Consensus Based Cooperative Terminal Guidance Law Design For Multiple Cruise Missiles

With the rapid development of anti-missile technology of enemy's Aegis ships,single missile's penetration becomes more and more difficult.Salvo attack on enemy's ship targets by cooperative operation of multiple cruise missiles can greatly improve the penetration probability of missile group.As one of the key technologies of cooperative attack,cooperative terminal guidance technology has important research value.According to the different coordination variables,cooperative terminal guidance technology can be divided into two categories: time coordination and line-of-sight(LOS)angle coordination.Time coordination can make multiple missiles attack targets simultaneously,which is helpful to improve the penetration probability of missiles without setting the expected impact time.LOS angle coordination can enable multiple missiles to hit targets from the desired relative direction of LOS,which is conducive to improving missiles' detecting precision,dispersing enemy firepower and saving control energy.In this paper,multiple cruise missiles are taken as the research object,and the ultimate goal is to complete the distributed cooperative attack on the target with LOS angle coordination and time coordination.The cooperative terminal guidance laws considering several problems,such as directed communication topology,switching communication topology,external interference,radial velocity measurement failure and finite time convergence,are studied.The main research contents include the following aspects:Base on the second-order consensus theory and integral sliding mode control theory,the design of cooperative guidance law of second-order multiple missiles with LOS coordination under undirected and directed topologies are studied.Firstly,combined with the flight characteristics of cruise missiles,the LOS angle cooperative guidance model of multiple missiles is obtained from the second-order differential equation of LOS angle.Then,in order to solve the problem of LOS angle cooperative guidance with finite time convergence under undirected topology,a distributed LOS angle cooperative guidance law with finite time convergence for multi-missiles under undirected and connected topology is designed based on the theory of multi-agent consensus.The homogeneity and stability of the closed-loop system are analyzed through the theory of homogeneous system.Finally,in order to solve the problem of LOS angle cooperative guidance considering external disturbances for multiple missiles in directed topology,the integrated sliding mode control theory is used to estimate and compensate the external disturbances.Based on the multi-agent consensus theory,a distributed LOS angle cooperative guidance law in directed and strongly connected topology is designed.The stability of the closed-loop system is analyzed by Lyapunov stability theory.Based on the first-order consensus theory,the design of first-order multi-missile time-cooperative guidance law under undirected topology is studied.Firstly,the multi-missile time-cooperative guidance model is obtained by deriving the time-to-go estimation formula of the missile under proportional guidance.Then,in order to solve the problem of multi-missile time-cooperative guidance with finite time convergence under undirected topology,a multi-missile time-cooperative guidance law is designed based on time-varying proportional navigation method and first-order consensus theory,which can make time-to-go converge in finite time.And the finite time stability of the closed-loop system is analyzed based on fast finite time stability theory.Finally,in order to make the time-to-go of multi-missile in switching topology converge quickly,based on the first-order consensus theory of multi-agent,a time-cooperative guidance law with finite time convergence under switching topology is designed,and the finite-time stability of closed-loop system is analyzed with the finite-time theory of switching system.Based on second-order consensus theory,integral sliding mode control theory and disturbance observer theory,the design of second-order multi-missile time-cooperative guidance law under undirected topology is studied.Firstly,based on the time-to-go estimation formula under proportional navigation,the time cooperative guidance model of multi-missile is obtained.Then,in order to solve the time-cooperative guidance problem considering finite time convergence under undirected topology,a time cooperative guidance law is designed based on the multi-agent consensus theory,which can make the time-to-go of multiple missiles achieve consensus in finite time.The finite time stability of the closed-loop system is analyzed by homogeneous system theory.Then,in order to solve the time-cooperative guidance problem under undirected topology which considers both external disturbances and convergence in finite time,a finite-time disturbance observer and integral sliding mode control method is adopted to estimate and compensate the disturbance,and a time-cooperative guidance law is designed based on second-order consensus theory.The finite-time stability of the system is analyzed by the fast finite-time stability theory.Based on second-order consensus theory and super-twisting integral sliding mode control theory,the design of second-order multi-missile time-cooperative guidance law under directed topology is studied.Firstly,in order to solve the problem of time-cooperative guidance considering external disturbances in directed topology,the time-continuous super-twisting integral sliding mode observer is used to observe and compensate the disturbances in finite time.And based on the multi-agent consensus theory,a time-cooperative guidance law for multi-missiles in directed and strongly connected topology is designed.The stability of the closed-loop system considering disturbance is analyzed through the finite-time theory and Lyapunov stability theory.Then,in order to solve the problem of time-cooperative guidance considering both radial velocity measurement fault and finite time convergence under directed topology,a velocity observer is used to estimate and compensate the radial velocity of the missile.And a distributed time-cooperative guidance law for multi-missile is designed based on second-order consensus theory,which can make the time-to-go achieve consensus in finite time under directed topology.The homogeneity and finite-time stability of the closed-loop system are analyzed by homogeneous system theory.In this paper,a large number of numerical simulations are carried out for various cooperative terminal guidance missions,and therefore the correctness and practical value of the designed methods are verified sufficiently.