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This paper presents Gradient-based Iterative (GI) and Two-Stage Gradient-based Iterative (2S-GI) identification algorithms for the Controlled Auto-Regressive Moving Average (CARMA) form of a multivariable tumor model. The mathematical proof of the 2S-GI algorithm for multivariable CARMA systems is provided, demonstrating its effectiveness in parameter estimation. The step-by-step introduction of the algorithm facilitates further studies and implementation. A comprehensive comparison between the GI and 2S-GI algorithms is conducted, evaluating their performance in terms of convergence rate and estimation accuracy. The introduced multivariable tumor model serves as a testbed for the algorithms’ effectiveness. The results of the comparison, supported by simulated data, demonstrate the superiority of the 2S-GI algorithm in accurately estimating the parameters of the CARMA system. This research provides valuable insights into the application of gradient-based iterative algorithms in controlling multivariable tumor models, paving the way for improved control strategies in cancer treatment. [ABSTRACT FROM AUTHOR]

Since system identification is a substantial part of many control algorithms, attaining a suitable model is necessary. In this paper, as a novelty, six standard identification methods are used so as to identify the linear ARMA forms of the proposed, widely used model of stirred tank heater. We have chosen these six methods because these methods fit to our desire for the parameter estimation of the ARMA model and they are new and applicable for modeling of all fields of engineering and systems. Beyond that, the mathematics of these methods are so easy to apply and they provide enough data for identifying a wide variation of systems. Furthermore, these algorithms are brought up in a simple and concise manner and easy to implement. In addition, the mathematical form of the suggested stirred tank heater is presented. Furthermore, identification methods are compared in terms of some measures, such as rate of convergence and produced error. Finally, the effectiveness of the six presented identification methods for estimating the stirred tank heater model is illustrated. [ABSTRACT FROM AUTHOR]