Optimal Steady-State Regulation of Nonlinear Systems: A Feedback Optimization Approach

Overview & Synopsis

This paper studies the optimal steady-state regulation problem for a class of nonlinear systems. The regulated output is required to track a trajectory that minimizes a steady-state cost depending on both the output and the exo-system. To characterize the desired steady-state behavior, we introduce a generalized regulator equation and develop a two-layer framework. The optimization layer generates the optimal reference online through a steady-state generator combined with gradient-feedback optimization dynamics, while the control layer employs backstepping to stabilize the plant and achieve the desired optimal steady-state regulation. Under suitable immersion and minimum-phase assumptions, global asymptotic stability is established.