Research On Guidance Law And Cooperative Guidance Law Based On Fixed-Time Stability

With the complexity of the combat environment and the rapid development of anti-missile technology,the traditional "one-to-one" combat mode has been difficult to complete the interception mission.It is necessary to enhance the missile’s guidance accuracy and cooperative combat ability in order to improve the interception probability.At the end stage of guidance,the target often escapes and then leaves a very short time for the final guidance,which puts forward higher requirements for the guidance law with the performance of strong robustness and fast convergence.Finitetime control has the advantages of fast convergence speed and strong robustness,but its convergence time is related to the system’s initial state which can not be obtained accurately.As a generalization of finite-time control,fixed-time control can get an upper bound of convergence time which is independent of the system’s initial conditions.It has great practical engineering significance.Therefore,aiming at the problems such as impact angle constraint,acceleration saturation constraint,target maneuvering information acquisition and so on in the guidance process,this paper studies fixed-time guidance law and multi-missile cooperative guidance law under the background of single missile or multiple missiles intercepting a maneuvering target.The main contents are summarized as follows.(1)Aiming at the problem of single missile intercepting a maneuvering target and considering the acceleration of target as a bounded external interference,two fixed-time convergent guidance laws with impact angle and input saturation constraints are designed respectively.Firstly,a second-order guidance model with impact angle constraint is established based on the relative motion relationship between missile and target.Secondly,a new nonsingular fast terminal sliding mode(NFTSM)is proposed by using terminal mode switching method.Then,a fixed-time convergence guidance law(Fx TCG)is designed,in which the acceleration saturation constraint is taken into account.Further,in order to reduce the influence of disturbance upper bound estimation on guidance performance,the fixed-time disturbance observer(Fx TDO)is introduced to estimate the disturbance caused by target maneuvering online.Finally,the effectiveness of the designed Fx TCG is verified by the simulation results.(2)Considering the constraints of impact angle and input saturation,a fast convergent adaptive Fx TCG is designed for the three-dimensional space guidance problem of single missile intercepting a maneuvering target.Firstly,a guidance model with line-of-sight(LOS)angle in three-dimensional space is established.Secondly,target maneuvering is regarded as bounded interference and the upper bound is unknown.An adaptive law is designed to estimate the interference online in order to reduce the influence of interference estimation on the performance of guidance law.Then,a fixed-time convergence three-dimensional guidance law combined with a new fast nonsingular terminal sliding method(NFTSM)is designed,and the stability of the closed-loop system is proved by Lyapunov stability theory.Finally,the simulation results show that the proposed guidance law can intercept targets with different maneuvering forms at the desired LOS angle,and has faster convergence speed and higher guidance accuracy than other methods.(3)Considering the problem of multiple missiles intercepting a maneuvering target,fixed-time cooperative guidance laws with LOS angle constraint are studied based on first-order consistency.Firstly,a cooperative guidance model based on the estimation of time-to-go in plane is established.Secondly,the fixed-time cooperative Guidance law(Fx TCGL)is designed based on the multi-agent consensus theory.Fx TDO is designed to estimate the interference upper bound which is applied to the design of guidance law.Thirdly,in order to further consider the LOS angle constraint,a Fx TCGL with LOS angle constraint is designed by integral sliding mode control(ISM)and adaptive super-twisting(ST)algorithm.The adaptive ST algorithm is used to estimate the target maneuvering interference online.Finally,the simulation results show that the proposed two cooperative guidance laws can ensure that the missile intercepts the target at the same time with a fixed time.The latter can also ensure that the missiles can intercept the target from different angles.(4)For the guidance problem of multiple missiles intercepting a maneuvering target,two cooperative guidance laws are studied based on second-order consistency.Firstly,an in-plane cooperative guidance model with LOS angle constraint based on second-order consistency is established.Secondly,a Fx TCGL with input saturation constraint is proposed based on multi-agent consistency theory and adaptive integral sliding mode algorithm.Thirdly,a fixed-time cooperative guidance law with LOS angle constraint is designed by using integral sliding mode control and nonsingular terminal sliding mode(NTSM)algorithm.The guidance law can ensure that the missile intercepts the target at the desired LOS angle within a fixed time.Finally,the simulation results show that the proposed two cooperative guidance laws can ensure that the missile intercepts the target simultaneously with a fixed time and have strong robustness to different types of target maneuvering.