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M. Soledad Aronna

Publications and source records attributed to M. Soledad Aronna.

At least 19 recordsLinked to original sources
arXiv2026

Host-Parasitoid Dynamics and Biological Control of the Sugarcane Borer

We investigate biological pest control strategies for the sugarcane borer Diatraea saccharalis through the combined action of two parasitoid species: the egg parasitoid Trichogramma galloi and the larval parasitoid Cotesia flavipes. We describe the population dynamics with a six-dimensional host-parasitoid model in which host-parasitoid interactions are represented through a Holling Type II functional response, extending previous models by coupling egg and larval stage dynamics and incorporating parasitism saturation observed in laboratory experiments. We characterize the equilibrium structure of the model and analyze the local stability of the extinction equilibrium. Bifurcation analysis reveals that, for a wide range of Holling parameters, the pest population exceeds the economic damage threshold, motivating the design of active control strategies. We formulate and compare three biological control approaches: open-loop optimal control, State-Dependent Riccati Equation (SDRE) feedback control, and impulsive feedback control based on Lyapunov arguments. We perform numerical simulations to show that all three strategies successfully keep the pest population below the economic damage threshold. The impulsive strategy, in particular, achieves effective suppression with substantially fewer parasitoid releases than the continuous approaches, making it the most practically viable option for field implementation.

math.OC↗
arXiv2026

A Novel Aggregated SIR Model for Spatial Epidemic Propagation

We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture the dynamics of disease spread across multiple interconnected cities or populated regions, while avoiding the high dimensionality and large parameter sets typical of network based or agent-based approaches. Instead of explicitly modeling individual locations or mobility networks, we introduce aggregate variables that describe whether the epidemic has not yet reached, is currently active in, or has already passed through different regions of the spatial domain. This formulation allows the model to reproduce key qualitative features observed in aggregated incidence data, such as prolonged plateaus and multiple infection waves arising from asynchronous local outbreaks. The resulting system consists of ordinary differential equations with a relatively small number of interpretable parameters, providing a tractable framework for analytical investigation and numerical simulation. Our approach offers a parsimonious alternative for studying spatially structured epidemic dynamics when only aggregated data are available or when model simplicity is essential.

math.NA↗
arXiv2025

Average Optimal Control of Uncertain Control-Affine Systems

This work studies optimal control problems of systems with uncertain, probabilistically distributed parameters to optimize average performance. Known as Riemann-Stieltjes, average, or ensemble optimal control, this kind of problem is crucial when parameter uncertainty matters. We derive necessary optimality conditions and characterize feedback controls for control-affine systems. Two scenarios are examined: known initial conditions (finite-dimensional case) and uncertain initial conditions (infinite-dimensional framework). The Pontryagin Maximum Principle is extended using a Hilbert space formulation.

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arXiv2025

On second order conditions for singular optimal control of port-Hamiltonian systems

We study nonlinear singular optimal control problems of port-Hamil-tonian (descriptor) systems. We employ general control-affine cost functionals that include as a special case the energy supplied to the system. We first derive optimality conditions for the case of ordinary differential equations with and without control bounds by applying the general theory to the specially structured port-Hamiltonian case, and show that this leads to elegant optimality conditions, in particular in the linear case. We then extend these results to classes of nonlinear port-Hamiltonian descriptor systems.

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arXiv2024

Dynamic Programming Principle and Hamilton-Jacobi-Bellman Equation for Optimal Control Problems with Uncertainty

We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and appear in the dynamics, in the terminal cost and in the initial condition, which yield an infinite-dimensional formulation. By stating the problem as an evolution equation in a Hilbert space, we show that the value function is the unique lower semi-continuous proximal solution of the Hamilton-Jacobi-Bellman (HJB) equation. Our approach relies on invariance properties and the dynamic programming principle.

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arXiv2023

Modeling and control of malaria dynamics in fish farming regions

In this work we propose a model that represents the relation between fish ponds, the mosquito population and the transmission of malaria. It has been observed that in the Amazonic region of Acre, in the North of Brazil, fish farming is correlated to the transmission of malaria when carried out in artificial ponds that become breeding sites. Evidence has been found indicating that cleaning the vegetation from the edges of the crop tanks helps to control the size of the mosquito population. We use our model to determine the effective contribution of fish farming practices on malaria transmission dynamics. The model consists of a nonlinear system of ordinary differential equations with jumps at the cleaning time, which act as impulsive controls. We study the asymptotic behaviour of the system in function of the intensity and periodicity of the cleaning, and the value of the parameters. In particular, we state sufficient conditions under which the mosquito population is eliminated or persists, and under which the malaria is eliminated or becomes endemic. We prove our conditions by applying results for cooperative systems with concave nonlinearities.

q-bio.PE↗
arXiv2021

First and Second Order Optimality Conditions for the Control of Fokker-Planck Equations

In this article we study an optimal control problem subject to the Fokker-Planck equation \[ \partial_t ρ- νΔρ- {\rm div } \big(ρB[u]\big) = 0. \] The control variable $u$ is time-dependent and possibly multidimensional, and the function $B$ depends on the space variable and the control. The cost functional is of tracking type and includes a quadratic regularization term on the control. For this problem, we prove existence of optimal controls and first order necessary conditions. Main emphasis is placed on second order necessary and sufficient conditions.

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arXiv2020

State constrained control-affine parabolic problems II: Second order sufficient optimality conditions

In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order sufficient conditions relying on the Goh transform. The appendix provides an example illustrating the applicability of our results.

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arXiv2020

State-constrained control-affine parabolic problems I: first and second order necessary optimality conditions

In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order necessary conditions relying on the concept of alternative costates and quasi-radial critical directions. The appendix provides an example illustrating the applicability of our results.

math.OC↗
arXiv2020

A model for COVID-19 with isolation, quarantine and testing as control measures

In this article we propose a compartmental model for the dynamics of Coronavirus Disease 2019 (COVID-19). We take into account the presence of asymptomatic infections and the main policies that have been adopted so far to contain the epidemic: isolation (or social distancing) of a portion of the population, quarantine for confirmed cases and testing. We model isolation by separating the population in two groups: one composed by key-workers that keep working during the pandemic and have a usual contact rate, and a second group consisting of people that are enforced/recommended to stay at home. We refer to quarantine as strict isolation, and it is applied to confirmed infected cases. In the proposed model, the proportion of people in isolation, the level of contact reduction and the testing rate are control parameters that can vary in time, representing policies that evolve in different stages. We obtain an explicit expression for the basic reproduction number $\mathcal{R}_0$ in terms of the parameters of the disease and of the control policies. In this way we can quantify the effect that isolation and testing have in the evolution of the epidemic. We present a series of simulations to illustrate different realistic scenarios. From the expression of $\mathcal{R}_0$ and the simulations we conclude that isolation (social distancing) and testing among asymptomatic cases are fundamental actions to control the epidemic, {and the stricter these measures are and the sooner they are implemented,} the more lives can be saved. Additionally, we show that people that remain in isolation significantly reduce their probability of contagion, so risk groups should be recommended to maintain a low contact rate during the course of the epidemic.

q-bio.PE↗
arXiv2019

A Higher-order Maximum Principle for Impulsive Optimal Control Problems

We consider a nonlinear system, affine with respect to an unbounded control $u$ which is allowed to range in a closed cone. To this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to $u$. This lack of coercivity gives the problem an {\it impulsive} character, meaning that minimizing sequences of trajectories happen to converge towards discontinuous paths. As is known, a distributional approach does not make sense in such a nonlinear setting, where, instead, a suitable embedding in the graph-space is needed. We provide higher order necessary optimality conditions for properly defined impulsive minima, in the form of equalities and inequalities involving iterated Lie brackets of the dynamical vector fields. These conditions are derived under very weak regularity assumptions and without any constant rank conditions.

math.OC↗
arXiv2019

Necessary conditions involving Lie brackets for impulsive optimal control problems

We obtain higher order necessary conditions for a minimum of a Mayer optimal control problem connected with a nonlinear, control-affine system, where the controls range on an m-dimensional Euclidean space. Since the allowed velocities are unbounded and the absence of coercivity assumptions makes big speeds quite likely, minimizing sequences happen to converge toward "impulsive", namely discontinuous, trajectories. As is known, a distributional approach does not make sense in such a nonlinear setting, where instead a suitable embedding in the graph space is needed. We will illustrate how the chance of using impulse perturbations makes it possible to derive a Higher Order Maximum Principle which includes both the usual needle variations (in space-time) and conditions involving iterated Lie brackets. An example, where a third order necessary condition rules out the optimality of a given extremal, concludes the paper.

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arXiv2017

Second order necessary and sufficient optimality conditions for singular solutions of partially-affine control problems

In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the initial and final values of the state. We investigate singular optimal solutions for this class of problems, for which we obtain second order necessary and sufficient conditions for weak optimality in integral form. We also derive Goh pointwise necessary optimality conditions. We show an example to illustrate the results.

math.OC↗
arXiv2016

Optimal control of PDEs in a complex space setting; application to the Schrödinger equation

In this paper we discuss optimality conditions for abstract optimization problems over complex spaces. We then apply these results to optimal control problems with a semigroup structure. As an application we detail the case when the state equation is the Schrödinger one, with pointwise constraints on the "bilinear" control. We derive first and second order optimality conditions and address in particular the case that the control enters the state equation and cost function linearly.

math.OC↗
arXiv2015

Second order analysis of control-affine problems with scalar state constraint

In this article we establish new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition.

math.OC↗
arXiv2015

Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control

The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of individuals carrying the Wolbachia parasite that need to be introduced into the natural population. The introduced mosquitoes are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human. In this study, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then use feedback control techniques to devise an introduction protocol which is proved to guarantee that the population converges to a stable equilibrium where the totality of mosquitoes carry Wolbachia.

q-bio.QM↗
arXiv2015

$\mathcal{L}^1$ limit solutions for control systems

For a control Cauchy problem $$\dot x= {f}(t,x,u,v) +\sum_{α=1}^m g_α(x) \dot u_α,\quad x(a)=\bar x, $$ on an interval $[a,b]$, we propose a notion of limit solution $x,$ verifying the following properties: i) $x$ is defined for $\mathcal{L}^1$ (impulsive) inputs $u$ and for standard, bounded measurable, controls $v$; ii) in the commutative case (i.e. when $[g_α,g_β]\equiv 0,$ for all $α,β=1,...,m$), $x$ coincides with the solution one can obtain via the change of coordinates that makes the $g_α$ simultaneously constant; iii) $x$ subsumes former concepts of solution valid for the generic, noncommutative case. In particular, when $u$ has bounded variation, we investigate the relation between limit solutions and (single-valued) graph completion solutions. Furthermore, we prove consistency with the classical Carathéodory solution when $u$ and $x$ are absolutely continuous. Even though some specific problems are better addressed by means of special representations of the solutions, we believe that various theoretical issues call for a unified notion of trajectory. For instance, this is the case of optimal control problems, possibly with state and endpoint constraints, for which no extra assumptions (like e.g. coercivity, bounded variation, commutativity) are made in advance.

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