离散广义大系统的Lyapunov稳定性分析

广义大系统的稳定性是广义大系统理论的基本问题之一,对其稳定性的研究要比状态空间大系统复杂得多,因为广义大系统不仅需要考虑稳定性,而且还要考虑正则性和因果性(离散广义系统)及脉冲自由(连续广义系统).本文在所有孤立子系统都是正则的且具有因果关系的条件下,利用Lyapunov方程,应用Lyapunov函数方法,研究了广义离散线性大系统和广义离散非线性大系统的稳定性和不稳定性问题,给出了离散广义大系统稳定性和不稳定性判定定理,得到了离散广义大系统的关联稳定参数域和不稳定域.     

An analog feedback associative memory

A method for the storage of analog vectors, i.e., vectors whose components are real-valued, is developed for the Hopfield continuous-time network. An important requirement is that each memory vector has to be an asymptotically stable (i.e. attractive) equilibrium of the network. Some of the limitations imposed by the continuous Hopfield model on the set of vectors that can be stored are pointed out. These limitations can be relieved by choosing a network containing visible as well as hidden units. An architecture consisting of several hidden layers and a visible layer, connected in a circular fashion, is considered. It is proved that the two-layer case is guaranteed to store any number of given analog vectors provided their number does not exceed 1 + the number of neurons in the hidden layer. A learning algorithm that correctly adjusts the locations of the equilibria and guarantees their asymptotic stability is developed. Simulation results confirm the effectiveness of the approach.     

Robust stabilization of nonlinearly perturbed large-scale systems by decentralized observer-controller compensators

This paper is concerned with the problem of robust stabilization for nonlinearly perturbed large-scale systems via decentralized observer-controller compensators. The large-scale system is composed of several interconnected perturbed subsystems, each containing a nonlinearly perturbed plant and an observer-controller compensator. Here a robust stability criterion for the perturbed large-scale system is introduced, and a simple but useful inequality is derived for synthesizing the decentralized observer-controller compensators. The main features of this paper are as follows: (i) the nominal plant of each subsystem is not constrained to be stable and/or minimum phase; (ii) the perturbations of the plants and/or interconnections are considered; and (iii) a two degree observer-controller compensating scheme is employed to treat the perturbed large-scale systems.     

非线性时变离散大系统的稳定性

本文应用标量李雅普诺夫函数法研究了线性时变离散大系统及非线性时变离散大系统的稳定性分解。同时分别给出了分解系数与稳定域的参数估计公式。     

Decentralized stabilization for expanding construction oflarge-scale systems

A decentralized stabilization problem compatible with expanding the construction of large-scale systems is considered. It is assumed that a large-scale system is obtained by adding new subsystems one after another. When a new subsystem is connected to an already interconnected portion, a local controller is designed for the new subsystem so that both the subsystem and the resultant expanded system are stable. The proper-stable-factorization approach is used for calculating the local controllers. Sufficient conditions on subsystems for such stabilization are presented. They are expressed in terms of the solvability of linear matrix equations over the ring of stable rational matrices     

A method for verifying sector conditions in nonlinear discrete-timecontrol systems

The stability of a discrete feedback system with a continuous broken-line nonlinearity is considered. Many nonlinearities in practice are included in this class. Sufficient conditions for this type of nonlinear feedback system to be asymptotically stable in the large are developed using the contraction mapping theory. It is then shown that Kalman's conjecture (1957) for a feedback system with a sector nonlinearity also applies to discrete systems under a restricted sector condition. A method for obtaining this restricted sector by solving a quadratic equation is presented     

离散时间系统的滑模控制器设计与仿真研究

针对不确定性离散时间系统,分析和设计了一类变结构控制器。当存在外界干扰和不确定性时,系统状态也是全局有界稳定的。一个新的切换面作为系统的输出信号被提出,特别用来设计滑模控制器。系统状态一旦进入到准滑动模态,就对设备参数变化和外界干扰显示出强的鲁棒性,因为控制器的设计完全考虑了边界层的影响。外推法被用来估计不确定离散时间系统的不确定值。两种方法均有效地消除了系统的抖振,确保了系统的稳定性,且保证了变结构控制系统良好的品质。最后,仿真结果证实了所提出方法的有效性。     

Frequency-Domain Stability Conditions for Discrete-Time Switched Systems

We consider discrete-time switched systems with switching of linear time-invariant right-hand parts. The notion of a connected discrete switched system is introduced. For systems with the connectedness property, we propose necessary and sufficient frequency-domain conditions for the existence of a common quadratic Lyapunov function that provides the stability for a system under arbitrary switching. The set of connected switched systems contains discrete control systems with several time-varying nonlinearities from the finite sectors, considered in the theory of absolute stability. We consider the case of switching between three linear subsystems in more details and give an illustrative example.     

Multi-agent compositional stability exploiting system symmetries

This paper considers nonlinear symmetric control systems. By exploiting the symmetric structure of the system, stability results are derived that are independent of the number of components in the system. This work contributes to the fields of research directed toward compositionality and composability of large-scale system in that a system can be “built-up” by adding components while maintaining system stability. The modeling framework developed in this paper is a generalization of many existing results which focus on interconnected systems with specific dynamics. The main utility of the stability result is one of scalability or compositionality. If the system is stable for a given number of components, under appropriate conditions stability is then guaranteed for a larger system composed of the same type of components which are interconnected in a manner consistent with the smaller system. The results are general and applicable to a wide class of problems. The examples in this paper focus on the formation control problems for multi-agent robotic systems.     

时滞离散广义不确定系统的变结构控制

研究了一类线性离散时滞广义不确定系统的变结构控制的综合与设计问题.首先引入了一种新的受限系统等价分解形式,把所给的系统分解成两个低维的不确定子系统.其次,在上述分解的基础上,根据离散时滞广义系统鲁棒稳定性的有关结果,设计了带有差分补偿器的切换函数,使得系统在准切换流形上的运动渐近稳定.然后设计了离散变结构控制律,使得在此控制律的作用下,系统的运动轨迹要么在有限步内到达准切换流形并在其上渐近滑向原点;要么在有限步内进入准切换流形的一个较小的邻域内并稳定于原点附近的某个小的抖振.最后，给出了两个数值例子以说明该综合设计方法的有效性与实用性.     

Robot discrete adaptive control based on dynamic inversion using dynamical neural networks

A stable discrete time adaptive control approach using dynamic neural networks (DNNs) is developed in this paper for the trajectory tracking of a robotic manipulator with unknown nonlinear dynamics. By using dynamic inversion constructed by a DNN, the assumption under which the system state should be on a compact set can be removed. This assumption is usually required in neuro-adaptive control. The NN-based variable structure control is designed to guarantee the stability and improve the dynamic performance of the closed-loop system. The proposed control scheme ensures the global stability and desired tracking as well.     

Decentralized PDC for large-scale T-S fuzzy systems

This paper studies the decentralized stabilization problem for a large-scale system. The considered large-scale system comprises of a number of subsystems and each subsystem is represented by a Takagi-Sugeno (T-S) fuzzy model. The interconnection between any two subsystems may be nonlinear and satisfies some matching condition. By the concept of parallel distributed compensation (PDC), the decentralized fuzzy control for each subsystem is synthesized, in which the control gain depends on the strength of interconnections, maximal number of the fired rules in each subsystem, and the common positive matrix P/sub i/. Based on Lyapunov criterion and Riccati-inequality, some sufficient conditions are derived and the common P/sub i/ is solved by linear matrix inequalities (LMI) so that the whole closed loop large-scale fuzzy system with the synthesized fuzzy control is asymptotically stable. Finally, a numerical example is given to illustrate the control synthesis and its effectiveness.     

Multilevel discrete time system identification in large scale systems†

Hierarchical decomposition is considered to be one of the most powerful and offective tools to deal with complexity. Hierarchical system theory, which deals with system decomposition and coordination, can be used to decentralize and reduce the computational efforts requirements for many large-scale problems. This is achieved by decomposing the original system problem into several lower order easier to handle sub-problems, which are then coordinated such that the overall system objectives are met. In this work a hierarchical system theory approach to the discrete-time system identification problem is considered for stochastic large-scale system applications. A set of sequential discrete-time hierarchical identification algorithms, suitable for known and unknown system noise moments, are first obtained using a maximum a posteriori (MAP) approach with covariance matching and maximum likelihood (ML) methods. This is conducted in a two level hierarchical structure with two principles of coordination. Next, the hierarchical system identification algorithms are extended to multilevel hierarchical structures based on system characteristics of priority of action, spatial structure and time behaviour. This results in multilevel and composite multilevel coordinated system identification procedures, where each subsystem unit can be treated independently in reaching the overall system optimality. Application of these algorithms for the purpose of decentralization and reduction of computational requirements as well as adaptation to structural changes in growth and merger are considered.     

Asymptotic stability and instability of large-scale systems

The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations. With minor technical adjustments, the theory is broadened to include considerations of unstable subsystems as well as instability of composite systems.     

Adaptive synchronization of master-slave large-scale systems against bias actuators and network attenuations

This paper utilizes the adaptive technique to design a class of active synchronizing masterslave large scale systems against imperfect actuators and networked interconnections with bias faults and signal attenuations, respectively. Without the requirement of knowledge of eventual faulty factors of bias-actuators on systems, and attenuation factors of connected networks, an adaptive mechanism is designed to estimate each unknown faulty factor on-line for constructing a class of distributed adaptive controllers. Then based on the adaptive adjustment parameters and Lyapunov stability theory, Lyapunov functions are addressed to prove that the proposed adaptive master-slave large-scale system can be guaranteed to be asymptotic synchronization with the improper actuator and faulty transmitted signals. Finally, a multiple vehicle large-scale system is used to verify the efficiency of the method.     

Decentralized Networked Control System Design Using Takagi-Sugeno (TS) Fuzzy Approach

This paper proposes a new method for control of continuous large-scale systems where the measures and control functions are distributed on calculating members which can be shared with other applications and connected to digital network communications.At first, the nonlinear large-scale system is described by a Takagi-Sugeno(TS) fuzzy model. After that, by using a fuzzy LyapunovKrasovskii functional, sufficient conditions of asymptotic stability of the behavior of the decentralized networked control system(DNCS),are developed in terms of linear matrix inequalities(LMIs). Finally, to illustrate the proposed approach, a numerical example and simulation results are presented.     

一类离散切换模糊系统的稳定性

针对离散模糊系统,提出一类离散切换模糊系统的稳定性问题.使用切换技术及单Lyapunov函数、多Lyapunov函数方法构造出连续状态反馈控制器,使得相应的闭环系统渐近稳定,同时设计可以实现系统全局渐近稳定的切换律.模型中的每个切换系统的子系统是离散模糊系统,取常用的平行分布补偿PDC控制器,主要条件以凸组合和矩阵不等式的形式给出,具有较强的可解性.计算机仿真结果表明设计方法的可行性与有效性.     

Feedback stabilization of discrete time singularly perturbed systems with communication constraints

In this paper, the quantized feedback problem for a class of discrete time singularly perturbed systems with information constraints is considered. First, a proper coder‐decoder pair is presented so that the transmission errors tend to zero exponentially under information constraints. Next, linear matrix inequalities are constructed such that the resulting closed‐loop system is input‐to‐state stable (ISS) with respect to the transmission error, and the asymptotic stability of the closed‐loop system also can be guaranteed. The theoretical results have shown that the presented method is simple and easy to operate. Moreover, the upper bound of the small perturbed parameter of the stable system can be explicitly estimated using this feasible method. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.     

Stability and stabilisation of a class of networked dynamic systems

We investigate the stability and stabilisation of a linear time invariant networked heterogeneous system with arbitrarily connected subsystems. A new linear matrix inequality based sufficient and necessary condition for the stability is derived, based on which the stabilisation is provided. The obtained conditions efficiently utilise the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, a sufficient condition only dependent on each individual subsystem is also presented for the stabilisation of the networked systems with a large scale. Numerical simulations show that these conditions are computationally valid in the analysis and synthesis of a large-scale networked system.