Aerospace systems are tasked with mission objectives that must be completed in the presence of various size, weight, power, fuel, and time constraints. As a result, optimal guidance and control methods are inherent and critical for the success of such missions. However, as high-performance systems stress nonlinear regimes and more flight systems benefit from greater autonomy, the development of optimal methods presents ever increasing challenges. Designing an optimal controller necessarily involves solving the Bellman (for discrete systems) or the Hamilton-Jacobi-Bellman (HJB) equations (for continuous systems). The HJB equations are a coupled set of nonlinear partial differential equations for which analytical solutions are difficult or impossible to find. As a result, typical solutions to the HJB are achieved backward in time through offline numerical integration. For some mission planning objectives in which time constraints are not as critical, such methods may continue to play an important role. However, for other mission scenarios, there is a present and growing need for online, forward-in-time, control policies.
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