Adaptive local tracking of a temperature profile in tubular reactor with partial measurements

In this work, a local constrained adaptive output feedback is presented for a class of exothermic tubular reactors models described by a nonlinear partial differential equations. The considered output is the measured temperature in a fixed zone of the reactor to regulate the temperature throughout the reactor to a ball with radius λ (arbitrarily small) centered at the fixed temperature profile. For a given measurement zone with length given in terms of the desired profile and λ and for initial temperature in a fixed domain, it is shown that the tracking error through the reactor tends asymptotically to a ball of arbitrary prescribed radius λ > 0, centered at the given temperature profile. Numerical simulations have been performed to illustrate the performance of the proposed approach.