Distributed Control And Filtering Of Networked Interconnected Large-scale Systems

Many practical engineering examples can be modeled as networked interconnected large-scale systems.Recently,control theory of networked interconnected large-scale systems has attracted intensive research attention from all over the world,which has led to a lot of theoretical results and has been applied into power electrical systems,intel-ligent traffic systems,robot formation systems and so on.In networked interconnected large-scale systems,information from subsystems is transmitted via network.There are many subsystems connected to the common shared network.In order to avoid the node collision problems,it is necessary to introduce different network protocols to schedule the subsystems to use the network.On the other hand,when the considered intercon-nected systems comprise of many subsystems,the augmented system matrices are of high dimensions.Applying the conventional controller and filter design methods may lead to complex matrix inversions.The matrix inversion computation is generally very complex and even cause numerical stability problems.In order to avoid the matrix in-versions,it is necessary to present computationally attractive method to design the dis-tributed controllers and filters.The main contents of this dissertation are summarized as follows:·Firstly,stability analysis and distributed L2-gain controller deign problems of interconnected systems under synchronized time model gossip protocol are stud-ied.According to synchronized time model gossip protocol,each sub-controller transmits its state information to only one randomly chosen neighbor(with equal chosen probability)at each instant.Sufficient conditions which ensure the ex-ponential mean-square stability and finite-time stability are established,respec-tively.Based on these results,distributed controller design method is derived to ensure the stability and the prescribed L2-gain of the closed-loop interconnected system.Distributed controller gains can be obtained by solving a set of weakly coupled linear matrix inequalities.·Secondly,consensus-based estimation and control problems of interconnected systems under asynchronous time model gossip protocol are considered.At each instant,only one randomly chosen node occupies the network and communicates with only one neighbor which is also chosen randomly.Novel observers which combine local Luenberger-like observers with consensus-based strategies are pro-posed.Each sub-controller generates the local control input based on the local state estimation.Sufficient conditions are established to ensure the exponential mean-square stability of the closed-loop system.Combining cone complemen-tary linearization algorithm with binary search method,a novel iterative algorithm has been given to obtain the observer and controller gains.·Next,the distributed L2-gain control problem of interconnected large-scale sys-tems subject to round-robin protocol is studied.Each sub-controller receives neighboring sub-controllers' state information periodically.The closed-loop sys-tem is modeled as a time delay system.Based on the stability analysis methods of time delay systems,sufficient conditions are established such that the closed-loop system is exponentially stable.The sufficient conditions are transformed into linear matrix inequalities.By solving the linear matrix inequalities,we can obtain the distributed controllers and minimize the L2-gain.·Then,a novel distributed L2-gain control approach is proposed based on the space construction method.According to "full-block S-procedure" lemma,two equiva-lent space are constructed,novel necessary and sufficient stability conditions are established for interconnected systems.The novel stability conditions are free of matrix inversions,which are computationally attractive.Base on elimination lemma,novel controller design conditions are derived in terms of linear matrix inequalities.The distributed controller gains can be constructed based on the solutions of the linear matrix inequalities to ensure the stability and prescribed L2-gain of the closed-loop system.?·Finally,a novel decentralized H? filtering strategy is proposed based on Finsler lemma.According to the two equivalent inequalities in Finsler lemma,novel de-centralized filtering design conditions are established.The novel conditions get rid of matrix inversion terms which are brought by applying traditional filtering design method.By solving the linear matrix inequalities,we can obtain the decen-tralized filter parameters and minimize the L2-gain.Numerical examples show that our decentralized filtering strategy is less conservative and achieves better H? performance.