Adaptive FRIT-based Recursive Robust Controller Design Using Forgetting Factors

TL;DR

This paper tackles the instability and degraded performance of adaptive FRIT (A-FRIT) under non-PE conditions by introducing two forgetting strategies: directional forgetting (DF) and exponential resetting (ER). DF preserves positive definiteness by decomposing the information matrix and forgetting only a rank-1 component, while ER introduces a target information matrix $R_{\infty}$ to stabilize updates when PE is absent, both enabling reliable online tuning without model identification. The methods are validated on a highly nonlinear, hysteretic artificial muscle, demonstrating improved robustness to load changes and target-trajectory variations compared with traditional EF-based approaches. The results show that DF-based A-FRIT achieves higher control performance with lower sensitivity to forgetting-factor choices, making the approach practical for time-varying systems without requiring prior experimentation.

Abstract

Adaptive FRIT (A-FRIT) with exponential forgetting (EF) has been proposed for time-varying systems to improve the data dependence of FRIT, which is a direct data-driven tuning method. However, the EF-based method is not a reliable controller because it can cause significant degradation of the control performance and instability unless the persistent excitation (PE) condition is satisfied. To solve this problem, we propose a new A-FRIT method based on directional forgetting (DF) and exponential resetting that can forget old data without instability regardless of the PE condition. To confirm the effectiveness of the proposed method, we applied it to artificial muscle control with strong asymmetric hysteresis characteristics and evaluated its robust performance against load changes during the experiment. The experimental results show that the proposed method based on DF achieves high control performance and is robust against changes in the characteristics and/or target trajectory. The proposed method is also practical because it does not require system identification, model structure, or prior experimentation.

Figures (12)

• Figure 1: Block diagram of the adaptive FRIT algorithm
• Figure 2: Experimental circuit
• Figure 3: Experimental equipment
• Figure 5: Comparative control performance of FF-based A-FRIT with forgetting factor $\mu=0.99$ for staircase square reference
• Figure 6: Evaluation results using box plots based on the MAE of the tracking error between the reference output and displacement before and after controller parameter tuning (number of each trial experiment: 10 times)

Theorems & Definitions (2)

• Remark 1
• Remark 2