Robust decentralized stabilization of uncertain large-scale discrete-time systems

This article describes the synthesis of robust decentralized controllers for large-scale discrete-time systems with uncertainties. Based on the Lyapunov method, a sufficient condition for robust stability is derived in terms of a linear matrix inequality (LMI). The solutions of the LMI can be easily obtained using efficient convex optimization techniques. A numerical example is given to illustrate the proposed method.     

Design of stable decentralized adaptive model-following controllers for large-scale systems

A decentralized model reference adaptive control for a class of large-scale inter-connected systems is developed. The proposed scheme does not require identification of the system parameters, or satisfaction of perfect model-following conditions (PMFC). The boundedness of the output error and the controller parameters is guaranteed using Lyapunov stability theory. The effectiveness of the developed algorithm is demonstrated using a numerical example.     

Adaptive discrete-time sliding-mode control of nonlinear systems described by Wiener models

In this paper, we propose an adaptive control scheme that can be applied to nonlinear systems with unknown parameters. The considered class of nonlinear systems is described by the block-oriented models, specifically, the Wiener models. These models consist of dynamic linear blocks in series with static nonlinear blocks. The proposed adaptive control method is based on the inverse of the nonlinear function block and on the discrete-time sliding-mode controller. The parameters adaptation are performed using a new recursive parametric estimation algorithm. This algorithm is developed using the adjustable model method and the least squares technique. A recursive least squares (RLS) algorithm is used to estimate the inverse nonlinear function. A time-varying gain is proposed, in the discrete-time sliding mode controller, to reduce the chattering problem. The stability of the closed-loop nonlinear system, with the proposed adaptive control scheme, has been proved. An application to a pH neutralisation process has been carried out and the simulation results clearly show the effectiveness of the proposed adaptive control scheme.     

Robust decentralized model reference adaptive control of discrete-time interconnected systems

A robust decentralized model reference adaptive controller is proposed for a class of large-scale systems composed of several interconnected subsystems and described by state space equations. We have formulated a local adaptive controller for each subsystem using only local information such that the state of this subsystem tracks the corresponding state of a reference model. The content of the paper is limited to interconnected subsystems which are described by linear, deterministic, single-input single-output and discrete-time models with unknown and/or slowly time-varying parameters. Sufficient conditions, formulated by utilizing Lyapunov theory, are given for the overall system to be stabilizable by decentralized state feedback adaptive control laws. The results are illustrated by a numerical example.     

A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems

In this note, the problem of decentralized model reference adaptive variable structure control for a class of perturbed large-scale systems with varying time-delay interconnections is investigated. Based on the Lyapunov stability theorem, an adaptive variable structure control strategy for solving the robust tracking problem without the knowledge of upper bound of perturbations is developed. The use of adaptive technique is to adapt the unknown upper bound of perturbations so that the objective of globally asymptotical stability is achieved. Once the system enters the sliding manifold, the dynamics of controlled systems are insensitive to matching perturbations. Finally, an example is given to demonstrate the feasibility of the proposed control scheme.     

离散模糊大系统的分散化PDC 控制器设计: LM I 方法

考虑了由N个相互关联的T—S子模糊系统组成的离散模糊大系统的分散镇定问题，给出了保证该模糊大系统闭环渐近稳定的分散化并行分布补偿(DPDC)控制器的设计方法，这些DPDC控制器的存在条件均以LMI的形式出现，LMI可通过MATLAB的LMI工具箱求解，因此提供了一条综合离散模糊大系统分散化PDC控制器的有效途径，仿真例子说明了所提出方法的有效性。     

Robust stability bounds on time-varying perturbations for state-space models of linear discrete-time systems

The stability robustness of linear discrete-time systems in the time domain is addressed using the Lyapunov approach. Bounds on linear time-varying perturbations that maintain the stability of an asymptotically stable linear time-invariant discrete-time nominal system are obtained for both structured and unstructured independent perturbations. Bounds are also derived assuming that various elements of the system matrix are perturbed dependently. The result for the structured perturbation case is extended to the stability analysis of interval matrices.     

On mathematical models of adaptive systems

The aim of this paper is to present a mathematical model for a system to control an object favourably which is unknown for the system—an adaptive system. We make the concept of adaptiveness precise first and consider systems as stochastic sequential machines (SSM's) to answer the question : what kind of logical structure is necessary and sufficient for a SSM to be adaptive. Some necessary conditions for a SSM to be adaptive are shown, and for a specified class of SSM's, the necessary and sufficient conditions to be adaptive are given. Furthermore, some examples of adaptive SSM's are shown.     

Parametric estimation of interconnected nonlinear systems described by input-output mathematical models

In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems,which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.     

一类组合系统的模型参考自适应分散控制

针对一类组合系统的模型参考自适应分散控制问题,提出一种新的考虑问题的思路.在选择参考模型时,根据系统所期望的性能指标,考虑各子系统间的相互作用,保留互联项;基于Lyapunov稳定性理论,给出了模型参考自适应控制方案,并证明了其整体一致收敛性.     

Composite adaptive fuzzy decentralized tracking control for pure-feedback interconnected large-scale nonlinear systems

Neural Computing and Applications - This paper focuses on a problem of composite adaptive fuzzy decentralized tracking control for a class of uncertain pure-feedback interconnected large-scale...     

具有动态和静态关联项大系统的鲁棒分散自适应镇定

对于一类具有动态和静态关联项的大系统，利用MT-滤波器和反推设计方法设计了一种鲁棒分散自适应输出反馈控制器．在各子系统为最小相位、静态关联项满足Lipschitz条件、动态关联项稳定且严格正则的假设下，证明了闭环系统的所有信号全局一致有界，且除了参数估计外的其他信号皆以指数速率收敛到零，该结果好于其他相关文献中的结果，仿真结果进一步验证了该方法的有效性。     

A new adaptive scheme for a class of discrete-time nonlinear systems

A new adaptive control scheme for discrete-time systems is proposed. The objective is the tracking of the trajectory. Global boundedness convergence and boundedness are obtained for a certain subclass of nonlinear systems.     

A new algorithm for decentralized adaptive control

A new algorithm for decentralized adaptive control is proposed in this paper. This algorithm consists of an ordinary local adaptive controller and a variable structure adaptive controller. The adaptive variable structure component of this algorithm is used to compensate for uncertain interconnections among the subsystems and to ensure global stability of the overall system. Simulation results are also presented to demonstrate the performance of the closed-loop control system     

Non-affine nonlinear adaptive control of decentralized large-scale systems using neural networks

This paper introduces a new decentralized adaptive neural network controller for a class of large-scale nonlinear systems with unknown non-affine subsystems and unknown interconnections represented by nonlinear functions. A radial basis function neural network is used to represent the controller’s structure. The stability of the closed loop system is guaranteed through Lyapunov stability analysis. The effectiveness of the proposed decentralized adaptive controller is illustrated by considering two nonlinear systems: a two-inverted pendulum and a turbo generator. The simulation results verify the merits of the proposed controller.     

A GGP approach to solve non convex min-max predictive controller for a class of constrained MIMO systems described by state-space models

This paper proposes a new method to solve non convex min-max predictive controller for a class of constrained linear Multi Input Multi Output (MIMO) systems. A parametric uncertainty state space model is adopted to describe the dynamic behavior of the real process. Moreover, the output deviation method is used to design the j-step ahead output predictor. The control law is obtained by the resolution of a non convex min-max optimization problem under input constraints. The key idea is to transform the initial non convex optimization problem to a convex one by means of variable transformations. To this end, the Generalized Geometric Programming (GGP) which is a global deterministic optimization method is used. An efficient implementation of this approach will lead to an algorithm with a low computational burden. Simulation results performed on Multi Input Multi Output (MIMO) system show successful set point tracking, constraints satisfaction and good non-zero disturbance rejection.     

Optimality of decentralized control for large-scale systems

A decentralized control scheme is given for the stabilization of large-scale linear systems composed of a number of controllable subsystems. A class of interconnection structures among subsystems is defined for which the overall system can always be stabilized by local state feedback which is optimal for a quadratic performance index. The resulting closed-loop system has robust stability properties against a wide range of variations in open-loop dynamics. Optimality of the decentralized control law is preserved for a modified performance index under perturbations in interconnections such that the strength of coupling does not increase. The class of decentrally stabilizable large-scale systems presented in this paper is the largest such class hitherto described by the structure of interconnections.     

RBFN-based decentralized adaptive control of a class of large-scale non-affine nonlinear systems

For a class of large-scale decentralized nonlinear systems with strong interconnections, a radial basis function neural network (RBFN) adaptive control scheme is proposed. The system is composed of a class of non-affine nonlinear subsystems, which are implicit function and smooth with respect to control input. Based on implicit function theorem, inverse function theorem and the design idea of pseudo-control, a novel control algorithm is proposed. Two neural networks are used to approximate unknown nonlinearities in the subsystem and unknown interconnection function, respectively. The stability is proved rigidly. The result of simulation validates the effectiveness of the proposed scheme.