Coordination of discrete‐time multi‐agent systems via relative output feedback

This paper investigates the joint effects of agent dynamic and network topology on the consensusability of linear discrete‐time multi‐agent systems via relative output feedback. An observer‐based distributed control protocol is proposed. A necessary and sufficient condition for consensusability under this control protocol is given, which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the eigenratio of the undirected communication graph affect consensusability. As a special case, multi‐agent systems with discrete‐time double integrator dynamics are discussed where a simple control protocol directly using two‐step relative position feedback is provided to reach a consensus. Finally, the result is extended to solve the formation and formation‐based tracking problems. The theoretical results are illustrated by simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Stability of quantized time-delay nonlinear systems: a Lyapunov–Krasowskii-functional approach

Lyapunov–Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to avoid chattering. Under appropriate conditions, our analysis applies to stabilizable nonlinear systems for any value of the quantization density. The resulting quantized feedback is parametrized with respect to the quantization density. Moreover, the maximal allowable delay tolerated by the system is characterized as a function of the quantization density.     

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     

On Near Optimal Lattice Quantization of Multi‐Dimensional Data Points

One of the most elementary application of a lattice is the quantization of real‐valued s‐dimensional vectors into finite bit precision to make them representable by a digital computer. Most often, the simple s‐dimensional regular grid is used for this task where each component of the vector is quantized individually. However, it is known that other lattices perform better regarding the average quantization error. A rank‐1 lattices is a special type of lattice, where the lattice points can be described by a single s‐dimensional generator vector. Further, the number of points inside the unit cube [0, 1)^s is arbitrary and can be directly enumerated by a single one‐dimensional integer value. By choosing a suitable generator vector the minimum distance between the lattice points can be maximized which, as we show, leads to a nearly optimal mean quantization error. We present methods for finding parameters for s‐dimensional maximized minimum distance rank‐1 lattices and further show their practical use in computer graphics applications.     

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     

An optimal quantized feedback strategy for scalar linear systems

We give an optimal (memoryless) quantized feedback strategy for stabilization of scalar linear systems, in the case of integral eigenvalue. As we do not require the quantization subsets to be intervals, this strategy has better performances than allowed by the lower bounds recently proved by Fagnani and Zampieri. We also describe a general setting, in which we prove a necessary and sufficient condition for the existence of a memoryless quantized feedback to achieve stability, and provide an analysis of Maxwell's demon in this context.     

Adaptive quantized tracking control for uncertain switched nonstrict‐feedback nonlinear systems with discrete and distributed time‐varying delays

This paper is concerned with an adaptive tracking problem for a more general class of switched nonstrict‐feedback nonlinear time‐delay systems in the presence of quantized input. The system structure in a nonstrict‐feedback form, the discrete and distributed time‐varying delays, the sector‐bounded quantized input, and arbitrary switching behavior are involved in the considered systems. In particular, to overcome the difficulties from the distributed time‐varying delays and the sector‐bounded quantized input, the mean‐value theorem for integrals and some special techniques are exploited respectively. Moreover, by combining the Lyapunov‐Razumikhin method, dynamic surface control technique, fuzzy logic systems approximation, and variable separation technique, a quadratic common Lyapunov function is easily built for all subsystems and a common adaptive quantized control scheme containing only 1 adaptive parameter is proposed. It is shown that the tracking error converges to an adjustable neighborhood of the origin whereas all signals of the closed‐loop systems are semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to verify the feasibility and effectiveness of the proposed design methodology.     

量化非线性控制——综述

量化控制系统设计通过将控制与通讯相结合来解决大量运用信息技术的现代工程系统的相关控制问题. 本文首先回顾近年来线性及非线性系统量化控制的结果. 其中, 非线性系统量化控制的发展尚处于初级阶段. 高维、量化、非线性及不确定性的共存导致量化非线性控制问题极具挑战性, 需要全新的思想和技术来解决. 本文重点回顾基于输入状态稳定性(ISS)及其回路小增益定理(Cyclic-small-gain theorem)的量化非线性控制设计方法, 同时列出该领域一些尚未解决的问题.     

Stabilization of impulsive hybrid systems using quantized input and output feedback

In this paper, we consider the feedback stabilization of impulsive control systems with quantized input and output signals. To study the problem, the notions of quasi‐invariant sets and attracting sets for impulsive systems with quantization are introduced first, and then applied to the control design. Hybrid quantized control schemes are proposed to stabilize the considered impulsive linear or nonlinear systems via either input or output feedback. Mathematical analysis and numerical simulations are given to show the principle and effectiveness of the proposed designs. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive output feedback control for a class of nonlinear uncertain systems with quantized input signal

In this paper, adaptive output feedback control for a class of nonlinear systems with quantized input is investigated. The nonlinearities of the nonlinear systems under consideration are assumed to satisfy linear growth condition on the unmeasured states multiplied by unknown growth rate and output polynomial function. By developing a dynamic high‐gain observer, a linear‐like output feedback controller is constructed, with which it is proved that the output of the quantized control system can be steered to within an arbitrarily small residual set while keeping all the other closed loop states bounded. In particular, if the growth rate is known, it is proved that all the states of the system can be steered to within an arbitrarily small neighborhood of the origin. Copyright © 2016 John Wiley & Sons, Ltd.     

具有数据丢包的非线性奇异脉冲系统量化控制

考虑网络传输中存在的数据丢包和信号量化问题, 研究了基于数据丢包的非线性奇异脉冲系统设量化反馈控制器的设计方法. 首先给出一般非线性奇异脉冲系统的数学描述, 并在此基础上建立相应的具有丢包的闭环量化反馈控制系统的数学模型. 其次, 根据李雅普诺夫稳定性理论, 给出了奇异脉冲系统的渐近稳定的充分条件以及量化反馈控制器的设计方法. 应用本设计方法, 可以选择满足代数矩阵不等式条件的量化反馈增益, 实现系统渐近稳定. 最后通过对Chua混沌系统仿真, 表明利用本文设计的量化控制器能够保证闭环非线性奇异脉冲系统在具有数据丢包的情况下渐近稳定.     

具有均匀量化器的非线性网络控制系统的一致有界性

建立一种非线性连续被控对象、系统总时延小于一个采样周期的网络控制系统连续模型.通过线性化及离散化的方法将非线性系统转换一种离散化的模型.利用Lyapunov稳定性理论和线性矩阵不等式方法,设计控制方法使系统稳定.在系统包含均匀量化器的情况下,设计控制方法使系统一致有界.通过调节量化器的误差范围,可以将系统状态控制在一定的范围内.实际中,据此可设计相应的量化级别及编码长度等参数.通过仿真验证控制方法的有效性,并分析了量化误差对系统收敛性的影响.     

一种新的量化反馈控制系统稳定性分析方法

针对一类量化反馈控制系统,在考虑量化范围和量化误差的情况下,建立该系统的动态数学模型.利用Lyapunov稳定性理论,结合线性矩阵不等式(LMI),给出了基于LMI和时变Lyapunov函数的渐近稳定性判据.假设量化器参数满足一定条件,则通过该判据能分析和判定量化反馈控制系统的渐近稳定性,并进一步设计相应的量化反馈控制律.与已有的方法相比,该方法更加有效且求解方便.数值仿真结果表明了该方法的有效性.     

Stability analysis and synthesis for scalar linear systems with a quantized feedback

It is well known that a linear system controlled by a quantized feedback may exhibit the wild dynamic behavior which is typical of a nonlinear system. In the classical literature devoted to control with quantized feedback, the flow of information in the feedback was not considered as a critical parameter. Consequently, in that case, it was natural in the control synthesis to simply choose the quantized feedback approximating the one provided by the classical methods, and to model the quantization error as an additive white noise. On the other hand, if the flow of information has to be limited, for instance, because of the use of a transmission channel with limited capacity, some specific considerations are in order. The aim of this paper is to obtain a detailed analysis of linear scalar systems with a stabilizing quantized feedback control. First, a general framework based on a sort of Lyapunov approach encompassing known stabilization techniques is proposed. In this case, a rather complete analysis can be obtained through a nice geometric characterization of asymptotically stable closed-loop maps. In particular, a general tradeoff relation between the number of quantization intervals, quantifying the information flow, and the convergence time is established. Then, an alternative stabilization method, based on the chaotic behavior of piecewise affine maps is proposed. Finally, the performances of all these methods are compared.     

A sliding sector approach to quantized feedback variable structure control

This paper is concerned with the quantized feedback quadratic stabilization problem for linear time-invariant systems. Sliding sector based quantized state feedback variable structure control schemes are established. The main benefit of the sliding sector technique is that it can avoid chattering caused by the utilization of variable structure control strategy. With the proposed discrete on-line adjustment of the quantization parameter, it is shown that the proposed sliding sector based sliding mode controllers can tackle state quantization and guarantee quadratic stability of the closed-loop system. Simulation results are given to verify the effectiveness of the proposed method.     

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.     

Robust adaptive fault‐tolerant quantized control of nonlinear systems with constraints on system behaviors and states

In this work, we develop a robust adaptive fault‐tolerant tracking control scheme for a class of input‐quantized strict‐feedback nonlinear systems in the presence of error/state constraints and actuation faults. The problem is rather complicated yet challenging if nonparametric uncertainties and unknown quantization parameters as well as time‐varying yet completely undetectable actuation faults are involved in the considered systems. Compared with the most existing approaches in the literature, the proposed control exhibits several attractive advantages: (1) upon using a nonlinear decomposition for quantized input and employing the robust technique for actuation fault, not only the exact knowledge of quantization parameters are not required, but also the actuation fault can be easily compensated since neither fault detection and diagnosis/fault detection and identification nor controller reconfiguration is needed; (2) based on the error/state‐dependent unified nonlinear function, the constraints on tracking error and system states are directly handled and the cases with or without constraints can also be addressed in a unified manner without changing the control structure; and (3) the utilization of unified nonlinear function‐based dynamic surface control not only avoids the problem of the explosion of complexity in traditional backstepping design, but also bypasses the demanding feasibility conditions of virtual controllers. Furthermore, by using the Lyapunov analysis, it is ensured that all signals in the closed‐loop systems are uniformly ultimately bounded. The effectiveness of the developed control algorithm is confirmed by numerical simulations.     

Nonlinear H∞ observer design for one‐sided Lipschitz discrete‐time singular systems with time‐varying delay

This paper investigates the H_∞ observer design problem for a class of nonlinear discrete‐time singular systems with time‐varying delays and disturbance inputs. The nonlinear systems can be rectangular and the nonlinearities satisfy the one‐sided Lipschitz condition and quadratically inner‐bounded condition, which are more general than the traditional Lipschitz condition. By appropriately dealing with these two conditions and applying several important inequalities, a linear matrix inequality–based approach for the nonlinear observer design is proposed. The resulting nonlinear H_∞ observer guarantees asymptotic stability of the estimation error dynamics with a prescribed performance γ. The synthesis condition of H_∞ observer design for nonlinear discrete‐time singular systems without time delays is also presented. The design is first addressed for one‐sided Lipschitz discrete‐time singular systems. Finally, two numerical examples are given to show the effectiveness of the present approach.     

Separation principle for quasi‐one‐sided Lipschitz nonlinear systems with time delay

In this article, we address the problem of output stabilization for a class of nonlinear time‐delay systems. First, an observer is designed for estimating the state of nonlinear time‐delay systems by means of quasi‐one‐sided Lipschitz condition, which is less conservative than the one‐sided Lipschitz condition. Then, a state feedback controller is designed to stabilize the nonlinear systems in terms of weak quasi‐one‐sided Lipschitz condition. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the observer‐based controller. Under the quasi‐one‐sided Lipschitz condition, state observer and feedback controller can be designed separately even though the parameter (A,C) of nonlinear time‐delay systems is not detectable and parameter (A,B) is not stabilizable. Finally, a numerical example is provided to verify the efficiency of the main results.