Computer control under time-varying sampling period: An LMI gridding approach

This paper addresses computer control under time-varying sampling period and delayed actuation. The proposed approach uses time-varying observers and state-feedback controllers designed by means of linear matrix inequalities (LMI) and quadratic Lyapunov functions. The use of non-stationary Kalman filters is also discussed. A separation principle applies in some cases. A DC motor control setup shows the applicability of the approach in a real implementation.     

Indirect sampled-data control with sampling period adaptation

It is known that if a continuous-time feedback system is exponentially stable, then the corresponding sampled-data system obtained by sample-hold discretisation with constant sampling period is also exponentially stable, provided that the sampling period τ?>?0 is sufficiently small. In general, it is difficult to estimate how small the sampling period has to be in order to achieve the stability of the sampled-data system. In this article, we present an adaptive mechanism for adjusting the sampling period. This mechanism has the properties that, for every initial state, (i) the adaptation of the sampling period terminates after finitely many time steps and (ii) the state of the adaptive sampled-data system is integrable and converges to zero as time goes to infinity.     

Allowable sampling period for consensus control of multiple general linear dynamical agents in random networks

This article studies the consensus problem for a group of sampled-data general linear dynamical agents over random communication networks. Dynamic output feedback protocols are applied to solve the consensus problem. When the sampling period is sufficiently small, it is shown that as long as the mean topology has globally reachable nodes, the mean square consensus can be achieved by selecting protocol parameters so that n???1 specified subsystems are simultaneously stabilised. However, when the sampling period is comparatively large, it is revealed that differing from low-order integrator multi-agent systems the consensus problem may be unsolvable. By using the hybrid dynamical system theory, an allowable upper bound of sampling period is further proposed. Two approaches to designing protocols are also provided. Simulations are given to illustrate the validity of the proposed approaches.     

基于子空间方法的非均匀周期刷新和采样系统辨识

针对非均匀周期刷新和采样系统的建模问题, 对于含有提升变量的状态空间模型, 提出基于子空间技术的辨识方法. 首先, 通过系统的采样数据建立由Hankel 矩阵组成的扩展状态空间方程; 然后, 利用斜交投影的原理、方法和奇异值分解, 通过子空间辨识算法确定增广观测矩阵和状态向量, 通过最小二乘方法确定模型的参数矩阵; 最后, 通过仿真实例表明了所提出算法的有效性.

     

Periodic optimization with applications to solar energy control

It is reasonable to assume in many temperature control applications, that disturbance signals, i.e. solar insolation, ambient temperature, etc. are periodic with 24 hour period and that these periodic disturbances persist over a sufficiently long time interval to allow the system response to settle into a steady-state periodic mode. In this study a linear model is assumed for the system being controlled. The steady-state average of an integral quadratic measure is selected as a performance index. Disturbance signals are assumed to be representable by Fourier series expansions. The periodic optimal control input, which minimizes the given performance index, is then computed in terms of its Fourier coefficient. The optimal control-input coefficients are obtained explicitly in terms of disturbance-input coefficients.     

Periodic and event-based impulse control for linear stochastic systems with multiplicative noise

This paper studies the performance comparison of periodic and event-based sampling for a class of linear stochastic systems with multiplicative noise, where the impulse control is adopted. By solving boundary value problems, we obtain the analytic expressions of the mean sampling time and the average state variance under the event-based sampling. It is shown that the event-based impulse control has substantially smaller average state variance than the periodic control under the same sampling frequency. Particularly, for the integrator case, the performance ratio of the two sampling methods is given explicitly. By simulation, it is demonstrated that the advantage of event-based sampling over periodic sampling is most obvious for unstable systems, followed by critical stable systems, and least obvious for stable systems.     

交换式以太网控制系统传感器变采样调度研究

针对基于交换式以太网的网络化控制系统的数据传输和控制性能优化问题,提出了传感器根据给定值与实测值差额的绝对值对照静态调度表变采样周期的调度优化方法.使用TrueTime 2.0工具箱搭建了交换式以太网控制系统仿真平台进行仿真研究,并与定采样周期方法进行了对比,仿真结果验证了其可行性.此方法在实际的工程应用中具有一定的参考价值.     

针对生物振荡网络分析的周期系统目标敏感性方法研究

生物学实验和模型计算结果表明振荡是一种常见的生物学现象, 越来越多的研究人员关注生物系统内部的振荡现象是如何产生的、引起振荡的关键因素是什么等问题. 敏感性分析定量分析系统行为在模型参数、系统输入或者初始条件发生变化时受影响的程度. 对周期系统进行传统的状态敏感性计算时, 得到的灵敏度指标随着时间的增加而发散, 因而对其进行敏感性分析是一项具有挑战性的工作. 本文针对这类系统, 首先提出基本状态敏感性的概念, 由此进一步推导出一种相敏感性分析方法. 在计算周期灵敏度过程中, 提出了一种基于奇异值分解的的改进算法, 简化了基本状态灵敏度的计算. 本文中的目标敏感性分析方法克服了因累积效应引起的发散问题. 通过对一个生物节律模型和一个复杂的信号转导网络系统模型进行敏感性分析, 可以看到改进的周期灵敏度计算方法得到的结果与已有方法一致, 并且新提出的目标敏感性分析方法及其计算在处理存在反应守恒的复杂生物振荡系统分析时是有效的.     

Periodic optimization of hammerstein-type systems

The output time average of a discrete time single-input single-output nonlinear system is maximized in cyclic operation under constraints on the power of the periodic component of the control. The least upper bound is obtained by making use of the Caratheodory theorem on trigonometric moments. An algorithm to find a solution, optimal within any prescribed threshold is given, which reduces to standard matrix eigenvalue calculations.     

Periodic event-triggering in distributed receding horizon control of nonlinear systems

How to efficiently use limited system resources in distributed receding horizon control (DRHC) is an important issue. This paper studies the DRHC problem for a class of dynamically decoupled nonlinear systems under the framework of event-triggering, to efficiently make use of the computation and communication resources. To that end, a distributed periodic event-triggered strategy is designed and a detailed DRHC algorithm is presented. The conditions for ensuring feasibility of the designed algorithm and stability of the closed-loop system are developed, respectively. We show that the closed-loop system is input-to-state stable if the energy bound of the disturbances, the triggering condition and the cooperation matrices fulfill the proposed conditions.     

多回路网络化控制系统中优化采样频率的确定

在多回路网络化控制系统中，通讯资源的共享和网络传输的时延为系统分析和设计带来新的问题．运用非线性规划理论，分析和推导了多回路网络化控制系统中采样频率优化问题，并由推导过程归纳出易于计算机编程实现的工程化求解方法．通过仿真示例验证了所提出方法的有效性．     

Control of constrained linear systems using fast sampling rates

This paper addresses the problem of optimal control of constrained linear systems when fast sampling rates are utilised. We show that there exists a well-defined limit as the sampling rate increases. An immediate consequence of this result is the existence of a finite sampling period such that the achieved performance is arbitrarily close to the limiting performance.     

Sampled-data control systems with non-uniform sampling: A survey of methods and trends

The convergence of sensing, computing, communication and control elements drives the traditional point-to-point control systems towards networked control systems. Sampled-data control systems, which focus on the significant interplay between sampling and control, play a critical role in modern networked control systems, including intelligent transportation systems, smart grids, and advanced manufacturing systems. This paper presents a survey of methods and trends in non-uniform sampled-data control systems, where sampling and control actions are performed in an aperiodic manner. First, some fundamental issues of both continuous- and discrete-time sampled-data control systems are discussed. Next, main methods in both continuous-time and discrete-time domains are elaborated, respectively. Then, event-triggered sampling, under which sampling is executed only when the system needs attention, is examined. Typical triggering mechanisms in the existing literature are reviewed and classified into four types according to different threshold functions. Furthermore, two applications in terms of automated vehicle platoons and islanded microgrids are provided to demonstrate that sampled-data control methods are capable to support relevant practical application scenarios. Finally, several challenging issues are envisioned to direct future research.     

时变采样周期网络控制系统的鲁棒容错控制器设计

研究具有时变采样周期网络控制系统的执行器失效的完整性问题．假设系统任意两个连续采样间隔具有上界,利用输入时延法,将时变采样周期网络控制系统等价转化为连续时变时延网络控制系统．在此基础上,基于时延条件,应用Ｌｙａｐｕｎｏｖ稳定性理论和线性矩阵不等式（ＬＭＩｓ）方法证明了鲁棒容错控制律的存在条件,设计了鲁棒容错控制器,并给出了系统完整性条件下的最大允许时延的估计方法．仿真结果验证了所提方法的可行性和有效性．     

非线性互联大系统的最优控制:逐次逼近法

The optimal control problem for nonlinear interconnected large-scale dynamic systems is considered. A successive approximation approach for designing the optimal controller is proposed with respect to quadratic performance indexes. By using the approach, the high order, coupling, nonlinear two-point boundary value (TPBV) problem is transformed into a sequence of linear decoupling TPBV problems. It is proven that the TPBV problem sequence uniformly converges to the optimal control for nonlinear interconnected large-scale systems. A suboptimal control law is obtained by using a finite iterative result of the optimal control sequence.     

Stabilization of networked control systems with nonuniform random sampling periods

In this paper, a new linear delayed delta operator switched system model is proposed to describe networked control systems with packets dropout and network‐induced delays. The plant is a continuous‐time system, which is sampled by time‐varying random sampling periods. A general delta domain Lyapunov stability criterion is given for delta operator switched systems with time delays. Sufficient conditions for asymptotic stability of closed‐loop networked control systems with both packets dropout and network‐induced delays are presented in terms of linear matrix inequalities (LMIs). A verification theorem is given to show the solvability of the stabilization conditions by solving a class of finite LMIs. Both the case of data packets arrive instantly and the case of invariant sampling periods in delta operator systems are given, respectively. Three numerical examples are given to illustrate the effectiveness and potential of the developed techniques. Copyright © 2010 John Wiley & Sons, Ltd.     

非线性系统自适应最优切换控制方法

针对具有未知动态和M个平衡点的连续时间非线性系统, 将线性自适应最优切换控制器和未建模动态补偿器相结合, 基于嵌入转换技术和近似动态规划思想, 提出一种自适应最优切换控制方法. 首先在非线性系统的M个平衡点建立M个线性化模型, 当模型参数已知时, 提出由线性最优切换控制器、切换准则、未建模动态补偿器以及非线性系统组成的控制系统结构; 当模型参数未知时, 在每个平衡点附近采集输入和状态数据, 利用黎卡提方程的迭代求解公式、最小二乘方法、极小值原理以及二次规划技术得到非线性系统的自适应最优切换控制器和最优切换序列; 最后进行仿真实验, 实验结果验证了所提方法的有效性、优越性和实际可应用性.     

Linear Periodic Systems Over Dioids

A specification of the linear system theory over dioids is proposed for periodic systems. Using the conventional periodic system theory as a guideline, we study periodic systems for which the underlying algebraic structure is a dioid. The focus is on representations (impulse response and state model) associated with such systems, the properties of these representations as well as the state space realization.     

Integral control by variable sampling based on steady-state data

In this paper we consider integral control algorithms with convergent adaptive sampling for multivariable infinite-dimensional systems. Steady-state gain information is used in choosing suitable integrator gains and we also consider robustness with respect to error in measuring the steady-state gain.