Decentralized Optimal Control and Stabilization of Interconnected Systems With Asymmetric Information

The paper addresses the decentralized optimal control and stabilization problems for interconnected systems subject to asymmetric information.Compared with previous work,a closed-loop optimal solution to the control problem and sufficient and necessary conditions for the stabilization problem of the interconnected systems are given for the first time.The main challenge lies in three aspects:Firstly,the asymmetric information results in coupling between control and estimation and failure of the separation principle.Secondly,two extra unknown variables are generated by asymmetric information(different information filtration)when solving forward-backward stochastic difference equations.Thirdly,the existence of additive noise makes the study of mean-square boundedness an obstacle.The adopted technique is proving and assuming the linear form of controllers and establishing the equivalence between the two systems with and without additive noise.A dual-motor parallel drive system is presented to demonstrate the validity of the proposed algorithm.

Control of Spatially Interconnected Systems with Random Communication Losses

This paper deals with analysis and synthesis problems of spatially interconnected systems where communicated information may get lost between subsystems. Spatial shift operator and temporal forward shift operator are introduced to model the interconnected systems as discrete time-space multidimensional linear systems with Markovian jumping parameters which reflect the state of communication channels. To ensure the whole system＇s well-posedness and mean square stability for a given packet loss rate, a condition is derived through analysis. Then a procedure of designing distributed dynamic output feedback controllers is proposed. The controllers have the same structure as the plants and are solved within the linear matrix inequality （LMI） framework. Finally, we apply these results to study the effect of communication losses on the multiple vehicle platoon control system, which further illustrates the effectiveness of the proposed model and method.

Delay-dependent decentralized H_∞ filtering for uncertain interconnected systems

This article considers delay dependent decentralized H∞ filtering for a class of uncertain interconnected systems, where the uncertainties are assumed to be time varying and satisfy the norm-bounded conditions. First, combining the Lyapunov-Krasovskii functional approach and the delay integral inequality of matrices, a sufficient condition of the existence of the robust decentralized H∞ filter is derived, which makes the error systems asymptotically stable and satisfies the H∞ norm of the transfer function from noise input to error output less than the specified up-bound on the basis of the form of uncertainties. Then, the above sufficient condition is transformed to a system of easily solvable LMIs via a series of equivalent transformation. Finally, the numerical simulation shows the efficiency of the main results.

DECENTRALIZED STABILIZATION OF A CLASS OF INTERCONNECTED SYSTEMS

This paper is concerned with the decentralized stabilization of continuous and discrete linear interconnected systems with the structural constraints about the interconnection matrices. For the continuous case,the main improvement in the paper as compared with the corresponding results in the literature is to extend the considered class of systems from S to S (both will be defined in the paper) without resulting in high decentralized gain and difficult numerical computation. The algorithm for obtaining decentralized state feedback control to stable the overall system is presented. The discrete case and some very useful results are discussed as well.

Disturbance Attenuation State-Feedback Control for Uncertain Interconnected Systems

This paper studies the problem of robust H∞ control design for a class of uncertain interconnected systems via state feedback. This class of systems are described by a state space model, which contains unknown nonlinear interaction and time-varying norm-bounded parametric uncertainties in state equation. Using the Riccati-equation-based approach we design state feedback control laws, which guarantee the decentralized stability with disturbance attenuation for the interconnected uncertain systems. A simple example of an interconnected uncertain linear system is presented to illustrate the results.

Finite-Time Distributed Identification for Nonlinear Interconnected Systems

In this paper,a novel finite-time distributed identification method is introduced for nonlinear interconnected systems.A distributed concurrent learning-based discontinuous gradient descent update law is presented to learn uncertain interconnected subsystems’dynamics.The concurrent learning approach continually minimizes the identification error for a batch of previously recorded data collected from each subsystem as well as its neighboring subsystems.The state information of neighboring interconnected subsystems is acquired through direct communication.The overall update laws for all subsystems form coupled continuous-time gradient flow dynamics for which finite-time Lyapunov stability analysis is performed.As a byproduct of this Lyapunov analysis,easy-to-check rank conditions on data stored in the distributed memories of subsystems are obtained,under which finite-time stability of the distributed identifier is guaranteed.These rank conditions replace the restrictive persistence of excitation(PE)conditions which are hard and even impossible to achieve and verify for interconnected subsystems.Finally,simulation results verify the effectiveness of the presented distributed method in comparison with the other methods.

Non-fragile guaranteed cost control for uncertain neutral large-scale interconnected systems

This paper focuses on the problem of non-fragile decentralized guaranteed cost control for uncertain neutral large-scale interconnected systems with time-varying delays in state,control input and interconnections.A novel scheme,viewing the interconnections with time-varying delays as effective information but not disturbances,is developed.Based on Lyapunov stability theory,using various techniques of decomposing and magnifying matrices,a design method of the non-fragile decentralized guaranteed cost controller for unperturbed neutral large-scale interconnected systems is proposed and the guaranteed cost is presented.The further results are derived for the uncertain case from the criterion of unperturbed neutral large-scale interconnected systems.Finally,an illustrative example shows that the results are significantly better than the existing results in the literatures.

STRING STABILITY OF INFINITE INTERCONNECTED SYSTEMS

The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced. Intuitively, string stability implies uniform boundedness of all the stares of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. Vector V-function method used to judge the stability is generalized for infinite interconnected system and sufficient conditions which guarantee the asymptotic string stability of a class of interconnected system are given. The stability regions obtained here are much larger than those in previous papers. The method given here overcomes some difficulties to deal with stability of infinite nonlinear interconnected system in previous papers.

ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING

The problem of robust exponential stability for a class of switched nonlineardynamical systems with uncertainties and unbounded delay is addressed. On the assump-tion that the interconnected functions of the studied systems satisfy the Lipschitz condition,by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions toensure the robust exponential stability of the switched interconnected systems under arbi-trary switching are obtained. The proposed method, which neither require the individualsubsystems to share a Common Lyapunov Function （CLF）, nor need to involve the values ofindividual Lyapunov functions at each switching time, provide a new way of thinking to studythe stability of arbitrary switching. In addition, the proposed criteria are explicit, and it isconvenient for practical applications. Finally, two numerical examples are given to illustratethe correctness and effectiveness of the proposed theories.

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 transformation, the adaptive laws were derived for measurement. Under the assumption 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）.

Delay-dependent stability of discrete-time interconnected systems

This paper studies the delay-dependent stability problem of discrete-time interconnected systems with time-varying delays.By using vector Lyapunov function approach and linear matrix inequalities （LMIs）,new stability conditions are derived.These results proposed in this paper are all at subsystems level.After comparing with the existing results,it is shown that these conditions are less conservative.A numerical example is presented to demonstrate the effectiveness of the results.

Decentralized impulsive control for a class of uncertain interconnected systems

A great deal of stabilization criteria has been obtained from study of stabilizing interconnected systems. The results obtained are usually based on continuous systems by state feedback. In this paper, decentralized impulsive control is presented to stabilize a class of uncertain interconnected systems based on Lyapunov theory. The system under consideration involves parameter uncertainties and unknown nonlinear interactions among subsystems. Some new criteria of stabilization under impulsive control are established. Two numerical examples are offered to prove the effectiveness and practicality of the proposed method.

DECENTRALIZED STABILIZATION OF LARGE-SCALE LINEAR INTERCONNECTED SYSTEMS WITH TIME-VARYING DELAYS

The decentralized stabilization conditions for large-scale linear interconnection systems with time-varying delays were established by using some different decomposition cases of interconnection matrices, and a method for designing the decentralized local memoryless state feedback controllers was proposed. All of the considered delays are continuous function, and satisfy some conditions.

Fault-tolerant control and vibration suppression of flexible spacecraft: An interconnected system approach

This paper considers a fault-tolerant control and vibration suppression problem of flexible spacecraft.The attitude dynamics is modeled by an interconnected system,in which the rigid part and the flexible part are coupled with each other.Such a model allows us to use the interconnected system approach to analyze the flexible spacecraft.Both distributed and decentralized observer-based fault-tolerant control schemes are developed,under which the closed-loop stability of flexible spacecraft can be ensured by using the cycle-small-gain theorem.Compared with the traditional method,this paper considers the faults occurred not only in the rigid parts,but also in the flexible parts.In addition,the application of the interconnected system approach simplifies the system model of flexible spacecraft,thereby the difficulty of theoretical analysis and engineering practice of fault-tolerant control of flexible spacecraft are greatly reduced.Simulation results show the effectiveness of the proposed methods and the comparison of different fault-tolerant control approach.

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 com- pensate 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.

Decentralised dynamic high-gain scaling-based output-feedback control of large-scale non-linear interconnected systems with delays

A general class of non-linear large-scale interconnected systems is considered,wherein each subsystem is comprised of a nominal part in a general strict-feedback-like structure and a set of appended dynamics.Parametric and functional uncertainties and time delays are allowed throughout the overall system structure including the nominal strictfeedback-like parts and appended dynamics of each subsystem as well as the non-linear subsystem interconnections.The controller design is based on the dual dynamic highgain scaling technique and provides a robust adaptive delay-independent globally stabilising decentralised output-feedback controller.The disturbance attenuation properties of the proposed output-feedback decentralised controller to an exogenous disturbance input are also analysed and specific conditions under which properties such as Input-toOutput-practical-Stability and asymptotic stabilisation are attained are also discussed.

Robust Exponential Stability of Switched Interval Interconnected Systems with Unbounded Delay

In this paper, a class of switched interval interconnected systems with unbounded delay were investigated. On the assumption that the interconnected functions of the systems satisfied the global Lipschitz condition, by using vector Lyapunov methods and M-matrix theory, the integrodifferential inequalities with unbounded delay were constructed. By the stability analysis of the integrodifferential inequalities, the sufficient conditions to ensure the robust exponential stability of the interval interconnected systems were obtained. By using average dwell time approach, conditions for guaranteeing the robust exponential stability of the switched delay interval interconnected systems were derived.Finally, two numerical examples were given to illustrate the correction and effectiveness of the proposed theory.

Nonlinear H_∞ filtering for interconnected Markovian jump systems

The problem of nonlinear H∞ filtering for interconnected Markovian jump systems is discussed. The aim of this note is the design of a nonlinear Markovian jump filter such that the resulting error system is exponentially meansquare stable and ensures a prescribed H∞ performance. A sufficient condition for the solvability of this problem is given in terms of linear matrix inequalities（LMIs）. A simulation example is presented to demonstrate the effectiveness of the proposed design approach.

Resilient Fixed-Order Distributed Dynamic Output Feedback Load Frequency Control Design for Interconnected Multi-Area Power Systems

The paper proposes a novel H∞ load frequency control(LFC) design method for multi-area power systems based on an integral-based non-fragile distributed fixed-order dynamic output feedback(DOF) tracking-regulator control scheme. To this end, we consider a nonlinear interconnected model for multiarea power systems which also include uncertainties and timevarying communication delays. The design procedure is formulated using semi-definite programming and linear matrix inequality(LMI) method. The solution of the proposed LMIs returns necessary parameters for the tracking controllers such that the impact of model uncertainty and load disturbances are minimized. The proposed controllers are capable of receiving all or part of subsystems information, whereas the outputs of each controller are local. These controllers are designed such that the resilient stability of the overall closed-loop system is guaranteed. Simulation results are provided to verify the effectiveness of the proposed scheme. Simulation results quantify that the distributed(and decentralized) controlled system behaves well in presence of large parameter perturbations and random disturbances on the power system.