Finite-time And Fixed-time Control Of Multi-agent Systems With State Constraints

With the progress of science and technology,the coordinated control of multi-agent systems has attracted the attention of a large number of scholars in the fields of mathematics,automatic control,computer and so on,especially in the research of high-order nonlinearities and strong coupling of complex systems.In practical applications,the input,state and output of the system will be affected by many factors,such as physical factors and external environment,and the system usually requires its performance to be achieved in finite-time and fixed-time.Therefore,it is of theoretical and practical significance to study the control problem of nonlinear multi-agent systems with state constraints.Based on Lyapunov stability theory and algebraic graph theory,this thesis studies the finite-time and fixed-time control problems of multi-agent systems with state constraints.The main works are as follows:(1)The finite-time control problem of multi-agent systems with input saturation,unknown nonlinear dynamics,external disturbances and partial state constraints is considered via output feedback.Fuzzy logic system and fuzzy state observer are introduced to approximate the uncertain nonlinearities and estimate the unmeasurable states,respectively.The partial state constraints are dealt with by using the barrier Lyapunov function,so that the partial states of the system do not exceed the preset boundary values.In order to reduce the computational complexity of the virtual controller and save communication resources,a first-order filter and an event-triggered mechanism are introduced,respectively.It is proved that the Zeno behavior does not occur via the proposed event-triggered controller.By stability analysis,the finite-time convergence of tracking error to a small neighborhood of the origin is ensured.Finally,two simulation examples are given to verify the validity of the theoretical results.(2)The event-triggered fixed-time control issue of multi-agent systems with unknown nonlinear dynamics and external disturbances in studied subjected to input delay and partial state constraints by backstepping method.The interconnected topology of agents is assumed to contain a directed spanning tree.An auxiliary system is introduced to handle the time-varying input delay.A tan-type barrier Lyapunov function is used to deal with partial state constraints by backstepping method.It can be guaranteed that the constrained states never exceed the preset boundaries.The uncertain nonlinearities are approximated by fuzzy logic systems,then an adaptive approach is adopted to estimate the unknown parameters.In order to save resources,an event-triggered mechanism is proposed and the Zeno behavior can be excluded.By stability analysis,the fixed-time convergence of tracking error to a small neighborhood of the origin is ensured.Finally,the effectiveness and reliability of the control method are verified by an example.