Optimal Steady-State Regulator Design for a Class of Nonlinear Systems With Arbitrary Relative Degree

In this article, we consider the regulator design problem for a class of uncertain multi-input–multioutput (MIMO) nonlinear systems with arbitrary relative degree. The objective is to regulate the output of the nonlinear system to an optimal steady state that solves a constrained optimization problem, without computing the optimal solution in advance. By embedding saddle-point dynamics, both state and output-feedback-based regulators are proposed and the resulting closed-loop systems are modeled in standard singularly perturbed forms. By invoking the singular perturbation analysis, exponential stability is established under some regularity condition. Compared with the existing methods, the proposed regulators can deal with a class of nonlinear systems with uncertainties and arbitrary relative degree. Furthermore, the current results can include some recent works on the distributed optimization problem as special cases. Finally, the effectiveness of the proposed methods is validated through numerical simulations.