Real-time approximately optimal guidance and control

An approximately optimal real-time guidance methodology is developed and applied to several applications. Real-time operation is obtained by calculating the approximately optimal trajectory at each sample time. Sample times of a fraction of a second to perform the computations are generated. The optimal guidance problem necessary conditions are expanded using regular perturbation methods. The first two terms of this expansion show close agreement with the optimal solution. The zeroth-order term is characterized by being analytically integrable and is augmented with state jumps viewed as coarse numerical integration. The value of the initial Lagrange multipliers are obtained through iteration of this closed-form zeroth-order solution. The first-order corrections require numerical quadrature integration, but no iteration. This technique augments previous work in this area by including in the numerical solution the full terms in zeroth-order Lagrange multiplier necessary conditions instead of a truncated binomial expansion of the condition. Optimality of the solution with the control split between zeroth- and first-order terms is investigated.