Nonsingular Adaptive Guidance for Impact Time and Angle Control

Abstract

The ultimate objective of guided missiles is to intercept targets as small miss distance as possible. Most of the guided missiles employ homing guidance which is a guidance process that can acquire the information of the target with respect to the pursuer and can formulate its own commands to guide itself toward the target. Improvements in missile defense systems pose a great challenge in enhancing the survivability and kill probability of conventional homing guided missiles. Moreover, as manervering capabilities of targets evolve, the more agile and accurate performance of missiles with various constraints are required. This dissertation proposes nonlinear guidance laws whose features are divided into four parts: (i) adaptive guidance, (ii) impact angle control guidance, (iii) impact time control guidance, and (iv) impact time and angle control guidance. First, an adaptive guidance law applicable to a short-range homing missile is investigated against a highly maneuvering target that has the same maximum maneuver acceleration as the missile. In practice, it is difficult to measure the target acceleration with precision and without time delay. The objective of this study is to design a guidance law that can intercept a target within the acceptable miss distance in the presence of unknown target acceleration and guidance command saturation. For this, the main idea of this paper is to apply the fast adaptive control approach to estimating the tangential component of the unknown target acceleration. Moreover, the auxiliary signal is introduced to prevent the presence of the guidance command saturation from destroying the desired adaptive performance. The proposed guidance law can be classied as an augmented proportional navigation guidance law with the actual target acceleration component being replaced by its accurate estimate. Second, a sliding mode guidance law for impact angle control is proposed against a maneuvering target with unknown acceleration, which is capable of achieving the acceptable miss distance and a wide range of the desired impact angle. The main idea is to separate the switching surfaces for the impact angle constraint and the homing constraint, then to associate the two surfaces by introducing an appropriate virtual controller. Because of the unknown target acceleration, an adaptive procedure is designed to select the gain of the switching controller which accounts for the uncertainty bound regarding the target acceleration. The stability of the proposed approach is analyzed by Lyapunov theory, and the capturability analysis is also presented. A guidance problem for impact time control applicable to salvo attacks is considered based on the sliding mode control. To prevent the singularity of the guidance command, a positive continuous nonlinear function of the lead angle is introduced to the guidance command, which makes the Lyapunov stability negative semi-denite. This issue is also resolved by the additional component of the guidance command, which makes the sliding mode the only attractor still without the singularity. The capturability analysis is presented, which is not dependent on the initial launching conditions and can guarantee a wide range of the capture region. The proposed guidance law is easily extended to a non-maneuvering and low-maneuvering target using the predicted interception point. A nonsingular guidance law for impact time and angle control applicable to more eective salvo attacks is proposed by combining the impact angle control guidance and impact time control guidance mentioned above. To incorporate two constraints, the guidance system forms an underactuated system. To deal with this, time-varying slack variables are introduced to form a square system. By introducing a positive continuous nonlinear function of the singular point, the singularity problem of the guidance command is prevented. The presented capturability results are independent on the initial launching conditions of