DATA-DRIVEN PRONTO iteratively estimates local linearized dynamics from perturbed closed-loop experiments, solves an LQR subproblem with those estimates, and provably converges to a neighborhood of the optimal solution whose size shrinks with the exploration dither amplitude.
On Sufficient Richness for Linear Time-Invariant Systems
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Persistent excitation (PE) is a necessary and sufficient condition for uniform exponential parameter convergence in several adaptive, identification, and learning schemes. In this article, we consider, in the context of multi-input linear time-invariant (LTI) systems, the problem of guaranteeing PE of commonly-used regressors by applying a sufficiently rich (SR) input signal. Exploiting the analogies between time shifts and time derivatives, we state simple necessary and sufficient PE conditions for the discrete- and continuous-time frameworks. Moreover, we characterize the shape of the set of SR input signals for both single-input and multi-input systems. Finally, we show with a numerical example that the derived conditions are tight and cannot be improved without including additional knowledge of the considered LTI system.
citation-role summary
background 1
citation-polarity summary
fields
eess.SY 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
DATA-DRIVEN PRONTO: a Model-free Solution for Numerical Optimal Control
DATA-DRIVEN PRONTO iteratively estimates local linearized dynamics from perturbed closed-loop experiments, solves an LQR subproblem with those estimates, and provably converges to a neighborhood of the optimal solution whose size shrinks with the exploration dither amplitude.