Collective Behavior Analysis And Security Control For Hybrid Systems

Hybrid systems are comprised of continuous dynamical behaviors and discrete dynamical events.Many important dynamical systems,such as multi-agent systems and neural networks,can be modeled and analyzed by hybrid system.In particular,the collective behavior analysis of hybrid systems plays an irreplaceable role in many fields such as aerospace,smart grid,smart transportation networks and chemical production process.At present,the most concerned hybrid systems contain impulse systems and switched systems.The two kinds of discrete events,impulse and switching,have both promoting and interfering effects on the stability of dynamical systems.It is necessary to analyze the influences of these two discrete behaviors on stability.In addition,the security control of hybrid systems has attracted considerable attention from many scholars.This paper mainly analyzes the collective behaviors and security control of hybrid systems.The main work of this paper can be listed as six parts:In the first chapter,the definition,manifestation and research significance of hybrid sys-tems are introduced.Firstly,the recent developments and problems that desperately needs to be solved for the stability of impulsive systems and switched systems are presented.Then,the security control of hybrid systems is introduced,including consensus problems under attacks and privacy protection of sensitive information.In the second chapter,the collective behaviors of two delayed impulsive systems under mixed impulsive effects is discussed.In Section 2.1,the synchronization problem of coupled neural networks with mixed impulses is studied.Here mixed impulses contain desynchroniz-ing delay-free impulses,synchronizing delay-free impulses,desynchronizing delayed impulses and synchronizing delayed impulses.A novel concept named average mixed impulsive gain is proposed to quantify the effects of mixed impulses.Besides,we establish a delayed impulsive differential inequality which extends the Halanay inequality,and apply it to study the synchro-nization problems for delayed neural networks with mixed impulses.It is interesting to notice that both delay-free impulses and delayed impulses can contribute to the synchronization of coupled neural networks.Meanwhile,the synchronization of neural networks only with delay-free impulses or delay-dependent impulses are also discussed.Some sufficient conditions are derived to ensure the exponential synchronization of delayed neural networks.In Section 2.2,some properties of a novel Halanay-type inequality containing impulses and delayed impulses simultaneously are studied.Two concepts with respect to average impulsive gain are proposed to describe hybrid impulsive strength and hybrid delayed impulsive strength.Then,using the obtained results concerning Halanay-type inequality,two stability criteria are derived for linear systems with impulses and delayed impulses.It is indicated that the stability of impulsive sys-tems is robust with respect to delayed impulses whose magnitude strength is relatively small.While,if the strength of impulses is small,the time-delayed impulses can also promote the stability of unstable systems.In the third chapter,two types of switching signals are designed to stabilize switched systems with unstable subsystems.In section 3.1,the stability problems of a class of switched systems with limiting average dwell time are concerned.The common average dwell time(ADT)is improved to a form of limit,and the limiting average dwell time even can be infi-nite.Different from previous results,in order to take full advantage of stabilizing switchings,switching-dependent switched parameters are firstly used to describe the relationship of two consecutive activated switchings.Then,stability criteria of switched systems with limiting average dwell time are established,which are less conservative comparing with the existing results.Additionally,some stability criteria of switched systems including continuous-time and discrete-time cases are derived.In section 3.2,the stability of a class of stochastic neural networks with switching signal is studied.Firstly,by means of the method of limiting average dwell time,we analyze the stability of switched systems which potentially contain unstable subsystems and stable subsystems simultaneously.Moreover,considering two types of switch-ings:stabilizing switchings and destabilizing switchings,we adopt time-dependent parameters to give a description of the relationship between two successive activated subsystems.Based on the obtained results for switched systems,some stability criteria for switched neural networks with stochastic disturbances are derived.In the fourth chapter,security control of multi-agent systems is discussed,that is,design-ing appropriate control protocol to ensure the consensus of multi-agent system under Denial-of-Service(Do S)attacks.Security control aims to guarantee the consensus of multi-agent systems in the present of Do S attacker.Most of the existing distributed controllers are invalid during the attack interval.In order to overcome this difficulty,a novel hybrid distributed control protocol is designed.Here the controller uses the latest information saved in the buffers in presence of malicious attacks,which will further enhance the security of multi-agent system-s.Some sufficient conditions on the coupled strength and attack parameters are derived to achieve the leader-following consensus of multi-agent systems.Furthermore,we estimate the upper bounds of Do S frequency and Do S duration that the multi-agent systems can tolerate before losing consensus.It is noted that we also reduce the computational complexity via the property of Kronecker product.Besides,observer-based model is proposed and corresponding consensus criterion is established.In the fifth chapter,two kinds of algorithms are proposed to achieve privacy-preserving consensus of undirected multi-agent system via node decomposition and homomorphic cryp-tography technique.Based on the number of neighbours,every agent is decomposed into|N_i|subagents,which are connected as a chain graph.Every subagent connects and only connects one non-homologous subagent.Information exchange between non-homologous subagents is encrypted by homomorphic cryptography algorithm,and homologous subagents exchange in-formation directly.The first privacy-preserving algorithm can achieve the accurate average consensus,which means that the agreement value of every subagent is consistent with original average consensus value.The second algorithm studies the privacy-preserving scaled consensus problem,which does not need the priori knowledge about the degree of graph.The final agree-ment values of subagents are not exactly the same,but homologous subagents can compute the original group decision value via the product of limit value and agent's degree.This algorithm also guarantees the privacy of group decision value of whole system.Besides,we prove that the privacy of initial value can be preserved if the agent has at least one neutral neighbour.In the sixth chapter,we summarize the above work,and make a general judgment and prospect for our further work.