  Analysis and synthesis of safety-critical autonomous systems are carried out
using models which are often dynamic. Two central features of these dynamic
systems are parameters and unmodeled dynamics. This paper addresses the use of
a spectral lines-based approach for estimating parameters of the dynamic model
of an autonomous system. Existing literature has treated all unmodeled
components of the dynamic system as sub-Gaussian noise and proposed parameter
estimation using Gaussian noise-based exogenous signals. In contrast, we allow
the unmodeled part to have deterministic unmodeled dynamics, which are almost
always present in physical systems, in addition to sub-Gaussian noise. In
addition, we propose a deterministic construction of the exogenous signal in
order to carry out parameter estimation. We introduce a new tool kit which
employs the theory of spectral lines, retains the stochastic setting, and leads
to non-asymptotic bounds on the parameter estimation error. Unlike the existing
stochastic approach, these bounds are tunable through an optimal choice of the
spectrum of the exogenous signal leading to accurate parameter estimation. We
also show that this estimation is robust to unmodeled dynamics, a property that
is not assured by the existing approach. Finally, we show that under ideal
conditions with no unmodeled dynamics, the proposed approach can ensure a
$\tilde{O}(\sqrt{T})$ regret, matching existing literature. Experiments are
provided to support all theoretical derivations, which show that the spectral
lines-based approach outperforms the Gaussian noise-based method when unmodeled
dynamics are present, in terms of both parameter estimation error and Regret
obtained using the parameter estimates with a Linear Quadratic Regulator in
feedback.

Systems and Control;Machine Learning;Systems and Control;Optimization and Control;Machine Learning