Parametrized controller for non-canonical form nonlinear systems using neural networks

This paper presents a new study on parametrized controller for non-canonical form nonlinear systems using neural networks. Unlike commonly studied canonical form systems whose neural-network based approximations have explicit relative degrees and can be directly used to derive controller parameters, non-canonical form systems usually do not have such a feature, because neural-network based approximations of such systems are still in a non-canonical form. It is well-known that control of non-canonical form nonlinear systems involves reparametrization of system dynamics. As demonstrated in this paper, it is also the case for neural-network approximated non-canonical form systems. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparametrize such neural-network systems for control design and that such reparametrization can be realized using a relative degree formulation, a concept yet to be studied for general neural network systems. The paper then derives a parametrized controller structure for effective control of general non-canonical form neural network systems, as the baseline controller for adaptation. An illustrative example is presented with simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new control design method.