An approximate optimal ballistic intercept guidance law

Development of efficient guidance laws for ballistic missile interceptions remains a challenge. The guidance problem is characterized by a set of nonlinear dynamical equations describing the translational motion of the interceptor vehicle. The application of a perturbation approximation results in a guidance law implementable with current or near-future on-board computing capability. The development of the guidance law begins with the assumption that certain forces such as thrust and gravity dominate the aerodynamic forces. The ratio of the atmospheric scale height to the radius of the Earth is used as a bookkeeping parameter; the Euler-Lagrange equations are expanded and grouped by powers of the parameter. Unfortunately, if the control does not appear in the dominant forces, the resulting zeroth-order optimization problem may not have a solution that meets all of the constraints. Techniques for circumventing this problem have been developed. The resulting approximate optimal guidance law has been tested and compared with solutions produced by a numerical optimization technique. The real-time guidance law produces trajectories that meet the end constraints and display a cost degradation of less than one percent from the optimum.<>