Control Theory & Systems
Maha Mohsin Mohammed Ali; Mahmoud Mahmoudi; Majid Darehmiraki
Abstract
This study addresses the numerical solution of an optimal control problem governed by a fractional convection–reaction–diffusion partial differential equation. The approach utilizes Radial Basis Function–Partition of Unity (RBF-PU) methods combined with the Grünwald-Letnikov approximation ...
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This study addresses the numerical solution of an optimal control problem governed by a fractional convection–reaction–diffusion partial differential equation. The approach utilizes Radial Basis Function–Partition of Unity (RBF-PU) methods combined with the Grünwald-Letnikov approximation for fractional derivatives, which provides a fundamental extension of classical derivatives in fractional calculus. To enhance sparsity in the control strategy, an $L_2$ norm is integrated into the objective function, along with quadratic penalties to reduce deviations from the desired state. This hybrid formulation facilitates the effective management of spatially sparse controllers, relevant in many practical applications. The RBF-PU technique offers a flexible and efficient framework by partitioning the domain into overlapping subregions, applying local RBF approximations, and synthesizing the global solution with compactly supported weight functions. Numerical experiments demonstrate the accuracy and effectiveness of this method.
Rasoul Heydari Dastjerdi; Ghasem Ahmadi; Mahmood Dadkhah; Ayatollah Yari
Abstract
This paper presents a novel approach using artificial neural networks to solve the SEIR (Susceptible, Exposed, Infected, and Recovered) model of infectious diseases based on dynamical systems. Optimal control techniques are employed to determine a vaccination schedule ...
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This paper presents a novel approach using artificial neural networks to solve the SEIR (Susceptible, Exposed, Infected, and Recovered) model of infectious diseases based on dynamical systems. Optimal control techniques are employed to determine a vaccination schedule for a standard SEIR epidemic model. The multilayer perceptron is utilized to approximate the state and co-state functions of the SEIR model and to solve the optimal control problem by utilizing a nonlinear programming approach. By constructing a loss function and using Pontryagin's Minimum Principle (PMP) for the SEIR model, a minimization problem is defined, a minimization problem is defined, and the approximate solution of the Hamiltonian system is computed. This method is compared with the fourth-order Runge-Kutta method. The proposed approach's effectiveness is demonstrated through illustrative examples.
