The extension of the gray-box controller to handle more general classes of nonlinear dynamical systems involves adapting the controller's design to accommodate the specific characteristics of the system. For systems with non-differentiable steady-state maps, the controller can be modified to work with subgradients or subdifferentials instead of gradients. This adjustment allows the controller to handle the non-smoothness of the steady-state map and still make informed decisions based on the available information.
Similarly, for systems with non-smooth objective functions, the gray-box controller can be enhanced to incorporate techniques from nonsmooth optimization. This may involve using subgradients or subdifferentials of the objective function to guide the optimization process. By incorporating these non-smooth elements into the controller's update rules, it can effectively navigate the optimization landscape and converge to optimal solutions even in the presence of non-smoothness.
Overall, the extension of the gray-box controller to handle more general classes of nonlinear dynamical systems involves adapting its algorithms and methodologies to accommodate the specific challenges posed by non-differentiable steady-state maps and non-smooth objective functions.