Analysis of the Unscented Transform Controller for Systems with Bounded Nonlinearities

In this paper, we present an analysis of the Unscented Transform Controller (UTC), a technique to control nonlinear systems motivated as a dual to the Unscented Kalman Filter (UKF). We consider linear, discrete-time systems augmented by a bounded nonlinear function of the state. For such systems, we review 1-step and N-step versions of the UTC. Using a Lyapunov-based analysis, we prove that the states and inputs converge to a bounded ball around the origin, whose radius depends on the bound on the nonlinearity. Using examples of a fighter jet model and a quadcopter, we demonstrate that the UTC achieves satisfactory regulation and tracking performance on these nonlinear models.