arXiv subjects

Yacouba Simpore

Publications and source records attributed to Yacouba Simpore.

6 recordsLinked to original sources

arXiv2026

Boundary null controllability of weakly coupled structurally damped beams

We prove boundary null controllability in any positive time for a finite system of Euler--Bernoulli beams with possibly non-diagonalizable coupling. For $0<\rho<2$, a Fourier--Jordan reduction yields a vector moment problem with polynomial--exponential modes. Under the Fattorini--Hautus condition, global spectral non-collision, and nonvanishing modal transfer factors, a suitably estimated block-biorthogonal family produces an $H^2$ boundary control. Geometric multiplicities of the coupling matrix determine the minimal control dimension, and Jordan-block lengths determine the degrees of the generalized moments. At $\rho=2$, an exact heat-system reduction gives the same result for $A=A^*\geq0$, despite the time-differential linkage of the reduced boundary inputs.

math.OC↗

arXiv2026

Kalman structure and observability for transport systems

We study observability and controllability for constant-coefficient first-order hyperbolic systems on the real line when only part of the state is observed or controlled. Even when the Kalman rank condition holds, the usual $L^2(\mathbb R)^N$-observability estimate may fail because some components are detected only through the dynamics. We show that the Kalman structure determines the appropriate observability estimate. A component that becomes visible after $k$ algebraic steps is measured at low Fourier frequencies with a weight of order $|\xi|^{2k}$ in the Fourier variable. This yields a natural Kalman-adapted observation space for the system. We also prove localized observability for diagonalizable systems on observation sets with uniformly bounded gaps and, separately, extend the whole-line construction to systems with real spectrum and Jordan blocks.

math.OC↗

arXiv2025

Global stabilization and emergence tracking via aquatic control in an age-structured mosquito model

This paper presents an age-structured, non-autonomous logistic model describing the aquatic and adult stages of the dynamics of malaria-vector mosquitoes. We propose a biological control strategy targeting the aquatic compartment and implement a tracking control for its emergence. A feedback control law guarantees stabilization of the emergent population density, specifically the global asymptotic stability of the logistic model. Additionally, a feedforward controller combined with feedback is introduced to steer the emergent density toward a time-varying reference trajectory. The analytical findings are corroborated and illustrated by numerical simulations.

math.AP↗

arXiv2025

Stabilization by Harvesting in Age-Structured Trophic Networks

We propose and analyze a nonlinear age-structured multi-species model that serves as a unifying framework for ecological and biotechnological systems in complex environments (microbial communities, bioreactors, and others). The formulation incorporates nonlocal intra- and interspecific interactions modulated by environmental covariates. Under general assumptions on mortality, reproduction rates, and interaction kernels, we establish existence, uniqueness, and positivity of solutions. We illustrate the model's practical relevance along two lines. First, multi-species examples, notably a non-transitive (cyclic) competition model, for which we show that, under the model assumptions, a control applied to a single species can achieve global stabilization of the system. Second, the population dynamics of malaria-vector mosquitoes, for which we develop two control strategies (biological and genetic). In the biological-control scenario, we prove global asymptotic stability of the aquatic compartment by constructing an explicit Lyapunov function. Numerical simulations validate the theoretical results and compare the effectiveness of the proposed strategies in reducing vector density and malaria transmission.

math.AP↗

arXiv2024

Birth control and turnpike property of Lotka-McKendrick models with diffusion

In this paper, we study the turnpike property in age structured population dynamics with birth control. These models describe the temporal evolution of one or more populations, incorporating age dependence and spatial structure. To this end, we first establish the null controllability of the system: we prove that for any T > A and any initial datum in L2(Omega x (0,A)), the population can be driven to zero using control functions that are spatially localized in time but act only at age a = 0. We then show that although this control is initially applied only at birth, it can be reformulated as a distributed control, and we demonstrate that the resulting control operator is admissible in the state space. Thus, to prove the turnpike property we combine our null controllability results with Phillips' theorem on exponential stability to design a suitable dichotomy transformation based on solutions of the algebraic Riccati and Lyapunov equations. Finally, we present numerical examples that substantiate our analytical findings.

math.OC↗

arXiv2022

Controllability and Positivity Constraints in Population Dynamics with age, size Structuring and Diffusion

In this article, we consider the infinite dimensional linear control system describing the Population Models Structured by Age, Size, and Spatial Position. The control is localized in the space variable as well as with respect to the age and size. For each control support, we give an estimate of the time needed to control the system to zero. We prove the null controllability of the model, using a technique avoids the explicit use of parabolic Carleman estimates. Indeed, this method combines final-state observability estimates with the use of characteristics and with $L^{\infty}$ estimates of the associated semigroup.

math.OC↗