Prescribed-Time and Hyperexponential Concurrent Learning with Partially Corrupted Datasets: A Hybrid Dynamical Systems Approach

TL;DR

This paper presents a hybrid dynamical systems approach to develop concurrent learning algorithms capable of achieving prescribed-time or hyperexponential convergence rates, even with partially corrupted datasets and switching data sources.

Contribution

It introduces a novel class of concurrent learning algorithms with dynamic gains that ensure flexible convergence rates and robustness against data corruption and switching datasets.

Findings

Achieves convergence faster than any exponential rate.

Guarantees uniform global ultimate boundedness despite disturbances.

Ultimate bound decreases as measurement noise and data corruption diminish.

Abstract

We introduce a class of concurrent learning (CL) algorithms designed to solve parameter estimation problems with convergence rates ranging from hyperexponential to prescribed-time while utilizing alternating datasets during the learning process. The proposed algorithm employs a broad class of dynamic gains, from exponentially growing to finite-time blow-up gains, enabling either enhanced convergence rates or user-prescribed convergence time independent of the dataset's richness. The CL algorithm can handle applications involving switching between multiple datasets that may have varying degrees of richness and potential corruption. The main result establishes convergence rates faster than any exponential while guaranteeing uniform global ultimate boundedness in the presence of disturbances, with an ultimate bound that shrinks to zero as the magnitude of measurement disturbances and corrupted data decreases. The stability analysis leverages tools from hybrid dynamical systems theory, along with a dilation/contraction argument on the hybrid time domains of the solutions. The algorithm and main results are illustrated via a numerical example.