Minimum time controller in a class of chemical reactors based on Lagrangian approach

The main goal of this work is the construction of a class of controller, which employs directly a Lagrangian formulation to resolve the classical brachistochrone problem, this allows to obtain an optimal controller which reaches in a minimum time the stabilization of an isothermal continuous stirred tank reactor, whose chemical kinetic model is based on the power law. The proposed methodology is compared with an input/output linearizing which achieve asymptotic and exponential closed-loop convergence, sliding-mode controller with a finite time convergence and an exact gradient optimal control to compare the time convergence performance. Numerical experiments show the satisfactory performance of the proposed controller, despite sustained disturbances in the concentration input feed.