Publication: Identificación, estimación y control de sistemas no-lineales mediante RGO
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1999
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2000-02-18
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Abstract
Se trata la identificación de sistemas, esto es: la estimación de modelos de sistemas dinámicos a partir de los datos observados. La estimación trata de evaluar y diseñar los estimadores de estado operando antes en un entorno estocástico. Se busca la mejora de la resolución de los problemas de identificación y estimación de estados de sistemas dinámicos no-lineales y el control adaptativo de los mismos. Se presenta un nuevo método híbrido para la optimización de funciones no lineales y no diferenciales que varían con el tiempo sin la utilización de demandas numéricas. Este método está basado en los Algoritmos Genéticos con una menor técnica de búsqueda que se ha llamado Optimización Genética Restringida. A partir de este algoritmo se presenta un método de altas prestaciones para la identificación de sistemas no lineales variables con el tiempo con modelos lineales y no lineales. Se presentan dos aplicaciones diferentes de estos métodos.
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The system identification deals with the problem of estimating modeis of dynamical systems from observed data. The estimation tries to evaluate and to design state estimators. The two of them are supposed to operate in a stochastic environment. In this thesis, It has been tried to improve the methods of identification and state estimation of non-linear dynamical systems and their adaptive control. A new optimization hybrid method of non-linear and non-differentiable, time varying functions without using numerical derivatives is presented. This is important because of noise. This method based on Genetic Algorithms introduces a new technique called Restricted Genetié Optimization (ROO). This optimization method unifies the thesis and due to the fact that it is a basic method, it can be applied to a lot of problems related with non-differentiable and time-varying functions. Based on this algorithm, a high performance method for the identification of non-linear, time-varying systems with linear and non-linear modeis, is presented. This method can be used on-line and in a closed loop. For this reason, it is well adapted to control. This method uses an on line identification algorithm that begins by calculating what ARX is the best adapted to the system. This way the order and the delay of the system are known. Then, an ARMAX that is used as a seed to start the RGO and to create a NARMAX model, is calculated. The RGO algorithm can describe a new non-linear estimator for filtering of systems with non-linear processes and observation modeis based on the RGO optimization. The simulation results are used to compare the performance of this method with EKF (Extended Kaiman Filter), IEKF (Iterated Extended Kaiman Filter), SNF (Second-order Non-linear Filter), SIF (Single-stage Iterated Filter) y MSF (Montecarlo Simulation Filter) with different levels of noise. When this method is applied to the state space identification a new method is obtained. This method begins by calculating an ARX and then uses RGO in order to improve the previous identification. This method is based on the fuil parametrization and balanced realizations. This way low sensitivity realizations are obtained and the structural issues of multivariable canonical parametrizations are circumvented. Two applications of this method are considered. The first application is the predictive control with RGO of the Twin Rotor MIMO System (TRMS), that is a laboratory set-up designed for control experiments. In certain aspects, its behaviour resembles that of a helicopter. From the control point of view, it exemplifies a high order non-linear system with significant cross-couplings. The second one is the robot localization based on different kind of sensor information. To fuse all the different information, an algorithm is necessary. In this case, it has been used an extension of the Kalman algorithm with RGO.
The system identification deals with the problem of estimating modeis of dynamical systems from observed data. The estimation tries to evaluate and to design state estimators. The two of them are supposed to operate in a stochastic environment. In this thesis, It has been tried to improve the methods of identification and state estimation of non-linear dynamical systems and their adaptive control. A new optimization hybrid method of non-linear and non-differentiable, time varying functions without using numerical derivatives is presented. This is important because of noise. This method based on Genetic Algorithms introduces a new technique called Restricted Genetié Optimization (ROO). This optimization method unifies the thesis and due to the fact that it is a basic method, it can be applied to a lot of problems related with non-differentiable and time-varying functions. Based on this algorithm, a high performance method for the identification of non-linear, time-varying systems with linear and non-linear modeis, is presented. This method can be used on-line and in a closed loop. For this reason, it is well adapted to control. This method uses an on line identification algorithm that begins by calculating what ARX is the best adapted to the system. This way the order and the delay of the system are known. Then, an ARMAX that is used as a seed to start the RGO and to create a NARMAX model, is calculated. The RGO algorithm can describe a new non-linear estimator for filtering of systems with non-linear processes and observation modeis based on the RGO optimization. The simulation results are used to compare the performance of this method with EKF (Extended Kaiman Filter), IEKF (Iterated Extended Kaiman Filter), SNF (Second-order Non-linear Filter), SIF (Single-stage Iterated Filter) y MSF (Montecarlo Simulation Filter) with different levels of noise. When this method is applied to the state space identification a new method is obtained. This method begins by calculating an ARX and then uses RGO in order to improve the previous identification. This method is based on the fuil parametrization and balanced realizations. This way low sensitivity realizations are obtained and the structural issues of multivariable canonical parametrizations are circumvented. Two applications of this method are considered. The first application is the predictive control with RGO of the Twin Rotor MIMO System (TRMS), that is a laboratory set-up designed for control experiments. In certain aspects, its behaviour resembles that of a helicopter. From the control point of view, it exemplifies a high order non-linear system with significant cross-couplings. The second one is the robot localization based on different kind of sensor information. To fuse all the different information, an algorithm is necessary. In this case, it has been used an extension of the Kalman algorithm with RGO.
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Sistemas dinámicos, Investigación operativa, Matemáticas