LIP6 1999/017
- Thesis
Méthodes Connexionnistes pour la Commande des Systèmes Non Linéaires:
Application à la Régulation des Rivières - A. Toudeft
- 206 pages - 12/08/1998- document en - http://www.lip6.fr/lip6/reports/1999/lip6.1999.017.ps.gz - 1,800 Ko
- Contact : Zahia.Guessoum (at) nulllip6.fr
- Ancien Thème : APA
- Keywords : Neural Networks, Nonlinear Control, Connexionnist Learning Control, Adaptive Control, System Modelisation Using Neural Networks, Varying Time-Delay Systems, Non-Minimum Phase Systems, Regulation of Water Delivery Systems.
- Publisher : Valerie.Mangin (at) nulllip6.fr
This thesis deals with the nonlinear systems control problem using neural networks. The complexity of the stability and convergence analysis has held up the development of a general framework to solve this problem.
To take advantage of the neural networks capabilities without complicating the stability analysis, we have proposed a neuro-adaptive approach combining an open loop neural network controller, to deal with the nonlinearities, and a closed loop linear adaptive controller, to handle the perturbations.
The approach has been developed step by step and experimented on a simulated model of a river. The later is a nonlinear non-minimum phase system with a varying time-delay and submitted to perturbations. The approach can however be applied in a general context.
We have first proposed an adaptive control system using one linear neuron with one input and a bias. By reformulating the Widrow-Hoff rule using linear transfer functions, we found an on-line adjustment law for the adaptation rate to achieve a linearization by adaptation of the control system. This linearization allows to adaquately cope with the perturbations acting on a linear process corresponding to a river in a stationary state.
We have then put in a preminent position the ability of the neural networks to learn the varying time-delay characteristic of the nonlinear process.
To control the process, we have first trained a neural network to implement an open lopp controller. Since the process is a non-minimum phase system, we were obliged to propose and compare several methods to obtain a satisfactory controller.
To handle the perturbations, we have added a closed loop linear adaptive controller in parallel to the neural network open loop controller. Our experiments have shown the validity of this approach and we have proposed a preliminary stability analysis. The constraints of the analysis need to be made more flexible and the robustness of the approach must be evaluated.
Finally, we have proposed several variants of the distal in space learning approach. The theoretical analysis of these variants has shown their usefulness.
To take advantage of the neural networks capabilities without complicating the stability analysis, we have proposed a neuro-adaptive approach combining an open loop neural network controller, to deal with the nonlinearities, and a closed loop linear adaptive controller, to handle the perturbations.
The approach has been developed step by step and experimented on a simulated model of a river. The later is a nonlinear non-minimum phase system with a varying time-delay and submitted to perturbations. The approach can however be applied in a general context.
We have first proposed an adaptive control system using one linear neuron with one input and a bias. By reformulating the Widrow-Hoff rule using linear transfer functions, we found an on-line adjustment law for the adaptation rate to achieve a linearization by adaptation of the control system. This linearization allows to adaquately cope with the perturbations acting on a linear process corresponding to a river in a stationary state.
We have then put in a preminent position the ability of the neural networks to learn the varying time-delay characteristic of the nonlinear process.
To control the process, we have first trained a neural network to implement an open lopp controller. Since the process is a non-minimum phase system, we were obliged to propose and compare several methods to obtain a satisfactory controller.
To handle the perturbations, we have added a closed loop linear adaptive controller in parallel to the neural network open loop controller. Our experiments have shown the validity of this approach and we have proposed a preliminary stability analysis. The constraints of the analysis need to be made more flexible and the robustness of the approach must be evaluated.
Finally, we have proposed several variants of the distal in space learning approach. The theoretical analysis of these variants has shown their usefulness.