Nonlinear H∞ Guidance Design for Missile against Maneuvering Target
Issue: 2017 - Volume 9 [Issue 4]
Jacqueline Munene Makena *
Department of Aerospace and Aviation Engineering, Technical University of Kenya, Haile Salassie Avenue, P.O.Box 52428, Nairobi, 00200, Kenya
Department of Physical Sciences, Jaramogi Oginga Odinga University of Science and Technology, P.O.Box 210-40601, Bondo, Kenya
*Author to whom correspondence should be addressed.
A new guidance law is derived for missile against maneuvering target by adopting nonlinear control theory. The guidance law is based on three dimension (3D) nonlinear kinematics described by modified polar coordinate (MPC). In MPC, only three differential equations are used to describe the 3D relative motion between missile and target. The new guidance law is designed by solving the Hamilton-Jacobi-Isaacs (HJI) equation by simultaneous policy update algorithm (SPUA). In SPUA a sequence of Lyapunov function equations (LFEs) are used in direct successive approximation of HJI equation resulting to one interactive loop instead of two loops. Gelerkin’s method is used to solve the LFEs and to develop Galerkin-based SPUA. Computationally efficient SPUA (CESPUA) based on Galerkin’s method was subsequently used to solve the LFE in each iterative loop of SPUA. The proposed guidance law does not require the information of the target accelerations and avoids control of relative velocity in the direction of line of sight. In comparison to sliding mode guidance law, the developed law utilizes less control energy, has smaller interception time, and offers better tracking performance against uncertain target accelerations.
Keywords: Nonlinear H_∞ control theory, modified polar coordinate, Hamilton-Jacobi-Isaacs equation, simultaneous policy update algorithm, Lyapunov function equation, Galerkin’s method