Recursive least squares with domain-driven variable-direction forgetting

Recursive least squares (RLS) algorithm assumes persistent excitation; but this condition is rarely fulfilled in closed-loop systems, where control performance has higher priority over persistent excitation. Variable-directional forgetting (VDF) partly mitigates the problem by confining forgetting to a low-dimensional subspace, thereby averting parameter divergence when the excitation is not persistent. Nevertheless, in this paper we argue that the VDF is sub-optimal: (i) it may forget the entire covariance matrix under rank-deficient excitation, and (ii) it introduces an additional tuning parameter that complicates system design.To overcome these drawbacks, a recursive least squares with domain-driven directional forgetting (RLS-3DF) is developed. Instead of minimizing the squared error over discrete samples, RLS-3DF minimizes the expected squared error over an operating region of the input domain, a region where the user wants the model to be accurate. This continuous-domain formulation, inspired by the separation of validity functions and local parameters in Takagi-Sugeno fuzzy models, decouples the influence of sampling distribution from the accuracy requirement. The resulting algorithm retains information along non-excited directions and does not introduce any additional hyper-parameters.The results look promising, as RLS-3DF improves RLS-VDF across the board by at least 20%, even under conditions that satisfy persistent excitation, which is the most surprising and encouraging result.

• Publication year

  2025

• Venue

  IEEE International Conference on Fuzzy Systems

• Publication date

  2025-07-06

• Fields of study

  Computer Science, Engineering

• Identifiers
  DOI 10.1109/FUZZ62266.2025.11152228
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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