Guidance Laws With Finite Time Convergence For Homing Missiles

Anti-missile missiles achieve direct collision with targets by precision guidance, and destroy the targets using kinetic energy. Since the relative velocity between the missile and target is great, only a few seconds are available for the precision guidance process. This requires a high precision guidance technique with finite time convergence. In this dissertation, under the background of a blended-controlled missile with tail fins and attitude thrusters intercepting a high speed maneuvering ballistic missile, we designed homing guidance laws with finite time convergence.First of all, based on nonlinear control system finite time stability theory, we proposed sufficient conditions for finite time convergence of the line-of-sight angular rate and design guidance laws which ensure the line-of-sight angular rates converge to zero or a small neighborhood of zero before the final time of the guidance process. Theoretically, such guidance laws guarantee the LOS angular rates converge to zero in finite time in both the planar and three-dimensional environments. Reasonable adjust the parameters of the guidance law, we can obtain different convergence speeds and performances and improve the robustness of the guidance system while alleviate the chattering, therefore we can make the LOS angular rates converge to zero before the final time to ensure high guidance precision.In consideration of the lag of the autopilot of endoatmospheric missiles, two guidance laws based on the non-singular terminal sliding mode control and regular sliding mode control are designed sequentially. Theoretically, both of them guarantee the variables in guidance system converge to sliding surface in finite time, furthermore, the former guarantees the LOS angular rates converge to zero in finite time on the sliding surface while the later guarantees the convergence at an exponential rate. Theoretical analysis and simulation results show that the proposed guidance laws are robust against target maneuvers and are able to compensate the lag of autopilot.The true proportional navigation guidance law, the augmented proportional navigation guidance law and the adaptive sliding-mode guidance law designed based on the planar target-to-missile relative motion dynamics have been widely used. By a proper construction of a Lyapunov function for the line-of-sight angular rates in the three dimensional guidance dynamics, it is shown that the three guidance laws presented are able to ensure the asymptotic convergence of the angular rates as they are directly applied to the three-dimensional guidance environment. Furthermore, considering the missile autopilot dynamics as a first order lag, we design three dimensional nonlinear guidance laws by using the backstepping technique for three cases: (1) the target does not maneuver; (2) the information of target acceleration can be acquired; and (5) the target acceleration is not available but its bound is known a priori. In the first step of the backstepping design of the control law, there is no need to cancel the nonlinear coupling terms in the three-dimensional guidance dynamics in such way that the final expressions of the proposed guidance laws are significantly simplified. The proposed three dimensional guidance laws are able to effectively compensate the lag of autopilot; moreover, the control inputs are directly measurable thus can be implemented conveniently.The problem of intercepting maneuvering targets with impact angle constrained flight trajectories is discussed to enhance the hitting precision. First, supposing the missile has an ideal autopilot, we designed two terminal guidance laws with impact angle constrained trajectories. Theoretically, both of them guarantee the LOS angles and LOS angular rates converge to sliding surface in finite time, and one guidance law guarantees the LOS angles converge to expected value and the LOS angular rates converge to zero in finite time at an exponential rate on the sliding surface while the other guarantees the LOS angles converge to expected value and the final miss distance converge to zero. Furthermore, considering the dynamics of missile autopilot as a first order lag, we extended the two guidance laws with autopilot lag. Simulation results showed that the guidance laws with autopilot lag are able to guide a missile to impact either a maneuvering target or a non maneuvering target with a desired angle and a small miss distance.Finally, considering of the discrete-time dynamical character of lateral thrusters on blended-controlled missile, three discrete sliding-mode guidance laws are proposed by using discrete siding-mode control theory. First, a discrete sliding-mode guidance law which needs not the bound of target acceleration is deduced. The second discrete sliding-mode law is designed with just knowing the possible variation range of target acceleration between two adjacent sampling instants rather than the target acceleration bound. Since the variations of target-to-missile range and the target acceleration are both small variable between two adjacent sampling instants, in the design of the third discrete sliding-mode guidance law all historical missile seeker's measurements are used to estimate the target acceleration, such that the noises in seeker measurements are effectively smoothen. It is theoretically proved that the proposed discrete sliding-mode guidance laws are finite time convergent. Quasi sliding-mode bands of the discrete sliding-mode guidance laws are discussed, and formulas to calculate the terminal miss distances of discrete sliding-mode guidance laws are presented.