Volterra series models are attractive for use in model-based control of nonlinear processes because they are direct extensions of linear impulse response models commonly used in process control. However, a limitation in their use is the fact that higher than second-order nonlinearities and/or multi-input multi-output Volterra models involve very large numbers of parameters. Here we address the problem with a parameter reduction method that utilizes a Laguerre basis function expansion of the Volterra kernels and orthogonal regression analysis for the determination of the dominating terms in the model. The conditions under which a nonlinear system can be approximated by a Volterra−Laguerre model are investigated. The technique is then applied to the identification of a 3 × 3 third-order nonlinear model for a simulated model IV fluid catalytic cracking unit.

Differentiable interface to FEniCS for JAX using dolfin-adjoint/pyadjoint - IvanYashchuk/jax-fenics-adjoint