Adaptive extremum-seeking control of convection-reaction distributed reactor with limited actuation

In this paper, we pose and solve an adaptive extremum control problem to optimize the productivity of a van de Vusse reaction taking place in a tubular reactor governed by a set of nonlinear hyperbolic partial differential equations. Estimation and control algorithms that take into account control input constraints are developed by using a Lyapunov-based procedure, ensuring stability and convergence under a persistency of excitation condition. Here, we assume that the temperature information along the reactor is the only available on-line measurement to estimate the unmeasured objective function at the reactor exit. Numerical application of the proposed method shows that the resulting feedback algorithm steers the system to its optimum using a non-distributed jacket temperature actuation. The time evolution of the cost function is compared with an idealized distributed version of the algorithm presented previously.