Faux-Riccati Synthesis of Nonlinear Observer-Based Compensators for Discrete-Time Nonlinear Systems

Pseudo-linear models of nonlinear systems use either a state-dependent coefficient or the Jacobian of the vector field to facilitate the use of Riccati techniques. In this paper we use the state-dependent Riccati equation (SDRE) and the forward propagating Riccati equation (FPRE) with pseudo-linear models to construct nonlinear observer-based compensators for output-feedback control of nonlinear discrete-time systems. While attractive due to their simplicity and potentially wide applicability, these techniques remain largely heuristic. The goal of this paper is thus to present numerical experiments to assess the performance of these "faux" Riccati techniques on representative nonlinear systems. The goal is to compare the performance of SDRE and FPRE when used with either a state-dependent coefficient or the Jacobian of the vector field. Stabilization and performance are considered, along with integral control for step command following