Forschungsbericht 2009



LPV Control based on Neural State-space models

Institut: Regelungstechnik
Projektleitung: Prof. Dr. Herbert Werner
Stellvertretende Projektleitung: Dr.-Ing. (Obering.) Gerwald Lichtenberg
Mitarbeiter/innen: MSc. Hossam Seddik Abbas
Projektnummer: E-14.028
Laufzeit: 15.10.2005 - 30.09.2009
Finanzierung: Stipendium der ägyptischen Regierung


 

 Many nonlinear systems found in real life situations are almost linear in a limited region of the relevant state space, but exhibit saturation and other nonlinear phenomena more strongly when the state of the system gets outside this region. Modern control paradigms such as robust control synthesis methods typically deal with this by requiring a linear nominal (state-space) model plus some kind of residual model for the control design. Recent work in linear parameter varying (LPV) control  has taken this idea further, compensating for known parameter variations directly in the control design. In LPV control design this knowledge is employed to provide systematic gain scheduling in order to guarantee  stability and performance of the closed loop. One problem with these types of approaches, however, is that it can be difficult to obtain a suitable model to build the control design o. With the right choice of neuron functions, artificial neural networks such as multilayer perceptron (MLPs) have been shown to be able to model the kind of nonlinear system described above accurately. If the system states cannot be measured directly, an MLP can also provide a nonlinear state estimator based only on samples of in- and output. The idea is, training a MLP as a discrete nonlinear state space model of the plant and then separates the neural state-space model into a linear and nonlinear part in a manner suitable for the synthesis by writing the neural state-space model on a linear fractional transormation (LFT) form in a neoconservative way. The LFT formulation allows for a quasi-LPV description of a nonlinear system. In this case, the extracted nonlinearities define the parameter variation, and it is hence possible to exploit this information to make the LPV control synthesis methods are applied to design a nonlinear control law for this system. On the other hand, the discrete neural state-space model provides a suitable model to design a discrete LPV controller, which is more suitable for eal life implementation. This project tries to combine the use of the feed forward MLP neural networks with quasi-LPV control synthesis for control a nonlinear system by the method described above and then compare the system response in this case with its response when an LPV controller is designed based on a classical way to model the system.

Weitere Informationen zu diesem Forschungsprojekt können Sie hier bekommen.

 

Publikationen
  • E-14.189V

    H. Abbas, S. Chughtai, H. Werner: A Hybrid Gradient-LMI Algorithm for Solving BMIs in Control Design, Proceedings of the IFAC World Contress, Seoul, South Korea, 2008, pp 14319-14323 

  • E-14.186V

     N. Lachhab, H. Abbas, H. Werner: A Neural-Network Based Technique for Modelling and {LPV} Control of an Arm-Driven Inverted Pendulum, Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, 2008