Research On Missile Terminal Guidance Laws Based On Finite-time Control Theory

The violent development of aeronautics and space technology leads to more and more high requirement for missile guidance precision. A typical missile guidance process includes three stages:initial, middle and terminal guidance. At the terminal guidance, i.e., the final guidance stage, target often escapes with high maneuvers, and the time left to precision terminal guidance is usually very short. The performance of this stage finally determines whether the missile can hit its target precisely and achieve the attacking. Therefore, new high precision guidance laws with strong robustness to disturbances from target maneuvers and finite-time convergent rate are needed for terminal guidance stage. For the system with disturbances and uncertainties, the non-smooth finite-time state feedback control can not only guarantee the controlled system converge and stable to the system equilibrium point in finite time, but also has better robustness and higher tracking accuracy than the asymptotically stable system. Hence, under the background of homing missile intercepting maneuvering targets, using the finite-time control theories, this dissertation focuses on the problems of the design of terminal guidance laws with finite-time convergence. The main results are summarized as the following:(1) For the problems of the interception of maneuvering target and finite-time convergence for planar terminal guidance systems with missile autopilot dynamics and impact angle constraint simultaneously, based on the finite-time sliding-mode control theory, the finite-time convergent sliding-mode terminal guidance laws are designed.Firstly, to solve the problem that the information of the target maneuver cannot be obtained precisely at terminal phase, a high accuracy nonlinear finite-time disturbance observer is employed to estimate the target accelerations. Then, considering the planar terminal guidance system with a first-order lag of missile autopilot dynamics, a guidance law which ensure the LOS angular rate converge to zero in finite time is designed. On this basis, further taking account of the impact angle constraint, a guidance law which can both ensure the LOS angular rate converge in finite time and intercept the target with specified impact angle is designed. There are no disturbance terms in the expressions of the presented terminal guidance laws, and also no needs for the estimation of the upper bound of the target accelerations. The guidance laws can effectively compensate the autopilot dynamics, have strong disturbance rejection ability and high guidance precision.(2) For the problems of the interception of maneuvering target and finite-time convergence for planar terminal guidance systems with guidance parametric errors and missile autopilot dynamics simultaneously, based on the continuous finite-time control method, the continuous finite-time convergent robust terminal guidance laws are designed.Firstly, considering two classes of general single-input linear systems, the schemes of control laws with finite-time convergence are studied, and two related conclusions are obtained. Then, considering the planar terminal guidance system with guidance parametric errors, a finite-time convergent guidance law is designed using the first conclusion directly. On this basis, further taking into consideration the first-order dynamics of missile autopilot, directly using the second conclusion, a finite-time convergent guidance law is designed. The presented guidance laws avoid the chattering which will be probably induced by the sliding-mode control, and can ensure the system states converge to a small neighborhood near the zero in finite time. The guidance laws can effectively compensate the autopilot dynamics, and has strong robustness to guidance parametric errors and target maneuvers, and have high guidance precision. Furthermore, the convergence domain is given, which is proved to be able to be adjusted to arbitrarily small by the corresponding guidance coefficients in the case when the upper bound of target accelerations are known.(3) For the problems of the interception of maneuvering target and finite-time convergence for three-dimensional coupling terminal guidance systems with missile autopilot dynamics, based on the new control theory of finite-time input-to-state stability (ISS), the three-dimensional finite-time ISS robust terminal guidance laws are designed.Firstly, considering two classes of general multi-input nonlinear systems, the schemes of finite-time ISS control laws are studied, and two related conclusions are obtained. Then, considering the three-dimensional terminal guidance system, viewing the target maneuvers as bounded distance inputs, a finite-time convergent guidance law is designed using the first conclusion directly. On this basis, further taking into consideration the first-order dynamics of missile autopilot, directly using the second conclusion, a finite-time convergent guidance law is designed. Under the presented guidance laws, the LOS angular rate can be stabled to a small neighborhood near the zero in finite time, and the convergence domain can be adjusted to arbitrarily small by the corresponding guidance coefficients. The guidance laws can effectively compensate the autopilot dynamics, have strong disturbance rejection ability and high guidance precision.(4) For the problems of finite-time convergence and the interception of maneuvering target for a three-dimensional coupling terminal guidance system with missile autopilot dynamics and missile acceleration constraint, based on the finite-time boundedness (FTB) theory, a three-dimensional FTB terminal guidance law with anti-saturation of missile acceleration is designed.Firstly, considering a class of nonlinear system with quasi-one-sided Lipschtiz condition, the scheme of FTB controller is designed, and a related conclusion is obtained. Furthermore, a solving method based on the differential linear matrix inequality is given. Then, considering the three-dimensional terminal guidance system with a first-order missile autopilot dynamics, by using the conclusion directly, a FTB guidance law is designed. The presented guidance law can guarantee not only that the LOS angular rate converge in finite time, but also the missile accelerations do not exceed the given practical limitation. The guidance law can effectively compensate the autopilot dynamics, and has high guidance precision.