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This paper continues the STACS contribution by Diekert, Ushakov, and the author as well as the IJAC publication by the same authors. We extend the results published there in two ways. First, we show that the data structure of power circuits can be generalized to work with arbitrary bases q≥2. This results in a data structure that can hold huge integers, arising by iteratively forming powers of q. We show that the properties of power circuits known for q=2 translate to the general case. This generalization is non-trivial and additional techniques are required to preserve the time bounds of arithmetic operations that were shown for the case q=2. The extended power circuit model permits us to conduct operations in the Baumslag-Solitar group BS(1, q) as efficiently as in BS(1,2). This allows us to solve the word problem in the generalization H(1, q) of Higman's group in polynomial time. The group H(1, q) is an amalgamated product of four copies of the Baumslag-Solitar group BS(1, q) rather than BS(1,2) in the original group H= H(1,2). As a second result, we allow arbitrary numbers f≥4 of copies of BS(1, q), leading to an even more generalized notion of Higman groups H(1, q). We prove that the word problem of the latter can still be solved within the ${\mathcal {O}}(n^{6})$ time bound that was shown for H(1,2). [ABSTRACT FROM AUTHOR]

For SOC (state of charge) assessment techniques based on electrical circuit models, the parameters of the model are strongly biased by: battery aging, temperature, causing some errors in the estimation of the SOC. One approach to solve this problem is to update the model parameters constantly. We suggest a new algorithm VRLS (variable recursive least squares) to update the parameters of a 2-resistor-capacitor (RC) network and to estimate the output battery voltage. VRLS is compared to the recursive least squares (RLS) and the adaptive forgetting factor recursive least squares (AFFRLS) algorithms. For algorithm assessment, we utilized real experimental data conducted on the Samsung 18650-20R lithium-ion cell. The tests indicate that compared to RLS and AFFRLS methods, VRLS recorded a low distribution in the high error range, in addition to small predictive performance indicators (RMSE, MAE, and MAPE) in all tests, which implies that VRLS has a good parameter identification ability. [ABSTRACT FROM AUTHOR]