State Estimation Of Discrete-Time Positive Systems Under Network Environment

As a special class of dynamical systems,positive systems have attracted considerable at-tention due to its potential applications in many fields,such as natural science,social science,biological systems,engineering,and so on.The nonnegative peculiarity of positive system-s makes it rather difficult to apply conventional control system theories and methods to state estimation problems of positive systems.On the other hand,with the rapid development of network communication technology,networked systems have brought great convenience to our society and become increasingly popularized in various fields due to its scalability,flexibility,low-cost maintenance and so on.When the concerned variables of the estimated plant are non-negative（such as population quantity,chemical concentration,water distribution,and electric energy etc.）,it can be described by a positive system.Many phenomena caused by network environment and wireless communication would have a severe impact on the signal transmis-sion and data update of positive systems.How to investigate and design effective,reliable and secure positive estimators for positive systems under the network communication environment is of theoretical and applicative significance.This thesis mainly addresses the state estimation problems of positive systems under network environment,taking into account the existence of the network-induced delays,packet dropouts,packet disorders,communication resource con-straints and cyber attacks.the main results of this thesis include:（1）The filtering problem of a class of nonlinear positive systems with discrete time varying and distributed random delays is investigated.A positive filter model is established consider-ing the probabilistic distribution of the distributed random delays,based on which the ₁-gain performance is studied,and the stochastic stability criterion of the filtering error system is obtained.A filter design approach to nonlinear delayed positive systems is then given in the thesis.（2）The networked filtering problem of positive systems based on an event-triggered trans-mission mechanism is studied.Considering a linear discrete time positive system under certain assumption,a linear event-triggered condition for data transmission into network is proposed.A unified framework of networked filtering for positive systems is established,based on which the ₁-gain filtering performance is studied,and the stability criterion of filtering error system is derived.A co-design approach to the parameters of the networked positive filter and linear triggering condition is then proposed.（3）The networked state observer design problem for positive systems based on an event-triggered transmission mechanism is studied.A series of positive constants are introduced to reasonably weaken the assumptions in the networked filtering problem mentioned before,based on which a linear event-triggered condition is proposed for nonlinear positive systems under network environment.Considering the probabilistic distribution property of network-induced delays,a unified framework of networked state observer for positive systems is then established.The ₁-gain stability criterion for the derived estimation error system is presented,and a co-design approach to the parameters of networked positive state observer and linear triggering condition is proposed.（4）The networked fault detection problem for positive systems based on an event-triggered transmission mechanism is studied.A mode-dependent triggering condition is introduced for positive Markov jump systems.A networked fault detection method based on a positive filter under network environment is proposed.The ₁-gain stability criterion for the derived error system is presented,and a co-design approach to the parameters of networked positive fault detection filter and linear mode-dependent triggering condition is proposed.（5）The distributed estimation problem of positive systems over sensor networks under deception attacks is addressed.Considering the information sharing and cooperation among neighboring sensors,a distributed estimation framework for positive systems is established in the presence of random sensor link failures and falsified data in network transmission caused by deception attacks.The finite-time ₁-gain boundedness of estimation errors is analyzed,based on which a design approach to the distributed secure estimators for positive systems is presented.（6）The distributed estimation problem of positive systems over heterogeneous sensor net-works under Do S attacks is investigated.Considering the heterogeneous interactions of mea-surement and estimate information in sensor networks,a distributed estimation framework for positive systems is established under compromised and repaired periods in the presence of in-termittent Do S attacks and information link repair procedures.The stability analysis of the dis-tributed estimation error system is comprehensively carried out during the two periods,based on which a corresponding distributed secure estimator design approach is provided.Finally,the thesis concludes the obtained results and presents some outlooks on future works.