Robust adaptive dynamic programming for nonlinear control design

This paper presents a robust optimal controller design for unknown nonlinear systems from a perspective of robust adaptive dynamic programming (robust-ADP). The proposed methodology has several novel features. First, the class of nonlinear systems studied in the paper allows for the presence of dynamic uncertainties with unmeasured state and uncertain system order/dynamics. Second, in the absence of the dynamic uncertainty, the online policy iteration technique developed in this paper can be viewed as an extension of the existing ADP method to affine continuous-time nonlinear systems with completely unknown dynamics. Third, the theory of approximate/adaptive dynamic programming (ADP) is integrated for the first time with tools from modern nonlinear control theory, such as the nonlinear small-gain theorem, for robust optimal control design. It is shown that, with appropriate robust redesign, the robust-ADP controller asymptotically stabilizes the overall system. A practical robust-ADP-based online learning algorithm is developed in this paper, and is applied to the robust optimal controller design for a two-machine power system.