Noureddine Elalami

A feedback control law to stabilise a harvested fish population system

In this paper, we consider the problem of stabilising a continuous fish population system via a state feedback control. The model considered is structured in n age classes and includes a non-linear stock-recruitment relationship. In our case, the variation of the fishing effort is used as a control term, the age classes as states and the quantity of captured fish per unit of effort as a measured output. The back stepping approach is employed to stabilise the studied system around a reference equilibrium point. Explicit expression of a bounded fishing effort and a Lyapunov function are given. An example is tested to illustrate the applicability of the proposed technique.

A SUFFICIENT CONDITION OF A POLYNOMIAL FISH POPULATION SYSTEM TO BE STABLE

In this paper, we use Lyapunov approach to study the stability of an exploited fish population system. The model considered is structured in n age classes and includes a nonlinear polynomial stock-recruitment relationship. Lyapunov candidate functions is investigated and sufficient conditions for global asymptotic stability of the studied polynomial system are proposed to allow computational implementation. The results obtained extend our previous study focusing on the solution to the same problem solved using other tools of control engineering. The advantage of the proposed approach is that the derived conditions proving the stability of the studied systems can be presented as in inequality in general and feasibility tests. The obtained results are tested by numerical examples.

Multimodel software sensor for a harvested fish population system

This paper deals with the problem of software sensor (state estimation) to study the continuous age structured model of a harvested fish population, in order to get an estimation of the biomass of fishes by age class. In our case the fishing effort is considered as a control term, the age classes as a states and the quantity of captured fish as a measured output. The continuous non-linear model is first represented by a Takagi-Sugeno multimodel. Next, we develop a technique for designing a multimodel software sensor (called also observer) corresponding to this system and show its asymptotic convergence. The design conditions are given in linear matrix inequalities (LMI) terms which can be solved efficiently using existing numerical tools. The simulation results demonstrate the effectiveness of the proposed method.

Output feedback Takagi Sugeno controller for a continuous fish population system

The aim of this paper is to study the problem of control for a fishery fuzzy system model by using an output feedback controller, in order to regulate the stock states around a non-trivial equilibrium. In our case, the continuous fishery model is considered, where the effort is used as a control term, the age classes as a states and the quantity of captured fish per unit of effort as a measured output. The continuous non-linear model is first represented by a Takagi Sugeno model. Next, we develop a technique for designing an output feedback control law which globally stabilises this fuzzy system model. A design method for constructing the output controller is given. A numerical simulation example is given to show the potential of the proposed techniques.

Multimodel robust observer for an uncertain fish population model

In this paper, a new method is proposed to design an observer for a nonlinear and uncertain system describing a continuous stage structured model of a harvested fish population. The aim is to get an estimation of the biomass of fishes by stage class. In the studied model the fishing effort is considered as a control term, the stage classes as states and the quantity of captured fish as a measured output. A Takagi-Sugeno multimodel first represents the uncertain non-linear model. Next, we develop a technique for designing a multimodel observer corresponding to this system, which attenuates the effect of modelling uncertainties and measurement noise on the state estimation. The design conditions are given in linear matrix inequalities (LMIs) terms that can be solved efficiently using existing numerical tools. The validity of the proposed method is illustrated by the simulation results.