The Lurie problem and its relationships with artificial neural networks and alzheimer-like disease.

• Ano de defesa: 2021
• Autor(a) principal: Pinheiro, Rafael Fernandes
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Alzheimer disease; Análise µ; Controle robusto; DK-iteration; Doença de Alzheimer; Hopfield network; Incertezas paramétricas; Iteração DK; Lurie problem; Parametric uncertainty; Problema de Lurie; Redes de Hopfield; Redes neurais; Robust control; µ-analysis
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/3/3139/tde-10022022-115037/

In this thesis, studies are presented that provide new sufficient conditions for the analysis of the absolute stability of Lurie type systems for the Single-Input-Single-Output (SISO) and Multiple-Input-Multiple-Output (MIMO) cases. From these new conditions obtained, controller designs for Lurie type systems are developed and applied to artificial neural networks. The results presented are based on the H control theory, using the mixed-sensitivity technique (S/KS/T) and the µ-analysis and synthesis technique. In addition, conditions for time-delay systems are also obtained. In the application, it is presented the model of a neuropathology that simulates memory loss using Hopfield networks in continuous time, which is called Alzheimer-like disease. Then, the developed controller, based on the theory of this work, is applied to correct the problem of memory failure. Examples are presented to illustrate the theory and simulations are performed to validate and show the effectiveness of the results.