Stability analysis of T–S fuzzy models for nonlinear multiple time-delay interconnected systems

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the stability analysis for nonlinear interconnected systems with multiple time-delays using linear matrix inequality (LMI) theory. In terms of Lyapunov’s direct method for multiple time-delay fuzzy interconnected systems, a novel LMI-based stability criterion which can be solved numerically is proposed. Then, the common P matrix of the criterion is obtained by LMI optimization algorithms to guarantee the asymptotic stability of nonlinear interconnect systems with multiple time-delay. Finally, the proposed stability conditions are demonstrated with simulations throughout this paper.     

Delay-dependent T–S fuzzy control for nonlinear interconnected systems: Using dithers as auxiliaries

In this study, a novel approach via the composite of fuzzy controllers and dithers is presented. According to this approach, we can synthesize a set of fuzzy controllers and find appropriate dithers to stabilize nonlinear multiple time-delay (NMTD) interconnected systems. A robustness design of model-based fuzzy control is first proposed to overcome the effect of modeling errors between the NMTD interconnected subsystems and Takagi–Sugeno (T–S) fuzzy models. In terms of Lyapunov's direct method, a delay-dependent stability criterion is then derived to guarantee the asymptotic stability of NMTD interconnected systems. Based on this criterion and the decentralized control scheme, a set of model-based fuzzy controllers is synthesized via the technique of parallel distributed compensation (PDC) to stabilize the NMTD interconnected system. When the designed fuzzy controllers cannot stabilize the NMTD interconnected systems, a batch of high-frequency signals (commonly referred to as dithers) is simultaneously introduced to stabilize it. If the frequencies of dithers are high enough, the outputs of the dithered interconnected system and those of its corresponding mathematical model–the relaxed interconnected system can be made as close as desired. This makes it possible to obtain a rigorous prediction of the stability of the dithered interconnected system based on the one of the relaxed interconnected system. Finally, a numerical example is given to illustrate the feasibility of our approach.     

On the stability of interconnected systems†

This paper investigates the stability of systems which can be regarded as composed of interconnected subsystems. A sufficient condition for inputs-output L ^p stability, in terms of the L ^p gains of the subsystems and their interconnections is derived. For the case of L ² stability, it is compared with other criteria for asymptotic stability, obtained by Lyapunov techniques, and shown to give better results for a certain class of systems.     

Hybrid BFOA–PSO algorithm for automatic generation control of linear and nonlinear interconnected power systems

In the bacteria foraging optimization algorithm (BFAO), the chemotactic process is randomly set, imposing that the bacteria swarm together and keep a safe distance from each other. In hybrid bacteria foraging optimization algorithm and particle swarm optimization (hBFOA–PSO) algorithm the principle of swarming is introduced in the framework of BFAO. The hBFOA–PSO algorithm is based on the adjustment of each bacterium position according to the neighborhood environment. In this paper, the effectiveness of the hBFOA–PSO algorithm has been tested for automatic generation control (AGC) of an interconnected power system. A widely used linear model of two area non-reheat thermal system equipped with proportional-integral (PI) controller is considered initially for the design and analysis purpose. At first, a conventional integral time multiply absolute error (ITAE) based objective function is considered and the performance of hBFOA–PSO algorithm is compared with PSO, BFOA and GA. Further a modified objective function using ITAE, damping ratio of dominant eigenvalues and settling time with appropriate weight coefficients is proposed to increase the performance of the controller. Further, robustness analysis is carried out by varying the operating load condition and time constants of speed governor, turbine, tie-line power in the range of +50% to ?50% as well as size and position of step load perturbation to demonstrate the robustness of the proposed hBFOA–PSO optimized PI controller. The proposed approach is also extended to a non-linear power system model by considering the effect of governor dead band non-linearity and the superiority of the proposed approach is shown by comparing the results of craziness based particle swarm optimization (CRAZYPSO) approach for the identical interconnected power system. Finally, the study is extended to a three area system considering both thermal and hydro units with different PI coefficients and comparison between ANFIS and proposed approach has been provided.     

Leader–follower tracking control with guaranteed consensus performance for interconnected systems with linear dynamic uncertain coupling

This paper considers the leader–follower tracking control problem for linear interconnected systems with undirected topology and linear dynamic coupling. Interactions between the systems are treated as linear dynamic uncertainty and are described in terms of integral quadratic constraints (IQCs). A consensus-type tracking control protocol is proposed for each system based on its state relative to its neighbours. In addition, a selected set of subsystems is used to control their relative states with respect to the leader. Two methods are proposed for the design of this control protocol. One method uses a coordinate transformation to recast the protocol design problem as a decentralised robust control problem for an auxiliary interconnected large-scale system. Another method is direct; it does not employ coordinate transformation, rather it also allows for more general linear uncertain interactions. Using these methods, sufficient conditions are obtained which guarantee that the system tracks the leader. These conditions guarantee a suboptimal bound on the system consensus and tracking performance. The proposed methods are compared using a simulation example, and their effectiveness is discussed. Also, algorithms are proposed for computing suboptimal controllers.     

Distributed fault diagnosis for process and sensor faults in a class of interconnected input–output nonlinear discrete-time systems

This paper presents a distributed fault diagnosis scheme able to deal with process and sensor faults in an integrated way for a class of interconnected input–output nonlinear uncertain discrete-time systems. A robust distributed fault detection scheme is designed, where each interconnected subsystem is monitored by its respective fault detection agent, and according to the decisions of these agents, further information regarding the type of the fault can be deduced. As it is shown, a process fault occurring in one subsystem can only be detected by its corresponding detection agent whereas a sensor fault in a subsystem can be detected by either its corresponding detection agent or the detection agent of another subsystem that is affected by the subsystem where the sensor fault occurred. This discriminating factor is exploited for the derivation of a high-level isolation scheme. Moreover, process and sensor fault detectability conditions characterising quantitatively the class of detectable faults are derived. Finally, a simulation example is used to illustrate the effectiveness of the proposed distributed fault detection scheme.     

Robust decentralized adaptive stabilization for a class of interconnected systems

The robust decentralized adaptive output-feedback stabilization for a class of interconnected systems with static and dynamic interconnections by using the MT-filters and backstepping design method is studied. By introducing a new filtered tramfomnation, the adaptive laws were derived for measurement. Under the assurnption of the nonlinear growth conditions imposed on the nonlinear interconnections and by constructing the error system and using a new proof method, the global stability of the closed-loop system was effectively analyzed, and the exponential convergence of all the signals except for parameter estimates were guaranteed.     

Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

This paper focuses on a class of T-S fuzzy interconnected systems with time delays and time-varying parameter uncertainties. Observer-based output feedback decentralized controller is designed such that the closed-loop interconnected system is asymptotically stable in the Lyapunov sense in probability for all admissible uncertainties and time delays. Sufficient conditions for robustly asymptotically stability of the systems are given in terms of a set of linear matrix inequalities （LMIs）.     

H∞control of interconnected nonlinear sampled-data systems with parametric uncertainty

This paper studies the problem of robust control design for a class of interconnected uncertain systems under sampled measurements. The class of system under consideration is described by a state space model containing unknown cone bounded nonlinear interaction and time-varying norm-bounded parameter uncertainties in both state and output equations. Our attention is focused on the design of linear dynamic output feedback controllers using sampled measurements. We address the problem of robust H_∞ control in which both robust stability and a prescribed H_∞ performance are required to be achieved irrespective of the uncertainties and nonlinearities. The H_∞ performance measure involves both continuous-time and discrete-time signals. It has been shown that the above problems can be recast into H_∞ syntheses for related N decoupled linear sampled-data systems without parameter uncertainties and unknown nonlinearities, which can be solved in terms of Riccati differential equations with finite discrete jumps. A numerical example is given to show the potential of the proposed technique.     

Decentralised H ∞ filtering of interconnected discrete-time fuzzy systems with time delays

This article considers the decentralised H _∞ filtering of interconnected discrete-time fuzzy systems with time delays based on piecewise Lyapunov–Krasovskii functionals. The fuzzy system consists of J interconnected time-delay discrete-time Takagi–Sugeno fuzzy subsystems and the decentralised H _∞ filter is designed for each subsystem. It is shown that the stability with H _∞ performance of overall filtering error system can be established if a piecewise Lyapunov–Kroasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities that are numerically feasible. A simulation example is given to show the effectiveness of the presented approach.     

Hierarchical system identification of states and parameters in interconnected power systems†

This paper presents an application of hierarchical identification procedures of the previous paper to the identification of interconnected power system states and parameters from input—output observed data. A three-area interconnected power system model is used to demonstrate the decomposition of the original system based on its particular characteristics and the implementation of hierarchical algorithms for system identification. The adaptivity of these procedures to structural changes are also illustrated. Numerical results are obtained by conducting a digital simulation of the three-area system and using the hierarchical identification and coordination algorithms to estimate the states and unknown system parameters. Computational aspects of the hierarchical system identification solutions are discussed.     

Stability,transient behaviour and trajectory bounds of interconnected systems†

In practice, many systems are complex and of high dimension. Many such systems may be viewed as being composed of several simpler sub-systems which when connected in an appropriate fashion yield the original composite system. The stability, the transient behaviour and estimates for the trajectory bounds of certain composite systems are analysed in terms of their sub-systems. This is accomplished by defining the stability of sub-systems and of composite systems in terms of certain time-varying sub-sets of the state space which are pre-specified in a given problem.

After stating definitions of stability for sub-systems which are under the influence of perturbing forces and for composite systems, theorems are stated and proved which yield sufficient conditions for stability. These theorems involve the existence of Lyapunov-like functions which do not possess any particular definiteness requirements on V and [Vdot].

The time-varying sub-sets of the state space which are utilized in the stability definitions and which arise in conjunction with the stability theorems yield estimates of the transient behaviour and of the trajectory bounds of both sub-systems and composite systems.

To demonstrate the generality of the developed theory, several special cases are considered. Also, some specific examples are worked out to demonstrate the methods involved.     

Decentralized H∞ control for large-scale interconnected nonlinear time-delay systems via LMI approach

In this paper, the problem of H_∞ control of nonlinear large-scale systems with interval time-varying delays in interconnection is considered. The time delays are assumed to be any continuous functions belonging to a given interval involved in both the state and observation output. By constructing a set of new Lyapunov–Krasovskii functionals, which are mainly based on the information of the lower and upper delay bounds, a new delay-dependent sufficient condition for the existence of decentralized H_∞ control is established in terms of linear matrix inequalities (LMIs). The approach is applied to decentralized H_∞ control of uncertain linear systems with interval time-varying delay. Numerical examples are given to show the effectiveness of the obtained results.     

Application of intelligence-based predictive scheme to load-frequency control in a two-area interconnected power system

This paper describes an application of intelligence-based predictive scheme to load-frequency control (LFC) in a two-area interconnected power system. In this investigation, at first, a dynamic model of the present system has to be considered and subsequently an efficient control scheme which is organized based on Takagi-Sugeno-Kang (TSK) fuzzy-based scheme and linear generalized predictive control (LGPC) scheme needs to be developed. In the control scheme proposed, frequency deviation versus load electrical power variation could efficiently be dealt with, at each instant of time. In conclusion, in order to validate the effectiveness of the proposed control scheme, the whole of outcomes are simulated and compared with those obtained using a nonlinear GPC (NLGPC), as a benchmark approach, which is implemented based on the Wiener model of this power system. The validity of the proposed control scheme is tangibly verified in comparison with the previous one.     

Reliable H ∞ control of a class of uncertain interconnected systems: an LMI approach

The aim of this work is to study the reliable control design problem for parameter-dependent interconnected systems in the presence of actuator failures. Moreover, the control ensures H _∞ performance in front of L ₂ perturbations. A more practical model of actuators or control channel failures than outage is adopted, considering partial achievement. The continuous H_∞ control problem is solved via elementary manipulations on linear matrix inequalities and the resulting control systems are robustly stable against plant uncertainties and failures.     

Boundary feedback stabilization of a Schr$\＂{o}$dinger equation interconnected with a heat equation

In this paper, we study stabilization for a Schoedinger equation, which is interconnected with a heat equation via boundary coupling. A direct boundary feedback control is adopted. By a detailed spectral analysis, it is found that there are two branches of eigenvalues： one is along the negative real axis, and the other is approaching to a vertical line, which is parallel to the imagine axis. Moreover, it is shown that there is a set of generalized eigenfunctions, which forms a Riesz basis for the energy state space. Finally, the spectrum-determined growth condition is held and the exponential stability of the system is then concluded.     

The integrated production–inventory–distribution–routing problem

The integration of production and distribution decisions presents a challenging problem for manufacturers trying to optimize their supply chain. At the planning level, the immediate goal is to coordinate production, inventory, and delivery to meet customer demand so that the corresponding costs are minimized. Achieving this goal provides the foundations for streamlining the logistics network and for integrating other operational and financial components of the system. In this paper, a model is presented that includes a single production facility, a set of customers with time varying demand, a finite planning horizon, and a fleet of vehicles for making the deliveries. Demand can be satisfied from either inventory held at the customer sites or from daily product distribution. In the most restrictive case, a vehicle routing problem must be solved for each time period. The decision to visit a customer on a particular day could be to restock inventory, meet that day’s demand or both. In a less restrictive case, the routing component of the model is replaced with an allocation component only. A procedure centering on reactive tabu search is developed for solving the full problem. After a solution is found, path relinking is applied to improve the results. A novel feature of the methodology is the use of an allocation model in the form of a mixed integer program to find good feasible solutions that serve as starting points for the tabu search. Lower bounds on the optimum are obtained by solving a modified version of the allocation model. Computational testing on a set of 90 benchmark instances with up to 200 customers and 20 time periods demonstrates the effectiveness of the approach. In all cases, improvements ranging from 10–20% were realized when compared to those obtained from an existing greedy randomized adaptive search procedure (GRASP). This often came at a three- to five-fold increase in runtime, however.