Euler-Lagrange Optimal Control for Symmetric Projectiles

摘要

The linear theory model of a symmetric projectile is well suited to optimal control methods, especially the finite horizon linear optimal regulator. Using a nine-state linear model with gravity treated as an uncontrollable mode, necessary conditions for optimal-ity are derived. These conditions are solved closed-form using a matrix exponential of the Hamiltonian matrix multiplied by distance to go in calibers. Control is thus found without a reference trajectory. A second method allowing system parameters to vary with time is developed and compared. The time-varying Riccati equation is solved recursively backward in time and control at the current state is found without a reference trajectory. Performance is demonstrated on linear and non-linear plant models using forward mounted canards.