Self-Organizing Radial Basis Function Networks for Adaptive Flight Control

Abstract

The performance of nonlinear control algorithms such as feedback linearization and dynamic inversion is heavily dependent on the fidelity of the dynamic model being inverted. Incomplete or incorrect knowledge of the dynamics results in reduced performance and may lead to instability. Augmenting the baseline controller with approximators which utilize a parametrization structure that is adapted online reduces the effect of this error between the design model and actual dynamics. However, currently existing parameterizations employ a fixed set of basis functions that do not guarantee arbitrary tracking error performance. To address this problem, we develop a self-organizing parametrization structure that is proven to be stable and can guarantee arbitrary tracking error performance.

Bayesian Nonparametric Adaptive Control Using Gaussian Processes

“…However, while reducing the modeling error guarantees that the tracking error is reduced [6], [12], the opposite need not always be true. Therefore, techniques such as those in [40], [55], [58] do not guarantee that the center updates reduce the modeling error. Another limitation of traditional RBFN based MRAC methods is that they model the uncertainty as smooth deterministic function.…”

“…One way to overcome the limitation of fixed centers is to move and add/remove RBF centers to better capture the modeling uncertainty. Conforming to the traditional approach in MRAC, authors in [40], [55], [58] have proposed RBF center tuning rules that attempt to minimize the instantaneous tracking error. However, while reducing the modeling error guarantees that the tracking error is reduced [6], [12], the opposite need not always be true.…”

Nonparametric adaptive control using Gaussian Processes with online hyperparameter estimation

“…where Kt := K(Zt, Zt) over the basis set BV. The second term II k; +1 -k�+l K t -1 kZ'+l II is bounded above by Etol due to Algorithm l. Using Lemma 3 it follows that (24) • The bounded ness of the tracking error can now be proven.…”

“…Typically, it is assumed in the GP literature [13,19,25] that data is available in batch. In order to optimize the joint likelihood, as is common in the literature, multiple points must be used, so the gradient cannot be calculated at each time instant using only the current measurement as with RBFN [15,24,26]. Additionally, gradient calculations scale poorly with the number of data points, so one cannot use many points before losing online tractability.…”

“…Following the pioneering work by Sanner and Slotine [22], Radial Basis Function Networks (RBFNs) are perhaps the most widely used adaptive elements when a basis for the modeling uncertainty is unknown. However, if the system operates outside of the domain of the RBF kernel's centers [18], or if the bandwidth of the kernel is not correctly specified [15,24,26], the modeling error will be high and stability cannot be guaranteed globally.…”