Abstract: A novel optimal guidance law is proposed for the terminal guidance with impact angle constraints by using the combination of the minimal principle and Gauss pseudospectral method. An impact angle coordinate system is defined with an coordinate axis in the direction of the desired impact angle, and the linear engagement kinematics is established using this coordinate system. The control system of missile is simplified into a first-order inertial system. The canonical equation is obtained via the minimal principle, and then translated into a set of algebraic equations by employing the Gauss pseudospectral method. According to the boundary conditions, an analytical solution is finally derived for the optimal guidance law with impact angle constraints without any integral process or solving the Riccati differential equation. Numerical simulations show that the proposed guidance law ensures the much fast convergence of impact angle to the reference line, and has smaller required terminal acceleration compared with other guidance laws. In addition, the proposed guidance law can easily tackle with the guidance problem with complex weighting matrices.

Key words: ordnance science and technology, impact angle constraint, optimal control, terminal guidance, minimal principle, indirect Gauss pseudospectral method