A New Method for Initial Parameters Optimization of Guided Projectiles

A new algorithm was developed for the initial parameters optimization of guided projectiles with multiple constraints. Due to the relationship between the analytic guidance logic and state variables of guided projectiles, the Radau pseudospectral method was used to discretize the differential equations including control variables and state variables with multiple constraints into series algebraic equations that were expressed only by state variables. The initial parameter optimization problem was transformed to a nonlinear programming problem, and the sequential quadratic programming algorithm was used to obtain the optimal combinations of initial height and range to target for the final velocity of guided projectiles maximum with constraints. Comparing with the appropriate initial conditions solved by Monte Carlo method and the flight characteristics solved by integrating the original differential equations in the optimal initial parameters computed by the new algorithm, the feasibility of new algorithm was validated. 1. Introduction The initial parameter optimization problem of guided projectiles with multiple constraints is considered. In addition to the constraints on its terminal position coordinates, the projectile must also impact the target from a specified direction with the required circular error probable (CEP) and make sure the impact velocity maximum. Presently, several studies are conducted for developing the guidance logic with multiple constraints [1, 2] and searching the launch acceptable region (LAR) of a guided bomb, while the initial conditions are known [3, 4]. However, a few studies pay attention to the initial parameters optimization for the guided projectiles with multiple constraints. The appropriate parameters are calculated based on different combinations of initial conditions (height above sea level, velocity, and path angles) by searching method to find out the largest LAR, but they are not optimal conditions [5]; the indirect method and direct method both are called calculative method which transforms the parameters optimization to the optimal control problem. Indirect method based on the Pontryagin maximum principle works out the analytical optimal control logic to obtain the optimal index for the guided projectiles in known initial conditions, for instance, maximum impact velocity or least energy [6, 7]; direct method based on pseudospectral method discretizes the equations of motion to obtain the numerical optimal control law for making parameters optimal with constraints [8, 9]. Now, when the analytical guidance logic