Further results on limitations of sampled-data feedback

To control continuous-time uncertain dynamical systems with sampled data-feedback is prevalent today,but the sampling rate is usually not allowed to be arbitrarily fast due to various physical and/or computational constrains.In this paper,the authors examine the limitations of sampled-data feedback control for a class of uncertain systems in continuous-time,with sampling rate not necessary fast enough and with the unknown system structure confined to a set of functions with both linear and nonlinear growth.The limitations of the sampled-data feedback control for the uncertain systems are established quantitatively,which extends the existing related results in the literature.     

Stabilization of switched linear systems with constrained inputs

The stabilization of switched linear systems with constrained inputs(SLSCI) is considered. The authors design admissible linear state feedbacks and the switching rule which has a minimal dwell time(MDT) to stabilized the system.First,for each subsystem with constrained inputs,a stabilizing linear state feedback and an invariant set of the closed-loop system are simultaneously constructed, such that the input constraints are satisfied if and only if the closed-loop system’s states lie inside this set.Then,by constructing a quadratic Lyapunov function for each closed-loop subsystem,an MDT is deduced and an MDT-based switching strategy is presented to ensure the stability of the switched system.     

Optimal Switching Integrity Attacks on Sensors in Industrial Control Systems

In this article, an optimal switching integrity attack problem is investigated to study the response of feedback control systems under attack. The authors model the malicious attacks on sensors as additive norm bounded signals. The authors consider an attacker who is only capable of launching attacks to limited number of sensors once a time and changing the combinations of attacked sensors all over the time. The objective of this paper is to find the optimal switching sequence of these combinations and the optimal attack input. The authors solve this problem by transforming it into a traditional optimal control problem with new control variables vary continuously in the range [0, 1]. The optimal solutions of the new control variables are of bang-bang-type. Therefore, an algebraic switching condition and an optimal attack input can be obtained. Finally, numerical results are provided to illustrate the effectiveness of the methods.     

Complexity analysis of network-based dynamical systems

This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyze the bifurcation and chaotic behavior of the non-smooth dynamical systems. The authors first prove that for almost all system parameters there are no periodic orbits. This result distinguishes this type of non-smooth dynamical systems from many others exhibiting border-collision bifurcations. Next, the authors show analytically that the chaotic sets are separated from the region containing the line segment of all fixed points with a finite distance. Finally, the authors employ a simple model to highlight that both the number of clients sharing a common network channel and fluctuations in the available network bandwidth have significant influence on the performance of such dynamical systems.     

一类时滞免疫反应系统动力学行为仿真

研究一类时滞免疫反应系统在机体清除靶细胞能力对浆细胞增长有影响的情形下的动力学行为,用时滞微分理论证明系统正平衡点的稳定性与时滞的关系,给出其稳定判定方法。在模型解基础上,用仿真方法研究部分参数变化对系统动力学行为的影响,给出了免疫系统呈现不同动力学行为的参数范围,实现免疫系统动态特性的仿真。结果表明,对于给定时滞,免疫反应系统的动力学行为不敏感地依赖于抗体清除抗原速率,而敏感地依赖于抗原繁殖系数。     

Stabilization of Continuous-Time Systems Against Stochastic Network Uncertainties: Fundamental Variance Bounds

This paper studies the stabilizability and stabilization of continuous-time systems in the presence of stochastic multiplicative uncertainties. The authors consider multi-input, multi-output(MIMO) linear time-invariant systems subject to multiple static, structured stochastic uncertainties,and seek to derive fundamental conditions to ensure that a system can be stabilized under a mean-square criterion. In the stochastic control framework, this problem can be considered as one of optimal control under state-or input-dependent random noises, while in the networked control setting, a problem of networked feedback stabilization over lossy communication channels. The authors adopt a mean-square small gain analysis approach, and obtain necessary and sufficient conditions for a system to be meansquare stabilizable via output feedback. For single-input, single-output(SISO) systems, the condition provides an analytical bound, demonstrating explicitly how plant unstable poles, nonminimum phase zeros, and time delay may impose a limit on the uncertainty variance required for mean-square stabilization. For MIMO minimum phase systems with possible delays, the condition amounts to solving a generalized eigenvalue problem, readily solvable using linear matrix inequality optimization techniques.     

Bidirectionally coupled synchronization of the generalized Lorenz systems

Wu, Chen, and Cai (2007) investigated chaos synchronization of two identical generalized Lorenz systems unidirectionally coupled by a linear state error feedback controller. However, bidirectional coupling in real life such as complex dynamical networks is more universal. This paper provides a unified method for analyzing chaos synchronization of two bidirectionally coupled generalized Lorenz systems. Some sufficient synchronization conditions for some special coupling matrices (diagonal matrices, so-called dislocated coupling matrices, and so on) are derived through rigorously mathematical theory. In particular, for the classical Lorenz system, the authors obtain synchronization criteria which only depend upon its parameters using new estimation of the ultimate bounds of Lorenz system (Chaos, Solitons, and Fractals, 2005). The criteria are then applied to four typical generalized Lorenz systems in the numerical simulations for verification.     

Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems

Hybrid systems are dynamical systems with interacting discrete computation and continuous physical processes, which have become more common, more indispensable, and more complicated in our modern life. Particularly, many of them are safety-critical, and therefore are required to meet a critical safety standard. Invariant generation plays a central role in the verification and synthesis of hybrid systems. In the previous work, the fourth author and his coauthors gave a necessary and sufficient condition for a semi-algebraic set being an invariant of a polynomial autonomous dynamical system, which gave a confirmative answer to the open problem. In addition, based on which a complete algorithm for generating all semi-algebraic invariants of a given polynomial autonomous hybrid system with the given shape was proposed. This paper considers how to extend their work to non-autonomous dynamical and hybrid systems. Non-autonomous dynamical and hybrid systems are with inputs, which are very common in practice; in contrast, autonomous ones are without inputs. Furthermore, the authors present a sound and complete algorithm to verify semi-algebraic invariants for non-autonomous polynomial hybrid systems. Based on which, the authors propose a sound and complete algorithm to generate all invariants with a pre-defined template.     

不确定切换系统基于切换时间的动态输出反馈鲁棒H∞控制

借助平均驻留时间方法，讨论了一类不确定切换系统的动态输出反馈鲁棒H_∞控制问题。利用多Lyapunov函数法，以线性矩阵不等式的形式给出了使得该类闭环系统的动态输出反馈控制器存在的充分条件。同时,构建了基于切换驻留时间的切换律。在综合考虑最优化干扰抑制性能指标γ和求解的简便性后，给出了动态输出反馈控制器的设计算法。进一步的，将所得结果推广到任意切换律的情况。     

Optimal Output Tracking Control and Stabilization of Networked Control Systems with Packet Losses

This paper studies the optimal output tracking control and stabilization for networked control systems with packet losses via output feedback control. Both finite-horizon and infinite-horizon cases are considered. For the finite-horizon case, the authors introduce an augmented system according to the state variable and the reference trajectory for the first time. Based on a set of difference Riccati equations, an optimal output feedback tracking controller is proposed by applying the stochastic maximum principle. And an optimal estimator is presented. For the infinite-horizon case, a necessary and sufficient condition for the stabilization of the system is provided. And an optimal output feedback stabilizing tracking controller is obtained by establishing a set of algebraic Riccati equations. Finally,numerical examples are given to verify the proposed results.     

Consensus control design for multi-agent systems using relative output feedback

This paper studies the consensus problem of multi-agent systems in which all agents are modeled by a general linear system. The authors consider the case where only the relative output feedback between the neighboring agents can be measured. To solve the consensus problem, the authors first construct a static relative output feedback control under some mild constraints on the system model. Then the authors use an observer based approach to design a dynamic relative output feedback control. If the adjacent graph of the system is undirected and connected or directed with a spanning tree, with the proposed control laws, the consensus can be achieved. The authors note that with the observer based approach, some information exchange between the agents is needed unless the associated adjacent graph is completely connected.     

Exponential Stability of the Euler-Bernoulli Beam Equation with External Disturbance and Output Feedback Time-Delay

This paper concerns the stability of a one-dimensional Euler-Bernoulli beam equation with external disturbance and output feedback time-delay, in which the disturbance is bounded by an exponential function. In order to estimate disturbance, the authors design an estimator of disturbance,which is composed of two parts: One is the system measurement that is called the eigen-measurement,another is a time-variant estimator of disturbance. Thus, the feedback controller which is based on the estimate of the disturbance is designed to stabilize the system. The finite-time stability of the system under this control law is proved by Lyapunov function method. Finally, some numerical simulations on the dynamical behavior of the closed-loop system is presented to show the correctness of the result.     

Dynamical Criticality: Overview and Open Questions

Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a dynamical regime between order and disorder attain the highest level of computational capabilities and achieve an optimal trade-off between robustness and flexibility. Recent results in cellular and evolutionary biology, neuroscience and computer science have revitalised the interest in the criticality hypothesis, emphasising its role as a viable candidate general law in adaptive complex systems. This paper provides an overview of the works on dynamical criticality that are — To the best of our knowledge — Particularly relevant for the criticality hypothesis. The authors review the main contributions concerning dynamics and information processing at the edge of chaos, and illustrate the main achievements in the study of critical dynamics in biological systems.Finally, the authors discuss open questions and propose an agenda for future work.     

New chaotic system and its hyperchaos generation

To seek for lower-dimensional chaotic systems that have complex topological attractor structure with simple algebraic system structure, a new chaotic system of three-dimensional autonomous ordinary differential equations is presented. The new system has simple algebraic structure, and can display a 2-scroll attractor with complex topological structure, which is different from the Lorenz’s, Chen’s and L¨u’s attractors. By introducing a linear state feedback controller, the system can be controlled to generate a hyperchaotic attractor. The novel chaotic attractor, hyperchaotic attractor and dynamical behaviors of corresponding systems are further investigated by employing Lyapunov exponent spectrum, bifurcation diagram, Poincar′e mapping and phase portrait, etc., and then verified by simulating an experimental circuit.     

Robust Feedback Controller for Exponential Stability of Nonlinear Systems with Mismatched Uncertainties

The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective.     

Coordination Control for a Class of Multi-Agent Systems Under Asynchronous Switching

This paper studies the coordination control of nonlinear multi-agent systems under asynchronous switching, including consensus, tracking control, and containment. The asynchronous switching considered here means that the switching of the controller lags behind the mode's switching for each agent. So the matched controller is interrupted by the delayed switching. For the situation, the authors give some new results by applying the conventional distributed control protocol. The authors show that all agents can achieve consensus. Secondly, the authors show that all followers can track the actual leader. Thirdly, the authors show that all followers will converge to the convex hull spanned by the dynamic leaders as time goes on. Numerical simulations are also provided and the results show highly consistent with the theoretical results.     

二阶动力学系统模型的跟踪设计

考虑了基于分散状态反馈控制律的二阶动力学系统输出渐近跟踪设计,该控制律包括被控对象状态和参考模型状态两部分。给出了问题解的存在条件:两个矩阵方程,其中一个为二阶Sylvester矩阵方程。给出了所有控制器增益阵的完全参数化表达式。归纳出了二阶动力学系统模型参考输出跟踪控制律的设计算法。该算法直接基于原系统的参数矩阵,无须对系统增广或变换,仅涉及自由参数的选取和一些简单的代数运算,便于工程应用。仿真结果说明所给出的算法是有效的。     

Boundary Control of Coupled Wave Systems with Spatially-Varying Coefficients

This paper considers the stabilization of the coupled wave systems with spatially-varying coefficients. The authors design a state feedback controller by backstepping method. In contrast to the previous work in the literature, the kernel equations become more complicated and the main difficulty lies in proving the existence and uniqueness of the solution to the kernel equations. Firstly, using the backstepping approach, the authors verify the kernel equations, which is a system of coupled hyperbolic equations with spatially-varying coefficients. Then, the existence and uniqueness of the kernel matrices is obtained. Finally, the authors use a Lyapunov function to get the exponential stabilization of the closed-loop system. A numerical example is presented to illustrate the effectiveness of the proposed controller.

     

Finite-time stability and stabilization of Markovian switching stochastic systems with impulsive effects

Many practical systems in physics,biology,engineering and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes.The problems of finite-time stability analysis are investigated for a class of Markovian switching stochastic systems,in which exist impulses at the switching instants.Multiple Lyapunov techniques are used to derive sufficient conditions for finite-time stochastic stability of the overall system.Furthermore,a state feedback controller,which stabilizes the closed loop systems in the finite-time sense,is then addressed.Moreover,the controller appears not only in the shift part but also in the diffusion part of the underlying stochastic subsystem.The results are reduced to feasibility problems involving linear matrix inequalities (LMIs).A numerical example is presented to illustrate the proposed methodology.     

分布式计算机控制系统的递阶优化控制算法

根据大系统分解协调原理，提出了一种适于分布式计算机控制系统（DCCS）的递阶优化算法。应用这种算法，可使各子系统的控制度为局部反馈控制和协调量开环控制的迭加。反馈控制仅与子系统的结构和状态有关，开环控制与系统的结构及系统的所有状态有关。通过动态调整松弛矩阵，可使协调量的收敛速度加快，实验表明，这种方法于DCCS的应用。