Greedy Extremum Seeking Control with Applications to Biochemical Processes

Extremum seeking control is a subclass of adaptive control, aimed at steady-state optimization. In this paper we apply ideas from extremum seeking control to optimize the transient performance of processes displaying multiple time-scale behavior. The main motivation is the need to optimize biochemical reactors where the biomass growth is significantly slower than the metabolism and where it is of interest to optimize the substrate conversion during the extended periods of net biomass growth or decay. Essentially, by employing singular perturbations, we design a controller that optimizes the fast boundary layer of the system ensuring that the process output is maintained near its maximum during transients towards the steady-state. Similar to greedy methods in optimization theory, we show that the local optimization of the fast layer under certain conditions will provide convergence to the overall optimal steady-state. In particular, this will apply to the type of biochemical reactors that are of main concern in this paper. The proposed controller is demonstrated by application to a model of the CANON process used for nitrogen removal in wastewater treatment.