the subspace identification algorithm, based on the measured input-output data of the FSM system. The accuracy of the state-space model is evaluated by comparing the model estimates with measurements. The variance-accounted-for value of the state-space model is better than 97%, not only for the modeling data but also for the validation data set, indicating high accuracy of the model. Comparison is also made between the proposed dynamic model and the conventional static model, where improvement in model accuracy is clearly observed. The model identified by the proposed method can be used for optimal controller design for closed-loop FSM systems. The modeling method is also applicable to FSM systems with similar structures.     

基于PI 观测器的奇异摄动系统故障诊断和最优容错控制

针对线性奇异摄动系统, 提出一种基于PI (proportional integral) 观测器的故障诊断和最优容错控制方法. 基于奇异摄动系统相关理论和矩阵变换技术, 给出PI 全维观测器存在的条件, 该观测器可以观测系统的快慢状态和故障系统的状态. 在估测到系统状态的基础上进一步考虑最优性, 应用最优控制理论, 设计状态反馈控制器, 提出基于PI 观测器的故障诊断器和最优容错控制器的设计方法. 最后的数值算例验证了所提出方法的可行性和正确性.

     

Set-valued observers and optimal disturbance rejection

A set-valued observer (also called guaranteed state estimator) produces a set of possible states based on output measurements and models of exogenous signals. We consider the guaranteed state estimation problem for linear time-varying systems with a priori magnitude bounds on exogenous signals. We provide an algorithm to propagate the set of possible states based on output measurements and show that the centers of these sets provide optimal estimates in an l^∞-induced norm sense. We then consider the utility of set-valued observers for disturbance rejection with output feedback and derive the following general separation structure. An optimal controller can consist of a set-valued observer followed by a static nonlinear function on the observed set of possible states. A general construction of this function is provided in the scalar control case. Furthermore, in the special case of full-control, i.e., the number of control inputs equals the number of states, optimal output feedback controllers can take the form of an optimal estimate of the full-state feedback controller     

Regulating an M/G/1 queue when customers know their demand

Customers do not necessarily join a queue at a socially optimal rate. Hence, queueing systems may call for regulation. For customers in an M/G/1 unobservable (not necessarily FCFS) queue and homogeneous with respect to waiting costs and service rewards, we show how queueing systems can be regulated by imposing an entry fee, a holding fee (based on time in the system), or a service fee (based on the required service time) when customers know their service requirements. We start with a unified approach and state the socially optimal fees. We show that customers are always worse off under a flat entry fee in comparison with holding and service fees. As for holding vs. service fees, the answer depends on the queueing regime and/or the service length itself. For example, under FCFS, service fees are preferred by all. Details are given on some common service regimes. We also review the case where customers know only the common distribution of service times, but not their actual requirements.     

输出概率密度函数的最优跟踪控制:均方根B - 样条模型

在分析均方根B样条模型在实现输出概率密度函数最优跟踪控制时存在的问题的基础上,提出了将最优跟踪控制转化为非线性状态约束下的跟踪误差最优调节器,然后依据非线性状态约束和系统模型的特点分别设计了鲁棒变结构控制器及非线性观测器,并利用误差补偿控制来保证非线性观测器误差的有界性.仿真结果表明了提出的转换控制策略的有效性.     

Robust and nonblocking supervisor for discrete-event systems withmodel uncertainty under partial observation

Addresses a robust and nonblocking supervisory control problem based on a framework of discrete-event systems with model uncertainty under partial observation. The uncertainty introduced in the paper is associated with internal and unobservable events occurring in systems. The paper presents a systematic method for modeling uncertainty described as a Δ-transition representing the internal and unobservable events. In particular, at a state with the assigned positive integer value p a system is assumed to experience at most a p-step state transition by the internal and unobservable event. Under the framework for model uncertainty, the paper presents necessary and sufficient conditions for the existence of a robust supervisor with the nonblocking property     

Equilibrium joining strategies in the single server queues with negative customers

We consider an M/M/1 queue with negative customers. An arriving negative customer will break the server down and the positive customer being served (if any) is forced to leave the system. Once a breakdown occurs, the server is sent immediately for repair while positive customers are not allowed to join the system during the repair process. When the server is available, positive arrivals decide whether to join or balk the system based on a common reward-cost structure. We consider an observable case that the positive arrivals are informed about the number of customers in the system and an unobservable case without any information. The corresponding Nash equilibrium strategies and the socially optimal joining strategies are explored. We get a socially optimal threshold in the observable case and a mixed joining strategy in the unobservable case. The profit maximization issue is studied, and we derive optimal strategies in two information cases. Finally, numerical examples are provided to show the influence of different parameters on the strategies and social benefit.     

FSM状态间逻辑条件检验的算法研究

有限状态机(FSM)是VLSI控制结构的一种映射,它的自动综合成为设计自动化的一个十分重要的环节和途径。本文讨论在FSM自动综合中输入阶段的状态间逻辑条件检验的问题,研究分析状态间逻辑条件检验的相互关系及影响,并提出了FSM状态间逻辑条件检验的优化算法,从而使时间复杂度降低,实现更加简便。最后,本文给出了优化算法的流程和一些实验结果,结果令人满意。     

Neural-network-observer-based optimal control for unknown nonlinear systems using adaptive dynamic programming

In this paper, an observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. First, a neural-network (NN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In this design, two NN structures are used: a three-layer NN is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics, and a critic NN is employed to approximate the value function. The optimal control law is computed using the critic NN and the observer NN. Uniform ultimate boundedness of the closed-loop system is guaranteed. The actor, critic, and observer structures are all implemented in real-time, continuously and simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

Observers for Lipschitz non-linear systems

In an interesting paper R. Rajamani and Y. M. Cho have proposed a systematic methodology to design observers. They have introduced a new problem: relation between distance to unobservability and convergence of 'Luenberger-like' observers. A result for the convergence of the observer has also been given. They have presented a quantity denoted by i, claimed as the distance to unobservability. We show that this number is not actually the distance from the system to the set of unobservable systems. Moreover, the result for the observer is incorrect. We provide a counterexample for the result of convergence. In this paper results for convergence are obtained, with additional strengthened hypothesis, to correct Rajamani and Cho's result. The results are used to design an observer for a, now classical, single-link flexible robot joint. The behaviour of the observer to noisy output is quite satisfactory.     

Water-quality estimation and control in streams

In this paper a methodology is given for the process of water-quality estimation and control in streams using a systems approach. The proposed procedure is based on the stream water quality model developed by Hassan et at. (1981). A linear observer is designed that can be used to estimate the unobservable states of the system. These states represent the concentration of the water-quality constituents in a given stream that are difficult, time-consuming or costly to measure. Although the system model is non-linear, the application of the developed linear observer in the case of the River Nile showed its stability and convergence to the actual states of the system. The output of this observer can also be used to derive the two-level hierarchical optimization scheme developed for this system in order to maintain water-quality standards in polluted reaches in a given water body with minimum cost.     

Pole placement and the observer-based controller parameterization

Two properties related to observer-based controller parameterization and pole placement are discussed. It is shown that the poles of the closed-loop system with observer-based controller parameterization can be classified into three groups, and each group of poles can be independently determined. These three groups of poles are the regulator poles, the observer poles, and the poles of the added dynamics. If the realization of the controller is not minimal, then the uncontrollable and/or unobservable controller poles can be removed and the order of the controller is minimized. The set of these removable controller poles is a subset of the regulator and the observer poles. The poles of the closed-loop system with the minimal order controller will include all the poles of a parameter matrix and some of the regulator and the observer poles which are not the removable controller poles     

Concurrent Secrets

Given a finite state system with partial observers and for each observer, a regular set of trajectories which we call a secret, we consider the question whether the observers can ever find out that a trajectory of the system belongs to some secret. We search for a regular control on the system, enforcing the specified secrets on the observers, even though they have full knowledge of this control. We show that an optimal control always exists although it is generally not regular. We state sufficient conditions for computing a finite and optimal control of the system enforcing the concurrent secret as desired. The biographies and photos of the authors are not available.     

Observer design for discrete systems with unknown exogenous inputs

A design procedure is developed for determining optimal discrete observers for estimating system states and unknown exogenous system inputs. This procedure is based on augmenting a standard system observer with an input model. The augmented model is then transformed into the discrete z-domain to determine relevant input/output transfer function matrices. The transfer function matrices are used to develop transfer function relationships between unknown exogenous inputs and the observer estimate of these inputs. It is shown that the optimal observer gains can be determined by implementing the observer as a Fisher filter. An example of the procedure is demonstrated with a third-order point-mass tracking filter