# Adaptive Control By Regulation-Triggered Batch Least-Squares Estimation of Non-Observable Parameters

arXiv: https://arxiv.org/abs/1811.10833 · HTML: https://mlsanity.com/paper/1811.10833/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2018.

## Built on by (most cited first, 3 of 3)

- [Deep Learning of Delay-Compensated Backstepping for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2308.10501/) (2023)
- [Policy Gradient Adaptive Control for the LQR: Indirect and Direct Approaches](https://mlsanity.com/paper/2505.03706/) (2025)
- [Backstepping Neural Operators for 2× 2 Hyperbolic PDEs](https://mlsanity.com/paper/2312.16762/) (2023)

## Abstract (arXiv)

The paper extends a recently proposed indirect, certainty-equivalence, event-triggered adaptive control scheme to the case of non-observable parameters. The extension is achieved by using a novel Batch Least-Squares Identifier (BaLSI), which is activated at the times of the events. The BaLSI guarantees the finite-time asymptotic constancy of the parameter estimates and the fact that the trajectories of the closed-loop system follow the trajectories of the nominal closed-loop system ("nominal" in the sense of the asymptotic parameter estimate, not in the sense of the true unknown parameter). Thus, if the nominal feedback guarantees global asymptotic stability and local exponential stability, then unlike conventional adaptive control, the newly proposed event-triggered adaptive scheme guarantees global asymptotic regulation with a uniform exponential convergence rate. The developed adaptive scheme is tested to a well-known control problem: the state regulation of the wing-rock model. Comparisons with other adaptive schemes are provided for this particular problem.