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Regret Bounds for Adaptive Nonlinear Control | | Nicholas M. Boffi
; Stephen Tu
; Jean-Jacques E. Slotine
; | | Date: |
26 Nov 2020 | | Abstract: | We study the problem of adaptively controlling a known discrete-time
nonlinear system subject to unmodeled disturbances. We prove the first
finite-time regret bounds for adaptive nonlinear control with matched
uncertainty in the stochastic setting, showing that the regret suffered by
certainty equivalence adaptive control, compared to an oracle controller with
perfect knowledge of the unmodeled disturbances, is upper bounded by
$widetilde{O}(sqrt{T})$ in expectation. Furthermore, we show that when the
input is subject to a $k$ timestep delay, the regret degrades to
$widetilde{O}(k sqrt{T})$. Our analysis draws connections between classical
stability notions in nonlinear control theory (Lyapunov stability and
contraction theory) and modern regret analysis from online convex optimization.
The use of stability theory allows us to analyze the challenging
infinite-horizon single trajectory setting. | | Source: | arXiv, 2011.13101 | | Services: | Forum | Review | PDF | Favorites | |
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