Robust adaptive estimation in the competitive chemostat

Abstract

In this paper, the problem of state estimation of a bioreactor containing a single substrate and several competing species is studied. This scenario is well-known as the competition model, in which multiple species compete for a single limiting nutrient. Considering the total biomass to be the only available measurement, the challenge is to estimate the concentration of the whole state vector. To achieve this goal, the estimation scheme is built by the coupling of two estimation techniques: an asymptotic observer, which depends solely on the operating conditions of the bioreactor, and a finite-time parameter estimation technique, which drops the usual requirement of the persistence of excitation. The presented methodology achieves the estimation of each competing species and a numerical example illustrates the intended application.

A Simplified Algorithm for Setting the Observer Parameters for Second-Order Systems with Persistent Disturbances Using a Robust Observer

“…In the monitoring and control of biological and biochemical processes, it is crucial to have real-time knowledge of variables such as the concentrations of biomass, products or reactants; the growth rate of microorganisms; and the substrate consumption rate [1][2][3][4]. Online knowledge of the substrate uptake rate is needed for the application of automatic control [4], whereas online knowledge of the specific growth rate (µ) is usually required in the following cases: (i) in automatic control with the biomass concentration as the output [5]; (ii) in automatic control with µ as the output (see [6,7]); (iii) in the maximization of growth rate via an extremum seeking controller [8]; (iv) in the maximization of the gaseous outflow rate via an extremum seeking controller [9].…”

“…Online knowledge of the substrate uptake rate is needed for the application of automatic control [4], whereas online knowledge of the specific growth rate (µ) is usually required in the following cases: (i) in automatic control with the biomass concentration as the output [5]; (ii) in automatic control with µ as the output (see [6,7]); (iii) in the maximization of growth rate via an extremum seeking controller [8]; (iv) in the maximization of the gaseous outflow rate via an extremum seeking controller [9]. The concentrations and reaction rates can be estimated by using state observers combined with the measurement of some state variables, and a known mass balance model for the measured states [1,[10][11][12]. Control design for multi-agent systems is another active area of observer design.…”