State-dependent Switching Control For Stability Of Nonlinear Systems In Complex Environment

With the continuous development of automatic control theory,more complex system models are receiving increasing attention,especially those composed of multiple modes or subsystems.Due to the change of external environment,system failure,or switching of control strategies,the system may exhibit different behaviors.Therefore,the study of switched system theory has become an important direction in the field of automatic control.Switched system theory is widely used in various engineering and scientific fields,such as control engineering,communication systems,robot control,biomedical engineering,etc.,covering multiple aspects such as multimodal system modeling,automatic control theory,and application requirements in engineering and scientific fields.However,in practical systems,various influences and challenges from the system itself or external complex environments are often faced,such as parameter uncertainty,sensor errors,external interference,random noise,state mutations,etc.These lead to poor control performance of the system and difficulty in achieving expectations.In addition,at present,most of these studies focus on switched systems in which subsystems are stable.When subsystems are all unstable or considering the stability of switched systems in the framework of discontinuous states,the research on related problems is not perfect.In addition,most of these studies currently focus on the study of switched systems with all stable subsystems.Faced with the instability of all subsystems or considering the stability of switched systems in discontinuous state frameworks,research on related issues is not yet complete.This thesis mainly studies the nonlinear switched systems in complex environment.By means of Lyapunov function technique,impulsive control theory and state-dependent switching control method,some conditions for robust stability and network synchronization under complex environment such as random noise,parameter uncertainty and impulse action are established,and effective control strategies are proposed.The main content of this thesis are included as follows:1.For stochastic switched neural networks with random noise and parameter uncertainty,the robust globally asymptotic stability of the network is achieved by the state-dependent switching method.Firstly,by extracting the information of random noise and uncertainty,the corresponding restriction assumptions are given,and the interference constraint conditions are designed.Then the switching regions and the state-dependent switching law are established.By combining the interference constraint with the state-dependent switching law,the robust globally asymptotical stability in mean square of stochastic switched neural networks is proposed in the form of linear matrix inequalities via Lyapunov function method and switching control theory.Finally,a numerical example is given to verify that the state-dependent switching control has good control performance for stochastic switched neural network with unstable subsystems and can guarantee the expected robust stability of the system.2.For nonlinear switched system with impulse action,the globally exponential stability of the system is realized by coupling impulse action with state-dependent switching in discontinuous environment.Firstly,considering that the system is affected by impulse action,the switching regions and switching law involving impulse information are designed to ensure that the two preconditions of state-dependent switching in discontinuous environment,coverage and overlap,can still be satisfied.On this basis,some conditions for uniformly globally exponential stability of the system under the switching law involving impulse action are given,in which the relationship between continuous dynamics and discrete dynamics is established,including destabilizing impulse and stable continuous dynamics,stabilizing impulse and unstable continuous dynamics.Secondly,an optimization problem is formulated to solve the linear matrix inequalities with relatively optimal parameters,which can ensure the stability and reduce the constraint on the impulse action.Finally,the effects of state-dependent switching and impulse action on the stability of system are illustrated by two simulation examples,and the effectiveness of the proposed results and method is demonstrated.3.For nonlinear switched systems with impulse action,the globally exponential stability of switched systems is realized by coupling the state-dependent switching with dwell time condition.Firstly,in view of the possible fast switching phenomenon in the switching process,the dwell time condition is proposed.Based on this,the algorithm of state-dependent switching law including the dwell time condition is given,which contains the information of impulse action.Secondly,by using the multiple Lyapunov function method,the system stability is analyzed by the time-dependent part,the state-dependent part and the switching time under the time-state hybrid switching law,and the sufficient conditions for the globally exponential stability of the system are given.When the impulse action is used as the control means,another result of the globally exponential stability of the switched system is obtained by the hybrid switching law,and the design of the impulsive gain matrix is given.Finally,the control effect of hybrid switching law in the stability of impulsive switched system is verified by simulation.4.For complex dynamical networks with switching topology and impulse action,the globally exponential synchronization is realized by state-dependent switching method.Firstly,the error network model is established between the switched complex dynamical network and the target system.By extracting network state and impulse information,the state-dependent switching is designed.Based on the dynamic analysis of the network,the relationship among network topology,impulse frequency,impulse amplitude and switching law is established,and the result of globally exponential synchronization of impulsive switched complex dynamical networks is given.When the continuous dynamics diverges,the control action of the synchronizing impulses coupled with the state-dependent switching law can realize the network synchronization.When the continuous dynamics are stable,the network synchronization can be realized even if the impulse is allowed to be disturbance.Finally,in view of the effect of impulse action and switching law to network synchronization,the validity of the proposed results is given by simulation examples under synchronizing impulses and desynchronizing impulses,respectively.