Event-triggered control for switched delay systems with dynamic input quantization

This paper is concerned with event-triggered control for the switched system with time-varying delay and dynamic input quantization. The work is aimed at solving the quantizer saturation in the finite-level quantized control design and the mismatch caused by event-triggered sampling and the switching. First of all, the quantization parameter updating laws are designed respectively in the case of match and mismatch between the system and the controller under the event-triggered mechanism without Zeno behavior. Then, the total variation of Lyapunov functional is transformed into discrete time updating of the dynamic quantization parameter. A switching law and a quantized control strategy are developed to ensure the exponential stability of switched systems with delay and input quantization. At last, two examples are given to illustrate the validity of the results.     

Consensus Control for Directed Networks Under Quantized Information Exchange

In this paper, without assuming balanced network topologies, we address the weighted average consensus problem for discrete‐time single‐integrator multi‐agent systems with logarithmic quantized information communication. By incorporating generalized quadratic Lyapunov function with the discrete‐time Bellman–Gronwall inequality, a new upper bound about the quantization precision parameter of the infinite‐level logarithmic quantizer is derived to design quantized protocol, under which agents in strongly connected directed networks can attain weighted average consensus. The obtained new upper bound clearly characterizes the intimate relation between the quantization precision parameter and the directed network topology. The proposed quantized protocol is particularly applicable to digital networks where balanced message passing among agents is not available.     

Distributed dynamic consensus under quantized communication data

Distributed dynamic average consensus is investigated under quantized communication data. We use a uniform quantizer with constant quantization step‐size to deal with the saturation caused by the dynamic consensus error and propose a communication feedback‐based distributed consensus protocol suitable for directed time‐varying topologies to make the internal state of each agent's encoder consistent with the output of its neighbors' decoder. For the case where the communication topology is directed, balanced and periodically connected, it is shown that if the difference of the reference inputs satisfies some boundedness condition, then the designed quantized dynamic consensus protocol can ensure the states of all the agents achieve dynamic average consensus with arbitrarily small steady state error by properly choosing system parameters. The lower bound of the required quantization levels and the method to choose the system parameters are also presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Stabilization of linear systems with limited information

We show that the coarsest, or least dense, quantizer that quadratically stabilizes a single input linear discrete time invariant system is logarithmic, and can be computed by solving a special linear quadratic regulator problem. We provide a closed form for the optimal logarithmic base exclusively in terms of the unstable eigenvalues of the system. We show how to design quantized state-feedback controllers, and quantized state estimators. This leads to the design of hybrid output feedback controllers. The theory is then extended to sampling and quantization of continuous time linear systems sampled at constant time intervals. We generalize the definition of density of quantization to the density of sampling and quantization in a natural way, and search for the coarsest sampling and quantization scheme that ensures stability. Finally, by relaxing the definition of quadratic stability, we show how to construct logarithmic quantizers with only finite number of quantization levels and still achieve practical stability of the closed-loop system     

Robust adaptive output feedback control for uncertain nonlinear systems with quantized input

In this paper, we study the input quantization problem for a class of uncertain nonlinear systems. The quantizer adopted belongs to a class of sector‐bounded quantizers, which basically include all the currently available static quantizers. Different from the existing results, the quantized input signal, rather than the input signal itself, is used to design the state observers, which guarantees that the state estimation errors will eventually converge to zero. Because the resulting system may be discontinuous and non‐smooth, the existence of the solution in the classical sense is not guaranteed. To cope with this problem, we utilize the non‐smooth analysis techniques and consider the Filippov solutions. A robust way based on the sector bound property of the quantizers is used to handle the quantization errors such that certain restrictive conditions in the existing results are removed and the problem of output feedback control with input signal quantized by logarithmic (or hysteresis) quantizers is solved for the first time. The designed controller guarantees that all the closed‐loop signals are globally bounded and the tracking error exponentially converges towards a small region around zero, which is adjustable. Copyright © 2016 John Wiley & Sons, Ltd.     

Quantized Iterative Learning Control Design For Linear Systems Based On A 2‐D Roesser Model

This paper considers the problem of iterative learning control design for linear systems with data quantization. It is assumed that the control input update signals are quantized before they are transmitted to the iterative learning controller. A logarithmic quantizer is used to decode the signal with a number of quantization levels. Then, a 2‐D Roesser model is established to describe the entire dynamics of the iterative learning control (ILC) system. By using the sector bound method, a sufficient asymptotic stability condition for such a 2‐D system is established and then the ILC design is given simultaneously. The result is also extended to more general cases where the system matrices contain uncertain parameters. The effectiveness of the proposed method is illustrated by a numerical example.     

离散时间系统量化动态输出反馈的H∞控制

The problem of quantized dynamic output feedback H_∞control for discrete-time linear time-invariant(LTI)systems is investigated in this paper.The quantizer considered is dynamic and composed of an adjustable"zoom"parameter and a static quantizer.Static quantizer ranges are of practical significance and are fully considered.First,taking quantization errors into account, a quantized control strategy is dependent not only on the controller states but also on the system measurement outputs,which is proposed such that the quantized closed-loop system is asymptotically stable and with a prescribed H_∞performance bound.Then, on the basis of this result,an iterative LMI-based optimization algorithm is developed to optimize the static quantizer ranges to meet H_∞performance requirements for closed-loop systems.An example is presented to illustrate the effectiveness of the proposed method.     

离散时间系统量化动态输出反馈的H∞控制

本文研究了离散时间线性时不变系统的量化动态输出反馈 H 无穷控制问题. 所考虑的动态量化器由动态调节参数和静态量化器组成. 静态量化器范围具有一定的实际意义, 这一点在本文充分考虑. 首先, 在考虑量化误差影响的情况下, 本文给出了既依赖于控制器状态又依赖于系统测量输出的量化控制策略使得闭环系统渐进稳定且具有指定的 H 无穷性能指标. 然后, 在这一结果的基础上, 又提出了基于线性矩阵不等式的迭代的优化算法来优化静态量化器范围, 从而得到能保证系统 H 无穷性能需求且具有最小量化器范围的量化控制策略. 最后通过仿真例子验证了所提出方法的有效性.     

State feedback H∞ control for quantized discrete‐time systems

This paper is concerned with the quantized state feedback H_∞ control problem for discrete‐time linear time‐invariant systems. The quantizer considered here is dynamic and composed of an adjustable “zoom” parameter and a static quantizer. Static quantizer ranges are with practical significance and fully considered here. A quantized H_∞ controller design strategy is proposed with taking quantizer errors into account, where an iterative linear matrix inequality (LMI) based optimization algorithm is developed to minimize static quantizer ranges with meeting H_∞ performance requirement for quantized closed‐loop systems. An example is presented to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

关联量化系统参数稳定性与控制器设计

量化问题广泛存在于计算机控制系统和数字通信的传输通道中. 本文研究一类非线性关联量化系统的参数稳定性及分散状态反馈控制器的设计问题. 每个控制器的输出经过对数量化器量化后输入到子系统中,其量化密度的大小会影响系统的稳定性. 首先,设计分散状态反馈控制器,使得无量化器存在时的关联闭环系统参数稳定,并确定参数稳定的区域;然后,对每个子系统的控制输入采用对数量化器进行量化,通过局部信息确定子系统中对数量化器量化密度的下界,使得整个闭环关联量化系统在参数稳定域内仍然保持稳定;最后,对给定量化密度,优化控制器使系统能容许最大的非线性. 仿真结果表明,本文所设计的分散量化控制器在参数稳定域内能够镇定关联大系统.     

Quantized sliding mode control in delta operator framework

This paper is concerned with quantized sliding mode control in the unified delta operator system framework. To solve the quantization measurement saturating problem, a dynamic quantization strategy including discrete on‐line open‐loop zooming‐out and closed‐loop zooming‐in policies is presented. By analyzing the sign relation between the traditional linear switching function and the quantized linear switching function, a novel quantized sliding mode control method is proposed, and both the amplitude of the control gain and the value of the quantization measurement saturating parameter are reduced compared with previous results. Some simulation results are presented to verify the effectiveness of the proposed method.     

Quantized feedback control for linear uncertain systems

This paper studies robust control problems under the setting of quantized feedback. We consider both the static and dynamic logarithmic quantizers. In the static quantization case, the quantizer has an infinite number of levels, and the design problem is to find the minimal quantization density required to achieve a given control objective. In the dynamic quantization case, the problem is to minimize the number of quantization levels to achieve a given control objective. We present a number of results for different controller‐quantizer configurations. These results are developed using the so‐called sector bound approach for quantized feedback control, which was initiated by the authors previously for systems without uncertainties. Copyright © 2009 John Wiley & Sons, Ltd.     

Stabilization of Markov jump linear systems using quantized state feedback

This paper addresses the stabilization problem for single-input Markov jump linear systems via mode-dependent quantized state feedback. Given a measure of quantization coarseness, a mode-dependent logarithmic quantizer and a mode-dependent linear state feedback law can achieve optimal coarseness for mean square quadratic stabilization of a Markov jump linear system, similar to existing results for linear time-invariant systems. The sector bound approach is shown to be non-conservative in investigating the corresponding quantized state feedback problem, and then a method of optimal quantizer/controller design in terms of linear matrix inequalities is presented. Moreover, when the mode process is not observed by the controller and quantizer, a mode estimation algorithm obtained by maximizing a certain probability criterion is given. Finally, an application to networked control systems further demonstrates the usefulness of the results.     

Control under quantization, saturation and delay: An LMI approach

This paper studies quantized and delayed state-feedback control of linear systems with given constant bounds on the quantization error and on the time-varying delay. The quantizer is supposed to be saturated. We consider two types of quantizations: quantized control input and quantized state. The controller is designed with the following property: all the states of the closed-loop system starting from a neighborhood of the origin exponentially converge to some bounded region (both, in Rⁿ and in some infinite-dimensional state space). Under suitable conditions the attractive region is inside the initial one. We propose decomposition of the quantization into a sum of a saturation and of a uniformly bounded (by the quantization error bound) disturbance. A Linear Matrix Inequalities (LMIs) approach via Lyapunov-Krasovskii method originating in the earlier work [Fridman, E., Dambrine, M., & Yeganefar, N. (2008). On input-to-state stability of systems with time-delay: A matrix inequalities approach. Automatica, 44, 2364-2369] is extended to the case of saturated quantizer and of quantized state and is based on the simplified and improved Lyapunov-Krasovskii technique.     

量化参数不匹配的线性系统监督滑模控制设计

在量化控制系统中,量化器灵敏度参数的不匹配现象会造成系统的性能下降,严重时甚至会导致系统不稳定。另一方面,量化器灵敏度参数的不匹配现象也会增加控制设计的复杂性与难度。针对量化器灵敏度参数不匹配的不确定线性系统,研究监督策略下的量化反馈滑模镇定控制问题。应用监督控制策略,提出的鲁棒量化反馈滑模控制法能够有效消除量化灵敏度参数不匹配与模型不确定性带来的影响,进而确保系统轨迹能渐近收敛到原点。经过Matlab仿真实验验证了该方法的有效性与优越性。     

State estimation for linear discrete-time systems using quantized measurements

In this paper, we consider the problem of state estimation for linear discrete-time dynamic systems using quantized measurements. This problem arises when state estimation needs to be done using information transmitted over a digital communication channel. We investigate how to design the quantizer and the estimator jointly. We consider the use of a logarithmic quantizer, which is motivated by the fact that the resulting quantization error acts as a multiplicative noise, an important feature in many applications. Both static and dynamic quantization schemes are studied. The results in the paper allow us to understand the tradeoff between performance degradation due to quantization and quantization density (in the infinite-level quantization case) or number of quantization levels (in the finite-level quantization case).     

Detection of intermittent faults for nonuniformly sampled multi-rate systems with dynamic quantisation and missing measurements

ABSTRACT

This paper is concerned with the fault detection problem for a class of networked multi-rate systems with nonuniform sampling and dynamic quantization. The sampling interval of the measurements is allowed to be nonuniform that is governed by a time-homogenous Markov process with partly unknown and uncertain transition probabilities. The measured output is quantized by a dynamic quantizer and then transmitted through communication network subject to data missing. The main purpose of the problem under consideration is to design sampling-interval-dependent fault detection filters such that, in the simultaneous presence of nonuniform sampling, dynamic quantization, intermittent faults as well as missing measurements, the robustness of residuals with respect to the disturbance and the sensitivity of the residuals against the fault are guaranteed. Finally, a three-tank system is utilized to illustrate the effectiveness of the proposed fault detection scheme.     

Quantized stabilization for stochastic discrete‐time systems with multiplicative noises

This paper considers the problem of quadratic mean‐square stabilization of a class of stochastic linear systems using quantized state feedback. Different from the previous works where the system is restricted to be deterministic, we focus on stochastic systems with multiplicative noises in both the system matrix and the control input. A static quantizer is used in the feedback channel. It is shown that the coarsest quantization density that permits stabilization of a stochastic system with multiplicative noises in the sense of quadratic mean‐square stability is achieved with the use of a logarithmic quantizer, and the coarsest quantization density is determined by an algebraic Riccati equation, which is also the solution to a special stochastic linear control problem. Our work is then extended to exponential quadratic mean‐square stabilization of the same class of stochastic systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Observer-based feedback stabilization of linear systems with event-triggered sampling and dynamic quantization

We consider the problem of output feedback stabilization in linear systems when the measured outputs and control inputs are subject to event-triggered sampling and dynamic quantization. A new sampling algorithm is proposed for outputs which does not lead to accumulation of sampling times and results in asymptotic stabilization of the system. The approach for output sampling is based on defining an event function that compares the difference between the current output and the most recently transmitted output sample not only with the current value of the output, but also takes into account a certain number of previously transmitted output samples. This allows us to reconstruct the state using an observer with sample-and-hold measurements. The estimated states are used to generate a control input, which is subjected to a different event-triggered sampling routine; hence the sampling times of inputs and outputs are asynchronous. Using Lyapunov-based approach, we prove the asymptotic stabilization of the closed-loop system and show that there exists a minimum inter-sampling time for control inputs and for outputs. To show that these sampling routines are robust with respect to transmission errors, only the quantized (in space) values of outputs and inputs are transmitted to the controller and the plant, respectively. A dynamic quantizer is adopted for this purpose, and an algorithm is proposed to update the range and the centre of the quantizer that results in an asymptotically stable closed-loop system.     

Dynamic output feedback control with output quantizer for nonlinear uncertain T‐S fuzzy systems with multiple time‐varying input delays and unmatched disturbances

The dynamic output feedback control problem with output quantizer is investigated for a class of nonlinear uncertain Takagi‐Sugeno (T‐S) fuzzy systems with multiple time‐varying input delays and unmatched disturbances. The T‐S fuzzy model is employed to approximate the nonlinear uncertain system, and the output space is partitioned into operating regions and interpolation regions based on the structural information in the fuzzy rules. The output quantizer is introduced for the controller design, and the dynamic output feedback controller with output quantizer is constructed based on the T‐S fuzzy model. Stability conditions in the form of linear matrix inequalities are derived by introducing the S‐procedure, such that the closed‐loop system is stable and the solutions converge to a ball. The control design conditions are relaxed and design flexibility is enhanced because of the developed controller. By introducing the output‐space partition method and S‐procedure, the unmatched regions between the system plant and the controller caused by the quantization errors can be solved in the control design. Finally, simulations are given to verify the effectiveness of the proposed method.