Decentralized control of a class of large-scale nonlinear systems using neural networks

This paper designs a decentralized neural network (NN) controller for a class of nonlinear large-scale systems, in which strong interconnections are involved. NNs are used to handle unknown functions. The proposed scheme is proved guaranteeing the boundedness of the closed-loop subsystems using only local feedback signals.     

Adaptive neural tracking control of a class of MIMO pure-feedback time-delay nonlinear systems with input saturation

Considering interconnections among subsystems, we propose an adaptive neural tracking control scheme for a class of multiple-input-multiple-output (MIMO) non-affine pure-feedback time-delay nonlinear systems with input saturation. Neural networks (NNs) are employed to approximate unknown functions in the design procedure, and the separation technology is introduced here to tackle the problem induced from unknown time-delay items. The adaptive neural tracking control scheme is constructed by combining Lyapunov–Krasovskii functionals, NNs, the auxiliary system, the implicit function theory and the mean value theorem along with the dynamic surface control technique. Also, it is proven that the strategy guarantees tracking errors converge to a small neighbourhood around the origin by appropriate choice of design parameters and all signals in the closed-loop system uniformly ultimately bounded. Numerical simulation results are presented to demonstrate the effectiveness of the proposed control strategy.     

非线性时滞大系统自适应神经网络分散控制

针对一类未知非线性时滞关联大系统，提出一种自适应神经网络分散跟踪控制方案．采用神经网络逼近各子系统内部的非线性函数和关联项中的时滞非线性函数；利用占有方法处理时滞项，采用Backstepping技术设计分散控制律和参数自适应律．基于Lyapunov-Krasoviskii泛函证明了闭环大系统所有信号半全局一致最终有界．通过调节设计参数和增加神经元个数，可以实现任意输出跟踪精度．实例仿真说明了该方案的可行性。     

Decentralized robust controller design for a class ofinterconnected uncertain systems: with unknown bound of uncertainty

In this paper, a simple decentralized robust control scheme is proposed for a class of interconnected time-varying systems with uncertainties. The uncertainties may appear in the interconnections between the subsystems and also within the subsystems, and they are possibly nonlinear and time-varying. The uncertainties are bounded, but the bounds of the uncertainties are unknown in controller design. When certain matching conditions are satisfied for the uncertain interconnections and the uncertainties within the subsystems, the proposed decentralized control scheme guarantees the controlled system to converge exponentially with a prescribed degree toward the equilibrium of the system, or a residual ball around the equilibrium     

Decentralized adaptive iterative learning control for interconnected systems with uncertainties

In many applications,the system dynamics allows the decomposition into lower dimensional subsystems with interconnections among them.This decomposition is motivated by the ease and flexibility of the controller design for each subsystem.In this paper,a decentralized model reference adaptive iterative learning control scheme is developed for interconnected systems with model uncertainties.The interconnections in the dynamic equations of each subsystem are considered with unknown boundaries.The proposed controller of each subsystem depends only on local state variables without any information exchange with other subsystems.The adaptive parameters are updated along iteration axis to compensate the interconnections among subsystems.It is shown that by using the proposed decentralized controller,the states of the subsystems can track the desired reference model states iteratively.Simulation results demonstrate that,utilizing the proposed adaptive controller,the tracking error for each subsystem converges along the iteration axis.     

A multilevel optimization of large-scale dynamic systems

A multilevel feedback control scheme is proposed for optimization of large-scale systems composed of a number of (not necessarily weakly coupled) subsystems. Local controllers are used to optimize each subsystem, ignoring the interconnections. Then, a global controller may be applied to minimize the effect of interconnections and improve the performance of the overall system. At the cost of suboptimal performance, this optimization strategy ensures invariance of suboptimality and stability of the systems under structural perturbations whereby subsystems are disconnected and again connected during operation.     

Decentralized output-feedback MRAC of linear state delay systems

In this note, we develop coordinated decentralized output-feedback adaptive controllers for a class of large-scale systems with state time delays in the subsystems and in the interconnections. We present a decentralized model reference adaptive control scheme which requires an exchange of signals between the different reference models, but does not involve the exchange of output signals between the different subsystems. It can not only guarantee closed-loop stability but also asymptotic zero tracking errors when uncertainties and delays are present in the subsystems and interconnections. Closed-loop signal boundedness and asymptotic output-feedback tracking are proven analytically and verified by simulation.     

Stability criteria for large-scale systems

Recent research into large-scale system stability has proceeded via two apparently unrelated approaches. For Lyapunov stability, it is assumed that the system can be broken down into a number of subsystems, and that for each subsystem one can find a Lyapunov function (or something akin to a Lyapunov function). The alternative approach is an input-output approach; stability criteria are derived by assuming that each subsystem has finite gain. The input-output method has also been applied to interconnections of passive and of conic subsystems. This paper attempts to unify many of the previous results, by studying linear interconnections of so-called "dissipative" subsystems. A single matrix condition is given which ensures both input-output stability and Lyapunov stability. The result is then specialized to cover interconnections of some special types of dissipative systems, namely finite gain systems, passive systems, and conic systems.     

Solution of optimal control problem of linear system with input derivative through Liapunov's method

Decentralized stabilization and control schemes for large-scale power systems are presented in this paper. The interconnections between the subsystems are assumed to be unknown, but bounded. The control design for the first scheme utilizes the knowledge of the bounds on the interconnections between the subsystems, whereas this information is not required in the second control design due to its adaptive nature. These schemes are applied to a power system with two generators and an infinite bus connected through a network of transformers and transmission lines. Simulation studies for unknown interconnections arising due to faults and subsequent line switchings in the transmission network are carried out. The studies not only illustrate the simplicity of the developed controls, but also validate the fact that connective stability and robust performance is maintained for unknown interconnection topology using these schemes.     

严格反馈互联系统分散式backstepping自适应迭代学习控制

基于Lyapunov分析方法,针对具有严格反馈形式的非线性互联系统,本文设计了一种分散式backstepping自适应迭代学习控制器.子系统之间的互联项为所有子系统输出项线性有界,为每个子系统设计的控制器仅采用该子系统的信息,不需要子系统之间相互传递信息.在控制器中,引入在时间轴和迭代轴上同时更新的自适应参数,以补偿子系统之间的互联项影响.通过采用本文给出的控制器,可使得每个子系统的输出跟踪相应的参考模型输出,仿真结果验证了本文算法的有效性.     

一类关联大系统的分散强镇定

研究由子系统通过输入输出通道实现连接的关联大系统的分散强镇定问题，对于静态连接或的动态连接的情形，给出了大系统可以实现分散强镇定的条件，这些条件的检验只在子系统一级进行，具有较低的计算维数。     

Local stability of composite systems--Frequency-domain condition and estimate of the domain of attraction

This paper is concerned with such composite systems whose subsystems contain one nonlinearity each and whose interconnections are functions of the scalar outputs of subsystems. A frequency-domain condition which assures local asymptotic stability is given under the assumptions that each nonlinearity satisfies a sector condition, that interconnections are linearly bounded, and that linear parts of subsystems may have unstable poles. In deriving the above result, such Lyapunov functions of subsystems are constructed so that their weighted sum is a Lyapunov function of the overall system. A method to estimate the domain Of attraction based on the above Lyapunov functions is also studied. When the bounds on nonlinearities hold true in the entire space and when the linear parts do not have unstable poles, the present condition turns out to be the same with the L2-stability condition which was obtained before by Araki.     

Stable decentralized adaptive control design of robot manipulators using neural network approximations

In this paper, we present a decentralized neural network (NN) adaptive technique for control of robot manipulators in the presence of unknown non-linear functions. Radial basis function NNs are used to approximate the non-linear functions to include the case of both parametric and dynamic uncertainty in each subsystem. The robustifying terms are added to the controllers to overcome the effects of the interconnections. The stability can be guaranteed by using a rigid proof. Finally, simulation is given to illustrate the effectiveness of the proposed algorithm.     

Vector dissipativity theory and stability of feedback interconnections for large-scale non-linear dynamical systems

Recent technological demands have required the analysis and control design of increasingly complex, large-scale non-linear dynamical systems. In analysing these large-scale systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solution properties of the large-scale system are then deduced from the solution properties of the individual subsystems and the nature of the system interconnections. In this paper we develop an analysis framework for large-scale dynamical systems based on vector dissipativity notions. Specifically, using vector storage functions and vector supply rates, dissipativity properties of the composite large-scale system are shown to be determined from the dissipativity properties of the subsystems and their interconnections. Furthermore, extended Kalman–Yakubovich–Popov conditions, in terms of the subsystem dynamics and interconnection constraints, characterizing vector dissipativeness via vector system storage functions are derived. Finally, these results are used to develop feedback interconnection stability results for large-scale non-linear dynamical systems using vector Lyapunov functions.     

Globally decentralized adaptive backstepping neural network tracking control for unknown nonlinear interconnected systems

A globally stable decentralized adaptive backstepping neural network tracking control scheme is designed for a class of large‐scale systems with mismatched interconnections. Under the assumption that the subsystems share the reference signals from the other subsystems, neural networks are used to approximate the unknown interconnections dependent on all reference signals such that the NN approximation domain can be determined a priori based on the bounds of reference signals. The proposed control approach can guarantee that all closed‐loop signals are globally uniformly ultimately bounded and that the tracking errors converge to a small residual set around the origin. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Lurie控制系统的关联绝对稳定性-双线性矩阵不等式方法

研究任意两个相互独立的Lurie控制系统能否通过关联或协调控制组成绝对稳定大系统的问题,给出两个Lurie控制系统可关联绝对稳定的充分条件,并给出了计算关联矩阵的双线性矩阵不等式方法.研究结果表明:两个非绝对稳定的系统可以通过关联或协调控制来实现关联大系统的绝对稳定性,取消了大系统稳定性分析中对关联的不合理限制.文末给出了本文结果的数值例子.     

DECENTRALIZED ROBUST CONTROL DESIGN FOR A CLASS OF SIMILAR COMPOSITE SYSTEMS WITH UNCERTAINTIES

A class of similar composite systems is researched. The interconnections of systems are not symmetric and do not satisfy the matching condition. By means of the advantage of interconnections of systems, a two-step method is proposed to study the decentralized stabilization problem for the similar composite systems in this paper. First, the interconnections between subsystems are changed into a new form to satisfy the matching condition; second, based on the new form of the systems, the decentralized robust controllers are designed. In this paper, the controllers guarantee the similar composite systems quadratic stability. At last, the simulation of example is given.     

Decentralised stabilisation for nonlinear time delay interconnected systems using static output feedback

In this paper, time delay interconnected systems are considered where the nominal isolated subsystems are fully nonlinear. The interconnections and the matched and mismatched disturbances are nonlinear and time-delayed. A decentralised static output feedback control strategy is proposed to stabilise the resulting interconnected system uniformly asymptotically. A novel approach is proposed to deal with the interconnections by introducing artificial interconnections, such that accessible information is fully exploited in the control design to reduce conservatism. Simulation results show the effectiveness of the proposed approach.     

Decentralized robust control for multiconnected objects with structural uncertainty

We solve the problem of constructing a decentralized robust regulating system for a multiconnected control object that provides for compensating interconnections in local subsystems and also parametric and external bounded perturbations, compensating with precision δ if one does not measure the derivatives of the local subsystems output vector and in full if the derivatives are measured.     

Decentralized adaptive tracking control of nonaffine nonlinear large-scale systems with time delays

This paper addresses the problem of decentralized tracking control of large-scale systems with uncertain nonaffine nonlinear isolated subsystems and nonlinear interconnections with time-varying delays. Based on Lyapunov-Krasovskii functional approach and implicit function theorem, a delay-independent decentralized tracking controller is proposed. Due to functional approximation capability of fuzzy logic systems (FLS), neither strict structure restrictions on the isolated subsystems nor a priori knowledge of the strong interconnections with time-varying delays is required in our control design. Furthermore, transient performance of the resulting closed-loop system is also addressed under an analytical framework. Finally, two numerical examples are provided to show the effectiveness of the proposed controller.