Differential Game And Finite Time Control Based Guidance Law Design For Exoatmospheric Missiles

Currently,main aerospace power countries have put a lot of manpower and material resources for developing exoatmospheric missiles.They have achieved lots of research results,even some key technologies have entered the engineering verification phase.China,as a world power country,should also develop the relational key technologies.This thesis deals with guidance problems for a class of exoatmospheric missiles.Guidance laws are designed to fulfill varies requirements.My research is devided into the folloing six sections:(1)Considering exoatmospheric missiles with nozzle equipped on the nose,after deeply analyzing the flight control mechanism and building the mathematical model,the concept and properties of nominal motion are derived to simplify the design of guidance law.To deal with non-ideal initial interception scenarios,a two-phase guidance scheme is derived.The interception process is derived into two phases: Phase 1 and Phase 2.In Phase 1,the missile performs nominal motion to make itself and the target on the collision triangle.In Phase 2,the missile performs a straight line motion with constant acceleration to hit the target.In order to implement the two-phase guidance scheme,differential game-based guidance laws are designed respectively for Phase 1 and Phase 2 to optimize the inner loop response.(2)Consider a class of differential game problems.An adaptive dynamic programming algorithm is designed for affine nonlinear systems.The weighted addition of basis functions is used to approximate the cost function.The parameter update law is designed to make the state variables and the weights uniformly ultimately bounded.It is done so that in the meantime of guaranteeing the stability of the closed loop system,the control law can also be optimized.Consider an interception model,where an exoatmospheric missile is to intercept an exoatmospheric missile.By utilizing virtual time domain,the finite-time guidance problem is transformed into an infinite-time control problem to simplify the analysis.Then the adaptive dynamic programming algorithm can be applied on the differential-game based guidance of the exoatmospheric missiles,which is suitable for simulation research.(3)Terminal phase interception is considered for exoatmospheric missiles to design finite-time guidance law.The target's evasive maneuver is zero.By analyzing the planer interception model,a Newton algorithm is derived to online estimate the time-to-go,nominal flight path angle and the nominal flight path angular rate.Guidance law is designed to guarantee finite-time tracking of flight path angle and flight path angular rate.The time derivative of the nominal flight path angle is not considered.The homogeneity of the closed loop system is utilized to guarantee finite-time stability.(4)Consider terminal phase interception,where the target's evasive maneuver is zero,for exoatmospheric missile.An impact angle constraint is enforced on the missile.The time derivative of the flight path angle is considered.The flight path angle tracking system is decoupled into a two-order guidance system and a one-order control system.A nonsingular terminal sliding mode control algorithm is designed to derive the guidance law for the guidance system.A finite-time control law is designed for the control system.By guaranteeing the finite-time convergence of the two system state variables,the finite-time tracking of flight path angle is guaranteed.Lyapunov theory is used for stability proof.(5)Based on the third and the fourth research contents,the case that the target performs constant evasive maneuver is considered.By using Newton's law,the time-to-go,nominal flight path angle and nominal flight path angular rate can be online estimated.To avoid time-scale decouple of the flight path angle tracking system,finite-time guidance law is designed for the complete order system.The guidance law design is mainly based on Young's inequality.A backstepping-based guidance law is designed,in which control laws are designed order by order for the flight path angle tracking system,such that the corresponding Lyapunov function and the time derivative of the Lyapunov function satisfies the functional relationship that guarantees finite-time convergence.(6)Consider a class of linear parameter-varying model with uncertain parameters.It is desired that the system state tracks a given nominal state trajectory.Two types of uncertainties,matched uncertainty and unmatched uncertainty,are considered.By utilizing the properties of left inverse,one can perform an orthogonal decomposition for the unmatched uncertainty to simplify the design of control law.To deal with the two types of uncertainties,adaptive control laws and corresponding parameter update laws are respectively designed to asymptotically stabilize the closed loop system and to make the adaptive parameters uniformly bounded.For the formerly mentioned six research contents,simulation studies,whose results are given in the thesis,are performed to verify the feasibility of the algorithms.