Discrete-time Large-scale Systems Research Articles

Criteria for finite-time stability of singular large-scale discrete-time delay systems

This paper concerns a problem of finite-time stability for a class of linear singular large-scale systems with delays. Based on matrix transformations, Lyapunov function method combined with new estimation techniques, we derive sufficient conditions for solving the finite-time stability of the system. A numerical example is given to illustrate the validity and effectiveness of the theoretical results.

Distributed [formula omitted]-gain control of large-scale systems: A space construction approach

This note studies the distributed L2-gain control problem for discrete-time large-scale systems. The considered system is transformed equivalently to a high dimensional system. The classical controller design methods are not suitable to be applied directly due to the matrix inversion terms in the transformed system. Using a space construction approach, this paper derives necessary and sufficient stability conditions in the form of linear matrix inequalities for large-scale systems. In addition, under given L2-gain γ, necessary and sufficient conditions are established such that the considered system is asymptotically stable and the prescribed L2-gain is satisfied. Then, these results are used to design distributed controllers for large-scale systems. Based on a matrix construction method, distributed controllers can be constructed via the solutions of a set of linear matrix inequalities to guarantee that the closed-loop system is stable with the given L2-gain. Finally, the advantages of the proposed theoretical results are demonstrated by two examples.

Distributed preview control for large-scale systems with time-varying delay

A distributed preview controller (DPC) design problem is discussed for discrete-time large-scale systems with time-varying delay and polytopic uncertainty in this paper. The original time-varying delay system is reformulated as a constant delay systems via a model transformation. The difference operator method is extended to derive an augmented error system (AES). The preview control problem is converted into a stabilization problem based on state augmentation technique. Sufficient conditions are derived from the scaled small-gain theorem (SSG). Additionally, a DPC is designed through some linear matrix inequality (LMI) techniques. Finally, two examples are provided to show the effectiveness of our controller for large-scale systems.

Distributed resilient filtering of large-scale systems with channel scheduling

This paper addresses the distributed resilient filtering for discrete-time large-scale systems (LSSs) with energy constraints, where their information are collected by sensor networks with a same topology structure. As a typical model of information physics systems, LSSs have an inherent merit of modeling wide area power systems, automation processes and so forth. In this paper, two kinds of channels are employed to implement the information transmission in order to extend the service time of sensor nodes powered by energy-limited batteries. Specifically, the one has the merit of high reliability by sacrificing energy cost and the other reduces the energy cost but could result in packet loss. Furthermore, a communication scheduling matrix is introduced to govern the information transmission in these two kind of channels. In this scenario, a novel distributed filter is designed by fusing the compensated neighboring estimation. Then, two matrix-valued functions are derived to obtain the bounds of the covariance matrices of one-step prediction errors and the filtering errors. In what follows, the desired gain matrices are analytically designed to minimize the provided bounds with the help of the gradient-based approach and the mathematical induction. Furthermore, the effect on filtering performance from packet loss is profoundly discussed and it is claimed that the filtering performance becomes better when the probability of packet loss decreases. Finally, a simulation example on wide area power systems is exploited to check the usefulness of the designed distributed filter.

Distributed simultaneous estimation of states and unknown inputs

In this paper, the problem of distributed estimation in linear discrete-time large-scale stochastic systems is explored. The objective is to estimate the states as well as the unknown inputs of the system under partial observation of the system states by utilizing a number of estimators. The main assumption is that the estimator at each node of the system can exchange its estimated state with the neighboring estimators through communication links. With this consideration, a recursive distributed filter is introduced and its unbiasedness and minimum variance are examined. Furthermore, the necessary and sufficient conditions for the stability and convergence of the proposed distributed filter are investigated. Finally the performance on a numerical example is presented.

A New Optimized Reduced Order Model of High-order Discrete Time Systems and Design

This paper presents a method of designing the Controller for large scale discrete time systems. The Controller is designed via a reduced order model for a given high order system. In the proposed reduction method, the numerator coefficients are obtained using Interpolation criteria while the denominator polynomial is obtained by using, one of the stability preserving methods, the Dominant pole method. An optimised reduced order model is derived with minimum ISE. It has been shown that the control designed for the reduced order model, when applied to the higher order system, improves the performance of the controlled system. The method has been tested by considering typical numerical examples, available in the literature, and the results are found to be satisfactory. Index Terms: Interpolation criterion; control; order reduction; controller simplification DOI : 10.7176/ISDE/11-1-04 Publication date: January 31 st 2020

Model order reduction for discrete-time linear systems with the discrete-time polynomials

In this article, the two-sided model order reduction (MOR) method based on the Charlier and discrete Laguerre polynomials is proposed for large-scale discrete-time linear systems. We first introduce some definitions and results of Charlier polynomials, which are extended from continuous orthogonal polynomial. Then we design the algorithm. The main assumption is that the solution is in the space spanned by Charlier orthogonal polynomials, and then the expansion coefficients of the solution are calculated to generate the projection matrix. Further, combining the frequency-domain techniques with the discrete-time domain techniques, we develop the two-sided projection MOR method, which is a hybrid reduction technique that can possess the nice properties of these two methods. The proposed approach has good computational efficiency and preserves the internal stability under certain condition. Numerical experiments verify the feasibility and effectiveness of the proposed method.

Distributed L 2-gain control of large-scale systems under gossip communication protocol

This paper studies the distributed controller design problem for linear discrete-time large-scale systems under gossip communication protocol. In this communication protocol, each sub-controller transmits the subsystem's state information to only one randomly chosen neighbour at transmission instants. Distributed controllers are designed such that the closed-loop system is exponentially mean-square stable and that the prescribed -gain performance is satisfied in the mean-square sense. The design condition is obtained based on Lyapunov stability theory and given in terms of linear matrix inequalities. Finally, two numerical examples are presented to illustrate the advantages of the proposed scheme.

Decentralized Polynomial Observer Design for Discrete-Time Large-Scale Polynomial T-S Fuzzy System

In this paper, a new approach for synthesizing a decentralized observer is proposed to estimate the unmeasurable states of a discrete-time large-scale nonlinear system. The large-scale nonlinear system in this study is modeled in terms of a set of discrete-time polynomial Takagi-Sugeno (T-S) fuzzy subsystems and interconnection terms. This modeling method will assist to reduce significantly the number of fuzzy rules. The interconnection terms are considered as the unknown inputs; then, the unknown input method is employed to design observer for this system. It should be emphasized that the interconnection parts in this paper are arbitrary and their effects are eliminated completely. On the basis of the Lyapunov methodology and SOS (Sum of Square) technique, the conditions for observer design expressed under the framework of SOS are derived in the main theorems. Finally, an illustrative example is presented to show the effectiveness and merit of the proposed method.

Asynchronous Piecewise Output-Feedback Control for Large-Scale Fuzzy Systems via Distributed Event-Triggering Schemes

This paper examines the problem of distributed event-triggering output-feedback control for discrete-time large-scale fuzzy systems in the network scenario. A novel distributed event-triggering control scheme is proposed, where each subsystem transmits its output information and premise variables only when its local output error exceeds a specified threshold. The resulting closed-loop fuzzy control system subject to nonsynchronous grades of membership is explored under such circumstances. In virtue of a piecewise Lyapunov function together with some matrix inequality convexification techniques, the solution to the distributed event-triggering output-feedback control problem is derived in the form of linear matrix inequalities. It will be shown that the closed-loop control system is asymptotically stable while significantly reducing the communications via networks. Finally, a direct current microgrid with solar photovoltaic arrays is utilized to illustrate the validity and practicability of the proposed results.

Aggregate State Control of Large-Scale Systems via Networked Controllers

The secure management of large-scale systems becomes more and more important in recent social infrastructures. In this study, we deal with an aggregate state control problem of a large-scale discrete-time system with networked controllers. First, we derive conditions on the parameters of the controller such that the aggregate state converges to zero with an assigned rate. Next, we design an optimal controller which minimizes components’ dissatisfaction under the aggregate state condition. Moreover, we compare the obtained solution with the solution of the original optimization problem without the aggregate state condition, and clarify the effect of the network topology to the solution. Finally, the effectiveness of the proposed method is verified through a simulation.

Fuzzy model-based decentralized robust piecewise static output feedback control for discrete-time large-scale nonlinear systems

This paper investigates the problem of decentralized robust output feedback control for a class of discrete-time large-scale nonlinear systems. The considered large-scale system consists of several nonlinear subsystems with interconnections and parametric uncertainties, and each nonlinear subsystem is represented by a Takagi–Sugeno (T–S) model. Our objective is to design a decentralized robust piecewise static output feedback (SOF) controller such that the closed-loop fuzzy control system is asymptotically stable with an disturbance attenuation level. Based on a piecewise Lyapunov function combined with some matrix inequality linearization techniques, and the descriptor system approach, sufficient conditions on the existence of a decentralized piecewise SOF controller are derived for the underlying large-scale T–S fuzzy system in terms of linear matrix inequalities. The effectiveness of the obtained results in this paper is validated by two numerical examples.

Decentralized iterative learning control for large-scale linear discrete-time systems with fixed initial state errors

AbstractThis article addresses the problem of iterative learning control for large-scale linear discrete-time systems with fixed initial state errors. And two kinds of the system structures are considered in this article, one of them is the system whose input signal's dimension is less than or equal to the output dimension and the other one is the system whose output signal's dimension is less than or equal to the input dimension. According to the characteristics of the systems, decentralized learning schemes are proposed for such large-scale linear discrete-time systems, and the corresponding discrete-time output limiting trajectories under the action of the decentralized learning schemes are presented. The proposed controller of each subsystem only relies on local output variables without any information exchanging with other subsystems. Using the contraction mapping method, we show that the schemes can guarantee the output of each subsystem to converge uniformly to the corresponding discrete-time output limiting trajectory over all the given discrete-time points within a finite time interval. Furthermore, the decentralized initial rectifying strategies are applied to the large-scale linear discrete-time systems for eliminating the effect of the fixed initial state errors, and the corresponding decentralized learning schemes are established. When the learning schemes are applied to the large-scale linear discrete-time systems, the output of each subsystem can converge to the desired reference trajectory of each subsystem over all the given discrete-time points within a pre-specified interval no matter what value the fixed state error takes. Simulation examples illustrate the effectiveness of the proposed method.

Distributed piecewise filtering design for large-scale networked nonlinear systems

This paper investigates the problem of distributed piecewise filtering for discrete-time large-scale nonlinear systems. The considered large-scale system is composed of a number of nonlinear subsystems and exchanges its information through communication network. Each nonlinear subsystem is described by a Takagi-Sugeno (T-S) model, and data-packet dropouts happen intermittently in communication network, and its stochastic variables are assumed to satisfy the Bernoulli random-binary distribution. Our objective is to design a distributed piecewise filter such that the filtering error system is stochastically stable with an performance. Based on a piecewise Lyapunov function and some convexifying techniques, less conservative results are developed for the distributed piecewise filtering design of the considered system in the form of linear matrix inequalities (LMIs). The effectiveness of the proposed method is validated by two examples.

On stability analysis methods for large-scale discrete-time systems

This paper proposes a set of Lyapunov-type conditions that are suited for stability analysis of large-scale discrete-time systems. A time-wise relaxation of the Lyapunov function decrease condition is employed to derive a set of global and distributed stability conditions. Essentially, these conditions allow to make a trade-off between complexity and conservatism by extending the time-horizon over which the decrease condition should hold. It is shown that for exponentially stable dynamics and any candidate Lyapunov function, there exists a finite time for which the proposed global or distributed stability conditions hold. Hence, it is possible to use functions with a particular structure to make verification of stability scalable for large-scale systems. The developed results are applied to establish stability of a benchmark power systems example.

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

This paper investigates the problem of decentralized piecewise H∞ filtering design for a class of discrete-time large-scale nonlinear systems with time-varying delay. The considered large-scale system consists of a number of nonlinear subsystems, and each nonlinear subsystem is represented by a Takagi–Sugeno (T–S) model. The time-varying state delay of each subsystem is assumed to be of an interval-like type with lower and upper bounds. The objective is to design a decentralized piecewise filter such that the filtering error system is asymptotically stable with a guaranteed H∞ disturbance attenuation level. A two-term approximation method is proposed to transform the filtering error system into an interconnected formulation, and the decentralized H∞ filtering problem is reformulated in the context of input–output (IO) stability. Based on a piecewise Lyapunov–Krasovskii functional (PLKF) combined with the scaled small gain (SSG) theorem, less conservative results are presented for the decentralized piecewise H∞ filtering design of the large-scale T–S fuzzy system in terms of linear matrix inequalities. Two examples are provided to illustrate the effectiveness of the proposed method.

A Local Controller for Discrete-Time Large-Scale System by Using Integral Variable Structure Control

A new local controller for discrete-time integral variable structure control of a large-scale system with matched and unmatched uncertainty is presented. The local controller is able to bring the large-scale system into stability by using only the states feedback from individual subsystem itself. A new theorem is established and proved that the controller is able to handle the effect of interconnection for the large-scale system with matched and unmatched uncertainty, and the system stability is ensured. The controller is able to control the system to achieve the quasi-sliding surface and remains on it. The results showed a fast convergence to the desired value and the attenuation of disturbance is achieved.

Stabilization Analysis for the Switched Large-Scale Discrete-Time Systems via the State-Driven Switching

A criterion of stabilization for the switched large-scale discrete-time system is deduced by employing state-driven switching method and the Lyapunov stability theorem. This particular method especially can be applied to cases when all individual subsystems are unstable.

Distributed Fault Detection and Isolation of Large-Scale Discrete-Time Nonlinear Systems: An Adaptive Approximation Approach

This paper deals with the problem of designing a distributed fault detection and isolation methodology for nonlinear uncertain large-scale discrete-time dynamical systems. As a divide et impera approach is used to overcome the scalability issues of a centralized implementation, the large scale system being monitored is modelled as the interconnection of several subsystems. The subsystems are allowed to overlap, thus sharing some state components. For each subsystem, a Local Fault Diagnoser is designed, based on the measured local state of the subsystem as well as the transmitted variables of neighboring states that define the subsystem interconnections. The local diagnostic decision is made on the basis of the knowledge of the local subsystem dynamic model and of an adaptive approximation of the interconnection with neighboring subsystems. The use of a specially-designed consensus-based estimator is proposed in order to improve the detectability and isolability of faults affecting variables shared among overlapping subsystems. Theoretical results are provided to characterize the detection and isolation capabilities of the proposed distributed scheme. Finally, simulation results are reported showing the effectiveness of the proposed methodology.

Local feedback Pareto strategy for weakly coupled large-scale discrete-time stochastic systems

In this study, the author discusses a Pareto strategy implemented via state and static output feedback for a class of weakly coupled large-scale discrete-time stochastic systems with state- and control-dependent noise. The asymptotic structure along with the uniqueness and positive semi-definiteness of the solutions of cross-coupled non-linear matrix equations (CNMEs) is newly established via the implicit function theorem. The main contribution of this study is the proposal of a parameter-independent local state and static output feedback Pareto strategy. Moreover, a computational approach for solving the CNMEs is also considered if the information about the small parameter is available. Particularly, a new iterative algorithm based on the linear matrix inequality is established to design a Pareto strategy. Finally, in order to demonstrate the effectiveness of the proposed design method, a numerical example is provided for practical aircraft control problems.