Indirect Optimal Control Bootstrapped via Suboptimal Policies

This paper presents a framework for numerical continuation that can transform a previously known, potentially suboptimal, control history into a minimum effort control history without needing to find the appropriate initial costate values for the known solution. This formulation is motivated by the fact that analytical and/or approximate solutions to aerospace control problems generally are significantly easier to compute compared to corresponding optimal trajectories for the same boundary conditions. Moreover, numerical methods for computing indirect optimal control solutions often greatly benefit from having an initial guess that is “close” to the optimal solution. For this reason, it is often desirable to produce a quickly computable approximate solution that can bootstrap an optimal control solution process. Salient to note here is that using an approximate solution as an initial guess for an indirect optimal control solver requires the user to find the appropriate initial costate values corresponding to the previously known control history, which is generally a nontrivial problem itself. The proposed algorithm provides a systematic framework for addressing this initial costate generation hurdle together with strong convergence properties. The methodology is applied and illustrated for a wide array of benchmark control problems.