Distributed piecewise filtering design for large-scale networked nonlinear systems

Decentralized piecewise [formula omitted] fuzzy filtering design for discrete-time large-scale nonlinear systems with time-varying delay

The decentralized \({\mathscr{H}}_{\infty }\) sampled-data control problem is investigated for a class of continuous-time large-scale networked nonlinear systems with interconnection. Each nonlinear subsystem in the considered large-scale system is represented by a Takagi–Sugeno model and is closed by a communication channel with transformed time delay. Our objective is to design a decentralized sampled-data fuzzy controller such that the resulting fuzzy control system is asymptotically stable with an \({\mathscr{H}}_{\infty }\) performance. Firstly, using an input delay approach, the sampled-data control system is formulated into the system with time-varying delay, and a two-term approximation method is proposed such that the delayed system is reformulated into an interconnected framework with input and output. Then, we introduce a Lyapunov–Krasovskii functional that all Lyapunov matrices are no longer required to be positive definite. Combined with the scaled small gain theorem, the less conservative solutions to the decentralized \({\mathscr{H}}_{\infty }\) sampled-data control problem for the considered system are derived in the form of linear matrix inequalities. Finally, the effectiveness of the proposed methods is illustrated by two numerical examples.

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Fuzzy-Model-Based Piecewise H∞ Decentralized Tracking Control of Discrete-time Networked Nonlinear Interconnected Systems

This study examines the stabilisation problem associated with a particular type of large‐scale system. This type of large‐scale system consists of several non‐linear subsystems, which are connected to each other via interconnections of variable weighting. Interconnections of variable weighting between two subsystems denote that the interaction strength between the two subsystems is variable. Moreover, the weight may even be zero at some times or in some cases. In this study the authors suppose that the range of weight variation between any two subsystems is known, and that the stabilisation conditions for the large‐scale system are derived and that decentralised controllers which satisfy the conditions are synthesised. In the main result derivation, the Takagi–Sugeno ( T – S ) fuzzy model of a large‐scale system is used and a parallel distribution compensation (PDC) type fuzzy controller is synthesised based on the linear‐matrix‐inequality (LMI) method. Finally, a numerical example is given to demonstrate that the main theorem is applicable and the synthesised controller is effective.

Mean-square practical stability for stochastic large-scale dynamical systems is studied. The vector Lyapunov functions and the basic comparison principle of stochastic systems as well as the decomposition-aggregation method for large-scale systems were used to obtain results for various types of mean-square practical stability of nonlinear stochastic large-scale dynamical systems. The objective is to analyze stochastic large-scale systems in terms of their lower-order subsystems and in terms of their interconnecting structure. These results make it possible to determine the mean-square practical stability of stochastic large-scale dynamical systems by testing the corresponding practical stability of the auxiliary deterministic systems. >

Decentralized Predictor Output Feedback for Large-scale Systems with Large Delays

: Controls research under this program concentrated on the development of a network thermodynamic stabilization framework for hybrid control design of large-scale and multiagent aerospace systems. In particular, we concentrate on hybrid control, hierarchical control, impulsive dynamical systems, nonnegative dynamical systems, compartmental systems, large-scale systems, nonlinear switching control, cooperative control, and adaptive control. Application areas include large flexible interconnected space structures, spacecraft stabilization, cooperative control of unmanned air vehicles, network systems, swarms of air and space vehicle formations, and pharmacological systems.

This paper addresses the problem of finite frequency (FF) H∞ filter design for nonlinear continuous-time systems described by Takagi-Sugeno (T-S) fuzzy models. The objective is to provide a new design sufficient condition via linear matrix inequality (LMI) formulation, ensuring both the stability of the filtering error system and H∞ performance when frequency ranges of noises are known beforehand. Less conservative results are obtained by using the generalised Kalman-Yakubovich-Popov (gKYP) lemma, Finsler's lemma and some independent matrices. Finally, three examples are given to show that the developed FF distributed filter design method has less conservation than the method for the entire frequency region.

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 Lyapunov-Krasovskii 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.

This paper presents a new design algorithm for the decentralized output feedback control problem of large- scale interconnected systems. A decentralized estimated state feedback controller and a decentralized observer are designed for each subsystem, based on linear matrix inequalities (LMIs). Sufficient conditions for the synthesis of feedback action are provided, under which the proposed controllers and observers can achieve robust stabilization of the overall large-scale system. An attractive feature of the proposed scheme is that it guarantees connective stability of the overall system, and requires no in- tersub system communication. The controller design is evaluated on a natural circulation drum boiler, where the nonlinear model describes the key dynamical properties of the drum, the risers, the downcomers and the turbine-generator unit. The linearized system has two poles at origin, one associated with water dynamics and the other with generator dynamics. Simulation results show the effectiveness of the proposed control against instabilities following sudden load variations. The control is also effective for steady state operation.

Event-triggered fault detection filter design for nonlinear networked systems via fuzzy Lyapunov functions

This study is concerned with an L∞ filtering problem for non-linear systems with persistent bounded disturbances and intermittent measurements. The non-linear plant is represented by the Takagi–Sugeno (T–S) fuzzy model that is employed to approximate the non-linear dynamic systems. The system measurements may be unavailable at any sample time and the probability of the occurrence of missing data is assumed to be known. In this study, to design the L∞ fuzzy filter with the estimation error, the estimation error because of persistent bounded disturbance is minimised by some linear matrix inequalities and the filter error system is stochastically stable in the mean square. A stochastic variable satisfying the Bernoulli random binary distribution is utilised to model the phenomenon of the missing data. Finally, the results indicate that the proposed method attenuates the peak of estimation error and preserves a guaranteed L∞-gain performance.

Non-fragile filtering for fuzzy stochastic systems over fading channel

Delay-dependent robust and reliable [formula omitted] fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems