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Optimal state-feedback controllers, capable of changing between differentobjective functions, are advantageous to systems in which unexpected situationsmay arise. However, synthesising such controllers, even for a single objective,is a demanding process. In this paper, we present a novel and straightforwardapproach to synthesising these policies through a combination of trajectoryoptimisation, homotopy continuation, and imitation learning. We use numericalcontinuation to efficiently generate optimal demonstrations across severalobjectives and boundary conditions, and use these to train our policies.Additionally, we demonstrate the ability of our policies to effectively learnfamilies of optimal state-feedback controllers, which can be used to changeobjective functions online. We illustrate this approach across two trajectoryoptimisation problems, an inverted pendulum swingup and a spacecraft orbittransfer, and show that the synthesised policies, when evaluated in simulation,produce trajectories that are near-optimal. These results indicate the benefitof trajectory optimisation and homotopy continuation to the synthesis ofcontrollers in dynamic-objective contexts.

Learning Dynamic-Objective Policies from a Class of Optimal Trajectories