Optimal control of batch electrochemical reactor using K–L expansion

Abstract

A control vector parameterization approach using the Karhunen–Loéve (K–L) expansion for optimal control is presented. Optimal control profiles at different initial conditions are represented by a truncated K–L expansion and the optimal control is thus transformed into a parametric optimization with the K–L coefficient(s) as the optimization variable(s). Closed-loop optimal control therefore becomes feasible because the number of optimization variables is minimized. The presented approach is demonstrated on a batch electrochemical reactor in which reduction of oxalic acid glyoxalic acid is carried out under conditions with known or unknown disturbance, or electrode deactivation. The closed-loop control with the K–L expansion outperforms the open-loop optimal control with very little computational effort.