170,052 research outputs found
Optimal resource allocation for spatiotemporal control of invasive species
No full textControlling and planning the removal of invasive species are topics of outmost importance in management of natural resources because of the severe ecological damages and economic losses caused by non-native alien species. Optimal management strategies often rely on coupling population dynamics models with optimization procedures to achieve an effective allocation of limited resources for removing invasive species from hosting ecosystems. We analyse a parabolic optimal control model to simulate the best spatiotemporal strategy for the removal of the species when a budget constraint is applied. The model also predicts the species spread under the control action. We improve the capability of the model to reproduce realistic scenarios by introducing an advection term in the state equation. That allows to model the action of external forces, like currents or winds, which might bias dispersal in certain directions. The analytical properties of the model are discussed under suitable boundary conditions. As a further original contribution, we introduce a novel numerical procedure for approximating the solution reducing the computational costs in view of its implementation as a support decision tool. Then we test the approach by simulating the spread and the control of a hypothetical invasive plant in the territory of the Italian Sardinia island. To reproduce the anisotropy of the diffusion we include the effect of the altitude in the habitat suitability of the species. (c) 2022 Elsevier Inc. All rights reserved
I media digitali come dimensione educativa comunitaria
No full textLe potenzialità delle tecnologie digitali per sperimentare con le scuole secondarie di secondo grado un percorso di esplorazione e conoscenza del territorio in senso storico e socio-culturale, utilizzando forme comunicative e logiche tipiche della comunicazione digitale in una prospettiva di sviluppo di consapevolezza critica e competenza relazion
Exponential Lawson integration for nearly Hamiltonian systems arising in optimal control
No full textWe are concerned with the discretization of optimal control problems when a Runge–Kutta scheme is selected for the related
Hamiltonian system. It is known that Lagrangian’s first order conditions on the discrete model, require a symplectic partitioned
Runge–Kutta scheme for state–costate equations. In the present paper this result is extended to growth models, widely used in
Economics studies, where the system is described by a current Hamiltonian. We prove that a correct numerical treatment of the
state–current costate system needs Lawson exponential schemes for the costate approximation. In the numerical tests a shooting
strategy is employed in order to verify the accuracy, up to the fourth order, of the innovative procedure we propose.We are concerned with the discretization of optimal control problems when a Runge Kutta scheme is selected for the related Hamiltonian system. It is known that Lagrangian's first order conditions on the discrete model, require a symplectic partitioned Runge Kutta scheme for state costate equations. In the present paper this result is extended to growth models, widely used in Economics studies, where the system is described by a current Hamiltonian. We prove that a correct numerical treatment of the state current costate system needs Lawson exponential schemes for the costate approximation. In the numerical tests a shooting strategy is employed in order to verify the accuracy, up to the fourth order, of the innovative procedure we propose. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved
Numerical methods based on Gaussian quadrature and continuous Runge-Kutta integration for optimal control problems
No full textThis paper provides a numerical approach for solving optimal
control problems governed by ordinary differential equations. Continuous
extension of an explicit, fixed step-size Runge-Kutta scheme is
used in order to approximate state variables; moreover, the objective
function is discretized by means of Gaussian quadrature rules. The resulting
scheme represents a nonlinear programming problem, which can
be solved by optimization algorithms. With the aim to test the proposed
method, it is applied to different problems.This paper provides a numerical approach for solving optimal control problems governed by ordinary differential equations. Continuous extension of an explicit, fixed step-size Runge-Kutta scheme is used in order to approximate state variables; moreover, the objective function is discretized by means of Gaussian quadrature rules. The resulting scheme represents a nonlinear programming problem, which can be solved by optimization algorithms. With the aim to test the proposed method, it is applied to different problems. © Springer-Verlag 2004
Direct optimization using Gaussian quadrature and continuous Runge-Kutta methods: application to an innovation diffusion model
No full textIn the present paper the discretization of a particular model
arising in the economic field of innovation diffusion is developed. It consists
of an optimal control problem governed by an ordinary differential
equation.We propose a direct optimization approach characterized by an
explicit, fixed step-size continuous Runge-Kutta integration for the state
variable approximation. Moreover, high-order Gaussian quadrature rules
are used to discretize the objective function. In this way, the optimal
control problem is converted into a nonlinear programming one which is
solved by means of classical algorithms.In the present paper the discretization of a particular model arising in the economic field of innovation diffusion is developed. It consists of an optimal control problem governed by an ordinary differential equation. We propose a direct optimization approach characterized by an explicit, fixed step-size continuous Runge-Kutta integration for the state variable approximation. Moreover, high-order Gaussian quadrature rules are used to discretize the objective function. In this way, the optimal control problem is converted into a nonlinear programming one which is solved by means of classical algorithms
Coupling quadrature and continuous Runge–Kutta methods for optimal control problems
No full textThis article deals with the numerical solution of optimal control problems for ordinary differential
equations. The approach is based on the coupling between quadrature rules and continuous Runge–
Kutta solvers, and it lies in the framework of direct optimization methods and recursive discretization
techniques. The analysis of discrete solution accuracy has been carried out and coupling criteria
are established to have global methods featured by a given accuracy order. Consequently, numerical
schemes are built up to high orders. The effectiveness of the proposed schemes has been validated on
several test problems arising in the field of economic applications. The search for optimal solutions has been performed by standard
algorithms in Matlab environment.This article deals with the numerical solution of optimal control problems for ordinary differential equations. The approach is based on the coupling between quadrature rules and continuous Runge-Kutta solvers, and it lies in the framework of direct optimization methods and recursive discretization techniques. The analysis of discrete solution accuracy has been carried out and coupling criteria are established to have global methods featured by a given accuracy order. Consequently, numerical schemes are built up to high orders. The effectiveness of the proposed schemes has been validated on several test problems arising in the field of economic applications. Results have been compared with the ones by classical Runge-Kutta methods, in terms of single function evaluations and average CPU time of the optimization process. The search for optimal solutions has been performed by standard algorithms in Matlab environment
Da Scenario a Sceneggiatura: Nuove Potenzialità per la Didattica di Ausilio ai Disabili
No full textNumerical solution of infinite-horizon optimal control problems based on quadrature and Runge-Kutta methods
No full textOur goal consists in providing an accurate numerical solution to optimal control problems with infinite time horizon. The procedure deals with a direct approach based on quadrature for the objective function discretization and explicit Runge-Kutta methods for the state variable approximation. The resulting algorithm performance is validated and compared with other approaches developed in the literature by solving a test model arising from the economic field
Exponential Runge-Kutta integrators for modelling Predator-Prey interacttions
No full textSpatially explicit models consisting of reaction-diffusion partial differential equations are considered in order to model prey-predator interactions, since it is known that the role of spatial processes reveals of great interest in the study of the effectsof habitat fragmentations on biodiversity. As almost all of the realistic models in biology, these models are nonlinear and their solution is not known in closed form. Our aim is approximating the solution itself by means of exponential Runge-Kutta integrators. Moreover, we apply the shift-and-invert Krylov approach in order to evaluate the entire functions needed for implementing the exponential method. This numerical procedure reveals to be very efficient in avoiding numerical instability during the simulation, since it allows us to adopt high order in the accuracy.Spatially explicit models consisting of reaction-diffusion partial differential equations are considered in order to model prey-predator interactions, since it is known that the role of spatial processes reveals of great interest in the study of the effects of habitat fragmentation on biodiversity. As almost all of the realistic models in biology, these models are nonlinear and their solution is not knwon is closed form. Our aim is approximating the solution itself by means of exponential Runge-Kutta integrators. Moreover, we apply the shift-and-invert Krylov approach in order to evaluate the entire functions needed for implementing the exponential method. This numerical procedure reveals to be very efficient in avoiding numerical instability during the simulation, since it allows us to adopt high order in the accuracy
Runge-Kutta Discretizations of Infinite Horizon Optimal Control Problems with Steady-State Invariance
No full textDirect numerical approximation of a continuous-time infinite horizon control problem, requires to recast the
model as a discrete-time, finite-horizon control model. The quality of the optimization results can be heavily degraded if
the discretization process does not take into account features of the original model to be preserved. Restricting their attention
to optimal growh problems with a steady state, Mercenier and Michel in [1] and [2], studied the conditions to be imposed for
ensuring that discrete first-order approximation models have the same steady states as the infinite-horizon continuous-times
counterpart. Here we show that Mercenier and Michel scheme is a first order partitioned Runge-Kutta method applied to the
state-costate differential system which arises from the Pontryagin maximum principle. The main consequence is that it is
possible to consider high order schemes which generalize that algorithm by preserving the steady-growth invariance of the
solutions with respect to the discretization process. Numerical examples show the efficiency and accuracy of the proposed
methods when applied to the classical Ramsey growth model
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