Fixed-time Stability Of Nonlinear Svstems And Its Cooperative Control

For cooperative control of nonlinear systems,its basis is stability theory of nonlinear system,which is applied to analysis of system stabilization,consensus of multi-agent systems,flocking of multi-agent systems,and so on.The objective of cooperative control is to design suitable protocols that can guarantee state of agents converges to ideal value.Due to unaccuracy of instrument,obstacles,and other interference factors,it is often difficult or impossible to obtain initial states of systems in many practical applications.Under the conditions that initial states are unknown,based on Lyapunov theory,matrix theory,and graph theory,fixed-time stability theory of nonlinear system,consensus of multi-agent systems,and stabilization of general neural networks are investigated in this theisis,respectivey.The main contributions are listed as follows:(1)Fixed-time stabilization of general network system is considered firstly.Based on fixed-time stability theorem,a class of fixed-time protocol is designed to solve stabilization problem of the neural network system.(2)For a first order multi-agent systems under time varying communication topology,a class of fixed-time consensus protocol is designed.By Lyapuov method,fixed-time stability theorem and graph theory,we proved feasibility of the ptotocol.For fixed-time bipartite flocling problem of second order multi-agent systems,an improved protocol is designed;moreover,a rigorious proof of bipartite flocking is given by means of fixed-time stability theory,Lyapunov theory,graph theory,structurally balanced signed graph.(3)A class of stochastic nonlinear systems is considered.By introducing a class of functions,a new concept that is said to be fixed-time stable in probability,is proposed,and its detailed definition is presented.In addition,a criterion(theorem)is proposed to judge fixed-time stability in probability for the stochastic nonlinear systems.Moreover,several corollaries are proposed for proving fixed-time stability in probability for the stochastic nonlinear systems.Furthermore,precise of settling time estimation is studied through proposing an improved fixed-time stability theorem.As a practical application,fixed-time consensus problem of stochastic multi-agent systems is discussed based on the obtained theoretical results.A class of distributed protocol is designed to solve fixed-time consensus problem of stochastic multi-agent systems,and its feasibility is proved rigriously by stochastic process theory and graph theory.