Optimal Steady-State Regulation by State Feedback

This article formulates the optimal steady-state regulation (OSSR) problem. In addition to asymptotic stability and regulation, the problem includes a cost on maintaining steady-state inputs and outputs to controllers contributing to regulation, contrasting with standard optimal steady-state problems that only include a cost on the steady-state inputs and outputs of the plant. Motivated by applications in neuroscience, we develop a two-timescale adaptive control architecture to solve a specific instance of the OSSR problem for the case of two control modules: an adaptive internal model and a state feedback. The correctness of the design is proved using two-timescale averaging analysis.