Stable adaptive control with recurrent networks
While significant progress has been achieved in applications of static neural networks (NN) for control, these are limited to the case of linear systems. The output feedback control for nonlinear systems remains one of the outstanding problems which are, at present, actively researched. It is then a belief of the authors that recurrent NNs of Hopfield type have the potential to provide useful models for adaptive control of many nonlinear systems. The point is that if a dynamic neural model can be trained so that in some region its input-output behaviour is close to that of the unknown system, then one should be able to obtain some kind of equivalent information about the state of the unknown plant from the state of the NN. Here, a linearizing feedback control law for the network is computed analytically and applied to the plant while the parameters of the network are updated on-line. Such an approach can be classified as indirect adaptive control, as the parameters of the plant model are adapted and the control is computed on the current model, rather than directly adapting the controller's parameters. Then sufficient conditions for stability are derived for exponentially stable nonlinear plants. To validate the limitations of the assumptions made during the stability analysis, a simulation study is performed, including an induction motor case study. But in this case, a structural error is present. So the recurrent network is not able to provide a global model of the complex dynamics of the motor and parameter adjustments are required if the operating point of the machine changes significantly. The analysis of the structural error is, according to the authors, beyond the scope of the theoretical work presented in the paper. The other question is how such an approach would work in the case of a strongly unstable nonlinear plant. It seems the method used should not be applicable in such a case.
scientific article; zbMATH DE number 1389421