Discretization-based Characteristic Modeling And Controlling Approaches Of High-order Systems

As a research focus in statistical physics and topology theory,the rapid growing researches on complex networks have presented new opportunities and challenges to modeling and controlling such networks.With the exponentially growing interactions of people and things,complex network theory is extensively applied to biology,technology,sociology,astronomy,and other related fields.In fact,since the Erd?s-E?nyi random network was proposed,the topology-based results of complex networks have been constantly enriched and enhanced.Meanwhile,network and control theories are getting together gradually because of the ultimate goal of understanding networks meaning to control them.Among the existing results,however,the absence of accurate microscopic models for complex networks limits our ability to predict and manipulate the behavior of these systems.Barring further investigated results,the previous works devoted to identification and controllability of complete networks cannot be easily realized due to computation tasks and engineering practices.To overcome these problems,a control and engineering-oriented modeling approach,known as the characteristic modeling,is studied for its potential application in complex networks.We have found that this modeling approach can effectively reduce the complexities of nodal dynamic and interaction functions.With structural alterations,the proposed approach also has the ability to reduce the complexity of network topologies.Furthermore,it is proved that the characteristic model-based control law,under some non-strict conditions,can guarantee the exact model of the network stable even though the control law is constructed from the approximate model.One of several unique features of the proposed modeling and controlling processes is that they are driven the sampled data completely,which means they only require nodal input and output data without knowing the full knowledges of nodal or network dynamics.The main results and contributions are summarized as follows:(1)The characteristic modeling approach is applied to linear dynamical networks for simplification and control.Usually,networked transfer functions are in the form of the highorder transfer functions,meaning that simplification of networks is equivalent to reduction of system orders.Despite the characteristic model is proposed for this purpose,the mathematical proof is still lacking.Here the theoretical analysis of characteristic modeling approach for high-order linear systems is presented.For the closed-loop stability analysis of the characteristic model-based controller,the consistency of characteristic model and exact model of the system is validated.(2)For nonlinear systems,the characteristic model is firstly constructed for a typical class of nonlinear dynamical networks.The prominent achievement is that this approach accomplishes translating the nonlinear dynamics into difference expressions,including the linear interactions,which provides more flexible models for control design and analysis.Structurally alterable characteristic model is also constructed for manipulation of nonlinear network structures.It shows that this approach can be effective in dealing with high-order nonlinear systems or large-scale nonlinear networks.(3)Based on the characteristic model of complex systems,a control framework is proposed.This control law can be applied to complex dynamical networks directly,for both linear and nonlinear systems,with one qualified condition of the sampling time interval.It is proved that the approximate model-based control law can guarantee the overall exact model Lyapunov asymptotic stability.It also should be noted that the proposed modeling and controlling approach are both derived for a family of sampling time intervals,which means it is feasible and has strong robustness.Then a more advanced control law,addressed as characteristic model-based sliding mode control law is designed to achieve high performance.Conclusively,the proposed method,as a whole package of modeling and controlling,can be applied to manipulate complex dynamical networks.The modeling error and control performance are highly related to the sampling time interval that is a key factor in characteristic model.Finally,some simulations are presented to validate the proposed approach where the results reveal its effectiveness.