Linear-quadratic and norm-bounded combined differential game guidance scheme with obstacle avoidance for attacking defended aircraft in three-player engagement OA

A differential game guidance scheme with obstacle avoidance,based on the formulation of a combined linear quadratic and norm-bounded differential game,is designed for a three-player engagement scenario,which includes a pursuer,an interceptor,and an evader.The confrontation between the players is divided into four phases(P1-P4)by introducing the switching time,and proposing different guidance strategies according to the phase where the static obstacle is located:the linear quadratic game method is employed to devise the guidance scheme for the energy optimization when the obstacle is located in the P1 and P3 stages;the norm-bounded differential game guidance strategy is presented to satisfy the acceleration constraint under the circumstance that the obstacle is located in the P2 and P4 phases.Furthermore,the radii of the static obstacle and the interceptor are taken as the design parameters to derive the combined guidance strategy through the dead-zone function,which guarantees that the pursuer avoids the static obstacle,and the interceptor,and attacks the evader.Finally,the nonlinear numerical simulations verify the performance of the game guidance strategy.

A trajectory shaping guidance law with field-of-view angle constraint and terminal limits

In this paper, a trajectory shaping guidance law,which considers constraints of field-of-view(FOV) angle, impact angle, and terminal lateral acceleration, is proposed for a constant speed missile against a stationary target. First, to decouple constraints of the FOV angle and the terminal lateral acceleration, the third-order polynomial with respect to the line-ofsight(LOS) angle is introduced. Based on an analysis of the relationship between the looking angle and the guidance coefficient,the boundary of the coefficient that satisfies the FOV constraint is obtained. The terminal guidance law coefficient is used to guarantee the convergence of the terminal conditions. Furthermore, the proposed law can be implemented under bearingsonly information, as the guidance command does not involve the relative range and the LOS angle rate. Finally, numerical simulations are performed based on a kinematic vehicle model to verify the effectiveness of the guidance law. Overall, the work offers an easily implementable guidance law with closed-form guidance gains, which is suitable for engineering applications.

Two-phase guidance law for impact time control under physical constraints

An impact-time-control guidance law is required for the simultaneous attack of suicide attack unmanned aerial vehicles.Based on the nonlinear model,a two-phase guidance strategy is proposed.The impact time is derived in a simple analytical form of initial states and switching states,and it can be controlled by switching at an appropriate range.Firstly,a two-phase guidance law is designed to make the magnitude of the heading error decrease monotonically from its initial value to zero.And then,the feasible interval of the switching ranges and of the impact times under the acceleration constraint are given analytically in sequence.Furthermore,a general form of twophase guidance law is proposed,which allows the magnitude of the heading error to increase in the first phase,to improve the applicability of the methodology.Having the same structure as proportional navigation guidance with a time-varying gain,the proposed algorithms are simple and easy to implement.The corresponding feedback form is presented for realistic implementation.When a predefined impact time is taken within its permissible set,the constraints on the acceleration and fieldof-view will not be violated during the interception.Finally,simulations validate the effectiveness of the methodology in impact time control and salvo attack.

Three-dimensional cooperative guidance strategy and guidance law for intercepting highly maneuvering target

Cooperative interception of the target with strong maneuverability by multiple missiles with weak maneuverability in the three-dimensional nonlinear model is studied.Firstly,the three-dimensional nonlinear model of cooperative guidance is established.The three-dimensional reachable region is represented composed of lateral acceleration and longitudinal acceleration in the two-dimensional coordinate system.Secondly,the problem of the multiple missile’s reachable coverage area is transformed into the problem of cooperative coverage.A cooperative coverage strategy is proposed and an algorithm for quickly calculating the number of required missiles is designed.Then,the guidance law based on the cooperative coverage strategy is proposed,and it is proved that cooperative interception of the target can be achieved under the acceleration limit.Moreover,the relations among the number of missiles,the initial array position of terminal guidance and the coverage area of the target’s large maneuver are analyzed.The dynamic adjustment strategy of guidance parameters is proposed to reduce the guidance error.Finally,simulation results show that multiple missiles with low maneuverability can achieve effective interception of target with strong maneuverability through the proposed cooperative strategy and cooperative guidance method.

Weighing neutrinos in dynamical dark energy models

The discovery of neutrino oscillation indicates that neutrinos have masses and each flavor state is actually a superposition of three mass states with masses m1,m2,and m3.However,the neutrino oscillation experiments are not able to measure the absolute masses of neutrinos,but can only measure the squared mass differences between the neutrino mass eigenstates—The solar and reactor experiments gave