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arXiv · 2606.08344

Temperature control by a state-delay nash strategy: theory and experiments

César Adair Rodríguez Castro·Manuel Alejando Jímenez Lizarraga·Jorge Manuel Ortega Martínez·Omar Jacobo Santos Sánchez
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Abstract

This work expands the Nash equilibrium algorithm to those systems that have a state delay within the deterministic case, a Linear-Quadratic (LQ) type performance index with generalized cross terms is used, following the constructive approach on optimal control: first, propose the strategies form, close the loop and find the Cauchy solution; secondly, express the cost function according to those expressions; and finally use the Bellman equation as restrictions to find the strategies parameters. The stability of the closed loop is demonstrated. The algorithm is applied to a thermal prototype with an ESP32 micro-controller and its performance is compared with optimal PI controls inside two commercial/industrial PID controllers REX-C100.

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César Adair Rodríguez Castro, Manuel Alejando Jímenez Lizarraga, Jorge Manuel Ortega Martínez, Omar Jacobo Santos Sánchez. 2026-06-06. Temperature control by a state-delay nash strategy: theory and experiments. https://arxiv.org/abs/2606.08344

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