  Parameter estimation is crucial for modeling, tracking, and control of
complex dynamical systems. However, parameter uncertainties can compromise
system performance under a controller relying on nominal parameter values.
Typically, parameters are estimated using numerical regression approaches
framed as inverse problems. However, they suffer from non-uniqueness due to
existence of multiple local optima, reliance on gradients, numerous
experimental data, or stability issues. Addressing these drawbacks, we present
a Bayesian optimization framework based on Gaussian processes (GPs) for online
parameter estimation. It uses an efficient search strategy over a response
surface in the parameter space for finding the global optima with minimal
function evaluations. The response surface is modeled as correlated surrogates
using GPs on noisy data. The GP posterior predictive variance is exploited for
smart adaptive sampling. This balances the exploration versus exploitation
trade-off which is key in reaching the global optima under limited budget. We
demonstrate our technique on an actuated planar pendulum and safety-critical
quadrotor in simulation with changing parameters. We also benchmark our results
against solvers using interior point method and sequential quadratic program.
By reconfiguring the controller with new optimized parameters iteratively, we
drastically improve trajectory tracking of the system versus the nominal case
and other solvers.
