Recent Results on Nonlinear, Optimal Regulation and Tracking: Theory and Applications

The topic of single or multiple objective, optimal control or design has been a very attractive and desirable feature for many dynamic and static systems such as aerospace, electrical, mechanical and robotics, nuclear and aerospace engineering. In particular, in dynamic optimization of nonlinear systems, recent research interest has been the nonlinear, optimal, feedback control using State-Dependent Riccati Equation (SDRE) arising in regulator and tracking problems. This topic can be thought of as the nonlinear counterpart of the most popular linear, quadratic regulator (LQR) based control design. This paper overviews the recent research results of the authors in the theory of the SDRE for regulation and tracking with applications to many engineering systems under deterministic and stochastic environments. Further, the paper presents some future research directions in the field.