Online Adaptive Identification of Switched Affine Systems Using a Two-Tier Filter Architecture with Memory

TL;DR

This paper introduces an online adaptive identification method for switched affine systems that uses a dual-layer filter with memory, enabling parameter convergence during active and inactive phases of subsystems.

Contribution

It proposes a novel memory bank and a new intermittent initial excitation condition to ensure exponential parameter convergence in switched affine systems.

Findings

Memory bank promotes learning during inactive phases.

Intermittent initial excitation guarantees exponential convergence.

Method effectively identifies switched affine system parameters online.

Abstract

This work proposes an online adaptive identification method for multi-input multi-output (MIMO) switched affine systems with guaranteed parameter convergence. A family of online parameter estimators is used that is equipped with a dual-layer low pass filter architecture to facilitate parameter learning and identification of each subsystem. The filters capture information about the unknown parameters in the form of a prediction error which is used in the parameter estimation algorithm. A salient feature of the proposed method that distinguishes it from most previous results is the use of a memory bank that stores filter values and promotes parameter learning during both active and inactive phases of a subsystem. Specifically, the learnt experience from the previous active phase of a subsystem is retained in the memory and leveraged for parameter learning in its subsequent active and inactive phases. Further, a new notion of intermittent initial excitation (IIE) is introduced that extends the previously established initial excitation (IE) condition to the switched system framework. IIE is shown to be sufficient to ensure exponential convergence of the switched system parameters.