Predictive control with mean derivative based neural euler integrator dynamic model

Abstract

Neural networks can be trained to get internal working models in dynamic systems control schemes. This has usually been done designing the neural network in the form of a discrete model with delayed inputs of the NARMA type (Non-linear Auto Regressive Moving Average). In recent works the use of the neural network inside the structure of ordinary differential equations (ODE) numerical integrators has also been considered to get dynamic systems discrete models. In this paper, an extension of this latter approach, where a feed forward neural network modeling mean derivatives is used in the structure of an Euler integrator, is presented and applied in a Nonlinear Predictive Control (NPC) scheme. The use of the neural network to approximate the mean derivative function, instead of the dynamic system ODE instantaneous derivative function, allows any specified accuracy to be attained in the modeling of dynamic systems with the use of a simple Euler integrator. This makes the predictive control implementation a simpler task, since it is only necessary to deal with the linear structure of a first order integrator in the calculations of control actions. To illustrate the effectiveness of the proposed approach, results of tests in a problem of orbit transfer between Earth and Mars and in a problem of three-axis attitude control of a rigid body satellite are presented.<br>Redes neurais podem ser treinadas para obter o modelo de trabalho interno para esquemas de controle de sitemas dinâmicos. A forma usual adotada é projetar a rede neural na forma de um modelo discreto com entradas atrasadas do tipo NARMA (Non-linear Auto Regressive Moving Average). Em trabalhos recentes a utilização de uma rede neural inserida em uma estrutura de integração numérica tem sido também considerada para a obtenção de modelos discretos para sistemas dinâmicos. Neste trabalho, uma extensão da última abordagem é apresentada e aplicada em um esquema de controle não-linear preditivo (NPC), com uma rede feed forward modelando as derivadas médias em uma estrutura de integrador numérico de Euler. O uso de uma rede neural para aproximar a função de derivadas médias, em vez da função de derivadas instantâneas do sistema dinâmico ODE, permite que qualquer precisão desejada na modelagem discreta de sistemas dinâmicos possa ser realizada, com a utilização de um simples integrador Euler, tornando a implementação do controle preditivo uma tarefa mais simples, uma vez que ela somente necessitará lidar com a estrutura linear de um integrador de primeira ordem na determinação das ações de controle. Para ilustrar a efetividade da abordagem proposta, são apresentados resultados dos testes em um problema de transferência de órbitas Terra/Marte e em um problema de controle de atitude em três eixos de satélite comportando-se como corpo rígido

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“…The term Euler Neural Networks will appear for the first time in Tasinaffo [4]. Thus, in references Tasinaffo [13] and [15][16][17][18][19] where it is read the "mean derivatives methodology" it can be understood as a synonym for Euler Neural Networks. In Tasinaffo [4] a universal numerical integrator it is mathematically defined.…”

“…In Tasinaffo & Rios Neto [15] a brief description of the Euler Neural Networks can be found, with problems for application in Aerospace Engineering. In Tasinaffo & Rios Neto [16] the Euler Neural Networks are applied in a predictive control structure proving its efficiency and applicability in Control Theory. There is still no application of Euler Neural Networks in adaptive control structures nor in IMC (Internal Model Control) structures.…”

“…Before 1997 there are many papers involving only high order numerical integrators and many other works involving only universal approximations of functions, but articles combining these two mathematical concepts does not exist at all. The application of these universal integrators in Control Theory can be wide and very promising, although there are only three articles in this respect (see [12,16,21]). The first theoretical discussion about the possibility of using universal numerical integrators in Control is presented in Rios Neto [21].…”

“…The first theoretical discussion about the possibility of using universal numerical integrators in Control is presented in Rios Neto [21]. References Tasinaffo & Rios Neto [12,16] are already able to present practical experiments. Comparing references Tasinaffo & Rios Neto [12,16] it is easy to see that the control policy, estimated for particular problems involving Aerospace Engineering, is noisier in the mean derivatives methodology than in the instantaneous derivatives methodology.…”

Three-Axis Stabilized Geostationary Satellite Attitude Control Using Neural Predictive Algorithms

“…A neural predictive control scheme, using Kalman filter algorithm (Silva and Rios Neto, 1999, 2000, 2001, Tasinaffo and Rios Neto, 2007) is applied to a geosynchronous satellite attitude control problem. One case of great interest is related with the design of a double gimbaled momentum wheel attitude control system employed in the three-axis stabilization of a satellite attitude in geostationary orbit.…”