This paper presents an adaptive extremum seeking control scheme for a class of nonlinear distributed parameter systems. It addresses the real time optimization of parallel chemical reactions that occurs in a tubular reactor with uniform distributed feed described by a set of hyperbolic partial differential equations for which we assume limited knowledge of the kinetics. An adaptive learning technique is introduced to design a seeking algorithm that drives the system states to the unknown setpoint that maximizes the value of an objective function. Lyapunov’s stability theorem is used in the design of the extremum seeking controller structure and the development of the parameter learning laws.
Cougnon, P., Dochain, D., Guay, M., & Perrier, M. (2005). Real-Time Optimization of a Tubular Reactor with Distributed Feed. A I Ch E Symposium Series, 1, 1-6. https://hdl.handle.net/2078.5/62892 (Original work published 2005)