  This study presents a policy optimisation framework for structured nonlinear
control of continuous-time (deterministic) dynamic systems. The proposed
approach prescribes a structure for the controller based on relevant scientific
knowledge (such as Lyapunov stability theory or domain experiences) while
considering the tunable elements inside the given structure as the point of
parametrisation with neural networks. To optimise a cost represented as a
function of the neural network weights, the proposed approach utilises the
continuous-time policy gradient method based on adjoint sensitivity analysis as
a means for correct and performant computation of cost gradient. This enables
combining the stability, robustness, and physical interpretability of an
analytically-derived structure for the feedback controller with the
representational flexibility and optimised resulting performance provided by
machine learning techniques. Such a hybrid paradigm for fixed-structure control
synthesis is particularly useful for optimising adaptive nonlinear controllers
to achieve improved performance in online operation, an area where the existing
theory prevails the design of structure while lacking clear analytical
understandings about tuning of the gains and the uncertainty model basis
functions that govern the performance characteristics. Numerical experiments on
aerospace applications illustrate the utility of the structured nonlinear
controller optimisation framework.
