Robust stabilization of competing species in the chemostat

Abstract

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.

State observer design for bilinear Persidskii systems

“…The system (6) includes the generalized Persidskii systems studied in [6], [12], [11] (the first line in ( 6)), but also additional bilinear terms multiplied by the state components (the second line). The motivation for considering this class is that it encapsulates some models of interest, which have been studied both in the context of observer design and of stabilization [5], [3].…”

“…Example III.1. The following model describes the bacterial growth of two distinct species inside a chemostat with a single limiting substrate [5]:…”

“…Moreover, this class of models has been found valuable in representing many physical and biological phenomena, and therefore, it has been studied from many viewpoints, including that of IOS-stability [12]. In this paper, we consider a more significant generalization of this class of systems, motivated by biological and physical examples [8], [5], [3], where some new classes of nonlinearities are taken into account, in particular allowing for the addition of bilinear cross-products. *This work was partially supported by the Hauts-de-France Region, France.…”

H∞ Control for the Nonlinear Markov Networked Control System in the Presence of Data Packet Loss and DoS Attacks via Observer

“…Te mode of the system under consideration is shown in Figure 2. Te data packet dropout in the S-C channel is shown in Figure 3, and the data packet dropout in the C-A channel is exhibited in (1) Set R max as the maximal iteration number, and let c � c 0 (2) Obtain a feasible solution (P 0 i , Y 0 i , K 0 , L 0 ) satisfying ( 23) and (31), and let l � 0 (3) Settle the optimization issue bellow: Min tr(􏽐 g i�1 P l i Y i + Y l i P i ) such that ( 27) and (40) (4) Set P l i � P i , Y l i � Y i , K l � K, L l � L (5) while iterations number <R max do (6) if (27) and ( 28) hold, then (7) c � c − μ, l � l + 1, go to step 3 (8) else (9) l � l + 1, go to step 3 (10) end if (11) end while (12) if c < c 0 , then (13) c min � c + μ (14) else (15) No solution can be obtained within R max (16) end if ALGORITHM 1: Computing steps of ( 24) and (25). As can be seen from Figure 3, the probability of data packet loss during the active attack period is signifcantly greater than that during the attack sleep period.…”

“…Te frst type is the deception attack, which destroys the system by inserting incorrect data or processing raw data. Te second type is the denial of service (DoS) attack, whose intent is to prevent intercourse between diferent system components, thereby degrading system functionality or destroying system stability [11][12][13]. DoS attacks are easy to implement.…”