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This work addresses the problem of robust stabilization of the concentration of two different species competing for a single limiting substrate. This stabilization is performed by means of discontinuous feedback control laws that ensure coexistence of all species. The control laws are designed considering bounded uncertainties on the kinetic rates.

This work addresses the problem of robust output feedback model predictive control for discrete-time, constrained, linear parameter-varying systems subject to (bounded) state and measurement disturbances. The vector of scheduling parameters is assumed to be an unmeasurable signal taking values in a given compact set. The proposed controller incorporates an interval observer, that uses the available measurement to update the setmembership estimation of the states, and an interval predictor, used in the prediction step of the MPC algorithm. The resulting MPC scheme offers guarantees on recursive feasibility, constraint satisfaction, and input-to-state stability in the terminal set. Furthermore, this novel algorithm shows low computation complexity and ease of implementation (similar to conventional MPC schemes).

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.

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In this article, the problem of state estimation of a microbial consortium is discussed. This microbial consortium is composed of two strains, called producer and cleaner, in continuous culture. The producer strain grows by consuming glucose, while the cleaner grows by consuming the acetate excreted by the producer and toxifies the environment. Considering two available measurements, the total biomass and a fluorescent reporter, an observability analysis is cast and state estimators are proposed for each state component of this system. Although the system is shown to be detectable using solely the total biomass as measurement, the advantage of measuring the fluorescent reporter on the observer design is highlighted. A numerical experiment illustrates the methodology.

This work addresses the problem of robust stabilization of the concentrations of two different species of living organisms, which compete for a single limiting substrate in a bioreactor. This stabilization is performed using discontinuous feedback control laws that ensure the coexistence of all species. The control laws are designed considering bounded parametric uncertainties on the kinetic rates.