The First Five Years of a Phase Theory for Complex Systems and Networks

In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical interpretations,the small phase theorem,and the sectored real lemma;The synchronization of a multi-agent network using phase alignment.Towards the end,we also summarize a list of ongoing research on the phase theory and speculate what will happen in the next five years.

Bipartite consensus problems of Lurie multi-agent systems over signed graphs: A contraction approach

This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix, and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results.

Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

Advances in Basic Theory Research of Mongolian Medicine and Prospects of Its Combination with Systems Biology Research

This paper sorted out the relevant literature on the basic theory of Mongolian medicine,explored the research methods and ideas of the basic theory of Mongolian medicine,and elaborated the idea of combining systems biology to study part of the basic theory of Mongolian medicine.Through searching classic works and research papers in academic journals,this paper sorted out and summarized the research progress of the basic theory of Mongolian medicine and the existing problems in the current research,analyzed its characteristics,combined with systems biology methods to systematically explain some content in the basic theory,reveal its scientific connotation,and provide a basis for further research.

Decentralized robust guaranteed cost control for a class of interconnected singular large-scale systems with time-delay and parameter uncertainty

The decentralized robust guaranteed cost control problem is studied for a class of interconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadratic cost performance function. The problem that is addressed in this study is to design a decentralized robust guaranteed cost state feedback controller such that the closed-loop system is not only regular, impulse-free and stable, but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of the decentralized robust guaranteed cost state feedback controllers is proposed in terms of a linear matrix inequality （LMI） via LMI approach. When this condition is feasible, the desired state feedback decentralized robust guaranteed cost controller gain matrices can be obtained. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.

Optimal tracking control for nonlinear large-scale systems with persistent disturbances

This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances.The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms.Based on the internal model principle,a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances.According to the sensitivity approach,the optimal tracking control law for the ith nonlinear subsystem can be obtained.The optimal tracking control law for the nonlinear large-scale systems can be obtained.A numerical simulation shows that the method is effective.

A LARGE-SCALE ESTIMATE OF THE NUMBEROF PERIODIC SMALL OSCILLATIONS OFNONLINEAR SYSTEMS

A conservative system performing a small oscillation near every equilibrium position is analysed in classical way. The paper tries to answer the following question: How many types of the periodic small oscillation in the whole configuration space of the system are there? Making some hypotheses, it expresses the lower bounds of the number of the types for two cases where critical points of the potential function are nondegenerate and degenerate respectively by the Betti numbers and dimension of the constraint manifold only.

Adaptive Decentralized Asymptotic Tracking Control for Large-Scale Nonlinear Systems With Unknown Strong Interconnections

An adaptive decentralized asymptotic tracking control scheme is developed in this paper for a class of large-scale nonlinear systems with unknown strong interconnections,unknown time-varying parameters,and disturbances.First,by employing the intrinsic properties of Gaussian functions for the interconnection terms for the first time,all extra signals in the framework of decentralized control are filtered out,thereby removing all additional assumptions imposed on the interconnec-tions,such as upper bounding functions and matching conditions.Second,by introducing two integral bounded functions,asymptotic tracking control is realized.Moreover,the nonlinear filters with the compensation terms are introduced to circumvent the issue of“explosion of complexity”.It is shown that all the closed-loop signals are bounded and the tracking errors converge to zero asymptotically.In the end,a simulation example is carried out to demonstrate the effectiveness of the proposed approach.

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.

STATIONARITY OF A CLASS OF LARGE-SCALE DISCRETE-TIME STOCHASTIC SYSTEMS

Stationarity of a class of stochastically interconnecteil discrete-timesystems is analyzed by utilizins results from ergodic theory of general stateMarkov chains, incorporated with the so called large-scale system approach.

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.

An Adaptive Sliding Mode Tracking Controller Using BP Neural Networks for a Class of Large-scale Nonlinear Systems

A new type controller, BP neural-networks-based sliding mode controller is developed for a class of large-scale nonlinear systems with unknown bounds of high-order interconnections in this paper. It is shown that decentralized BP neural networks are used to adaptively learn the uncertainty bounds of interconnected subsystems in the Lyapunov sense, and the outputs of the decentralized BP neural networks are then used as the parameters of the sliding mode controller to compensate for the effects of subsystems uncertainties. Using this scheme, not only strong robustness with respect to uncertainty dynamics and nonlinearities can be obtained, but also the output tracking error between the actual output of each subsystem and the corresponding desired reference output can asymptotically converge to zero. A simulation example is presented to support the validity of the proposed BP neural-networks-based sliding mode controller.

THE ASYMPTOTIC STABILITY OF THE LINEAR.DISCRETE LARGE-SCALE SYSTEMS

In this paper, we directly use the tirear norm Liapunov function to investigate the stability of the linear discrete large-scale systems and obtain some criteria for the asymptotic stability of such a system.

Partial stability of a class of large-scale systems with partiallystable isolated subsystems

The problem of partial stability is investigated for a class of continuous-time large-scale systems. Under assumption that the null solution of the isolated subsystems is stable, based on decomposition-aggregation methods and Lyapunov second method, some theorems concerning the globally partial asymptotic stability and globally partial exponential stability are obtained via utilizing the inequality analysis technique and comparison technique. Finally, an example is presented to illustrate the results.

Robust non-fragile control for discrete-delay nonlinear large-scale systems

Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.

Challenges and Considerations in Developing and Architecting Large-Scale Distributed Systems

This paper investigates large-scale distributed system design. It looks at features, main design considerations and provides the Netflix API, Cassandra and Oracle as examples of such systems. Moreover, the paper investigates the challenges of designing, developing, deploying, and maintaining such systems, in regard to the features presented. Finally, the paper discusses aspects of available solutions and current practices to challenges that large-scale distributed systems face.

STABILITY OF NONLINEAR COMPARISON EQUATIONS FOR DISCRETE LARGE-SCALE SYSTEMS

On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparison equations was studied in the past. In this paper, various criteria of stability for discrete nonlinear autonomous comparison equations are completely established. Among them, a criterion for asymptotic stability is not only sufficient, but also necessary, from which a criterion on the function class C, is derived. Both of them can be used to determine the unexponential stability, even in the large, for discrete nonlinear (autonomous or nonautonomous) systems. All the criteria are of simple algebraic forms and can be readily used.

Immune multi-agent model using vaccine for cooperative air-defense system of systems for surface warship formation based on danger theory

Aiming at the problem on cooperative air-defense of surface warship formation, this paper maps the cooperative airdefense system of systems （SoS） for surface warship formation （CASoSSWF） to the biological immune system （BIS） according to the similarity of the defense mechanism and characteristics between the CASoSSWF and the BIS, and then designs the models of components and the architecture for a monitoring agent, a regulating agent, a killer agent, a pre-warning agent and a communicating agent by making use of the theories and methods of the artificial immune system, the multi-agent system （MAS）, the vaccine and the danger theory （DT）. Moreover a new immune multi-agent model using vaccine based on DT （IMMUVBDT） for the cooperative air-defense SoS is advanced. The immune response and immune mechanism of the CASoSSWF are analyzed. The model has a capability of memory, evolution, commendable dynamic environment adaptability and self-learning, and embodies adequately the cooperative air-defense mechanism for the CASoSSWF. Therefore it shows a novel idea for the CASoSSWF which can provide conception models for a surface warship formation operation simulation system.

Foundations and Applications of Information Systems Dynamics

Although numerous advances have been made in information technology in the past decades,there is still a lack of progress in information systems dynamics(ISD),owing to the lack of a mathematical foundation needed to describe information and the lack of an analytical framework to evaluate information systems.The value of ISD lies in its ability to guide the design,development,application,and evaluation of largescale information system-of-systems(So Ss),just as mechanical dynamics theories guide mechanical systems engineering.This paper reports on a breakthrough in these fundamental challenges by proposing a framework for information space,improving a mathematical theory for information measurement,and proposing a dynamic configuration model for information systems.In this way,it establishes a basic theoretical framework for ISD.The proposed theoretical methodologies have been successfully applied and verified in the Smart Court So Ss Engineering Project of China and have achieved significant improvements in the quality and efficiency of Chinese court informatization.The proposed ISD provides an innovative paradigm for the analysis,design,development,and evaluation of large-scale complex information systems,such as electronic government and smart cities.

Group Support Systems: Implications for Multi-Disciplinary Theory Building

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