Deep subspace encoders for nonlinear system identification

Learning-based augmentation of physics-based models: an industrial robot use case

“…To improve upon the physics-only model, we compare several ways to augment the physics-based model with ANNs, particularly with multilayer perceptrons (MLPs) that have a residual connection (an additional linear layer directly between the inputs and outputs). We have implemented normalization of the input and output features to standard deviation σ = 1 and mean μ = 0, based on previous results discussed in Beintema et al (2023). As mentioned there, weight initialization methods such as Glorot and Bengio (2010) assume normalized inputs and outputs.…”

Observer-Based State Estimation for Recurrent Neural Networks: An Output-Predicting and LPV-Based Approach

“…with ∀Ψ, Ψ h x ∈ V H n , then, multiplying both sides of ( 21) on the left and on the right by diag{I, I, I, PZ −1 , PS −1 } and its transpose, respectively, and using the inequalities −PZ −1 P ≤ −2ρ 1 P + ρ 2 1 Z, −PS −1 P ≤ −2ρ 2 P + ρ 2 2 S, we can deduce that ( 12) is a sufficient condition for (21). We finish the proof.…”

“…For example, in most of the works mentioned above, the output states do not have a time delay or the size of the delay is limited to a small range, and a full-order observer is designed based on the measured output. In [21], during the identification of RNN models, a subspace encoder is co-estimated to reconstruct the state of the model from past input and output data. However, such an explicit form of an observer might run into difficulties if the state delay is not known, and needs an excessively large number of past input-output samples.…”