Parametric uncertainty and disturbance attenuation in the suboptimal control of a non‐linear electrochemical process

The optimal control of the hydrogen evolution reactions is attempted for the regulation and change of set-point problems, taking into account that model parameters are uncertain and I/O signals are corrupted by noise. Bilinear approximations are constructed, and their dimension eventually increased to meet accuracy requirements with respect to the trajectories of the original plant. The current approximate model is used to evaluate the optimal feedback through integration of the Hamiltonian equations. The initial value for the costate is found by solving a state-dependent algebraic Riccati equation, and the resulting control is then suboptimal for the electrochemical process. The bilinear model allows for an optimal Kalman–Bucy filter application to reduce external noise. The filtered output is reprocessed through a non-linear observer in order to obtain a state-estimation as independent as possible from the bilinear model. Uncertainties on parameters are attenuated through an adaptive control strategy that exploits sensitivity functions in a novel fashion. The whole approach to this control problem can be applied to a fairly general class of non-linear continuous systems subject to analogous stochastic perturbations. All calculations can be handled on-line by standard ordinary differential equations integration software. Copyright © 2007 John Wiley & Sons, Ltd.