Métodos neuronais para a solução da equação algébrica de Riccati e o LQR

• Ano de defesa: 2008
• Autor(a) principal: SILVA, Fabio Nogueira da
• Orientador(a): FONSECA NETO, João Viana da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Maranhão
• Programa de Pós-Graduação: PROGRAMA DE PÓS-GRADUAÇÃO EM ENGENHARIA DE ELETRICIDADE/CCET
• Departamento: DEPARTAMENTO DE ENGENHARIA DA ELETRICIDADE/CCET
• País: Brasil
• Palavras-chave em Português: Equação Algébrica de Riccati; Regulador Linear Quadrático; Redes Neuronais; Redes Neuronais Recorrentes; Redes Neuronais Diretas; Otimização; Controle
• Palavras-chave em Inglês: Algebraic Riccati Equation; Linear Quadratic Regulator; Neural Networks; Recurrent Neural Networks; Feedforward Neural Networks; Optimization; Control
• Área do conhecimento CNPq: Automação Eletrônica de Processos Elétricos e Industriais
• Link de acesso: http://tedebc.ufma.br:8080/jspui/handle/tede/1817

We present in this work the results about two neural networks methods to solve the algebraic Riccati(ARE), what are used in many applications, mainly in the Linear Quadratic Regulator (LQR), H2 and H1 controls. First is showed the real symmetric form of the ARE and two methods based on neural computation. One feedforward neural network (FNN), that de¯nes an error as function of the ARE and a recurrent neural network (RNN), which converts a constrain optimization problem, restricted to the state space model, into an unconstrained convex optimization problem de¯ning an energy as function of the ARE and Cholesky factor. A proposal to chose the learning parameters of the RNN used to solve the ARE, by making a surface of the parameters variations, thus we can tune the neural network for a better performance. Computational experiments related with the plant matrices perturbations of the tested systems in order to perform an analysis of the behavior of the presented methodologies, that are based on homotopies methods, where we chose a good initial condition and compare the results to the Schur method. Two 6th order systems were used, a Doubly Fed Induction Generator(DFIG) and an aircraft plant. The results showed the RNN a good alternative compared with the FNN and Schur methods.