Optimal Guidance Law Design with Overload Saturation via Adaptive Dynamic Programming and Policy Iteration

The optimal guidance problem with overload saturation problem is addressed in this paper by model-based policy iteration method. First of all, the guidance problem is formulated as an optimal control problem with constrained input, which is addressed by Adaptive dynamic programming (ADP) method. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the optimality of the solution to the equation is proved. Secondly, based on numerical method, an iteration policy is given to acquire the numerical optimal solution of the HJB equation. The admissibility of the solution of each iteration and the monotonicity of the value function are provided and two neural networks are given to approximate the solution in each iteration. Finally, a numerical example is given to verify the proposed method.