develop a continuous-time optimal control model for allocating agricultural crop residues between bioenergy production and soil fertility restoration. The system includes a circular reinvestment channel: a portion of the accumulated bioenergy stock is reinvested to enhance soil fertility, thereby closing the loop between energy use and ecological regeneration. The dynamics are governed by a three-state system with a single allocation control. The objective is to maximize a discounted net benefit that accounts for energy revenue, soil value, and operational costs. We apply the Pontryagin Maximum Principle in current-value form to derive necessary optimality conditions and a bang-interior-bang control; no singular arc under our parameterization. Direct optimization confirms a quasi-turnpike phase and shows how the planning horizon and reinvestment efficiency shift switching times and interior duration. The results highlight the strategic role of energy reinvestment in sustainable residue management.
paper presents a theoretical investigation of an air pollution model formulated as a free boundary problem. The study examines the dynamics of pollutant dispersion in the atmosphere, where the boundaries of the polluted region are not fixed but evolve over time. Using advanced mathematical techniques and partial differential equations, we construct a model that accounts for various factors influencing air pollution, including emission sources, meteorological conditions, and chemical reactions. The incorporation of a free boundary framework provides a more realistic representation of pollutant spread and environmental interactions. To analyze the model, we employ the Friedman-Rubinstein integral representation method and apply the Banach contraction theorem to solve an equivalent nonlinear Volterra integral equation.
challenge with rehabilitation exoskeletons is the potential for reaching singular configurations, reducing efficiency. Additionally, paths generated for an exoskeleton may not always exhibit optimal manipulability and dexterity, unlike healthy humans who perform tasks with maximum manipulability. This paper considers a multi-degree-of-freedom model for the exoskeleton robot, deriving its kinematic and dynamic equations. The robot's kinematic manipulability is formulated based on the Jacobian, and Model Predictive Control (MPC) is employed for control. The novelty lies in incorporating the cost function related to the robot's kinematic manipulability alongside other cost functions within the MPC framework. Dynamic simulations evaluate this approach, showing that the manipulability criterion conflicts with tracking error. This research demonstrates that using the manipulability index as a constraint or part of the cost function in MPC can help prevent the robot from reaching singular points and enhance manipulability and dexterity in hand rehabilitation.
paper introduced a novel approach for resolving fractional partial differential equations. The time fractional nonlinear Burgers equation of order kappa was solved to illustrate the efficacy of the technique, where kappa is an element of (0, 1]. The quintic B-spline method facilitated spatial partitioning, while the finite difference method addressed the fractional Caputo derivative, which simulates anomalous diffusion processes influenced by memory effects. The proposed methods stability is demonstrated utilizing the von Neumann technique; it has been shown to be unconditionally stable. Additionally, a convergence study is shown, demonstrating that the approach exhibits uniform convergence of (gamma h4 + sigma (triangle eta 2)). We validated the methods correctness through numerical tests by comparing it with the exact solution and alternative numerical methods. Based on L2 and L infinity error norms, the quintic B-spline approach exhibits improved convergence rates and reduced computing costs.
This paper presents a numerical method for solving the second-kind Fredholm integral equations using the least squares approach via QR decomposition. The proposed technique employs Gaussian quadrature for numerical integration and efficiently applies QR decomposition for minimization. This strategy not only simplifies the implementation but also significantly enhances computational performance. A convergence analysis is provided, and several numerical examples demonstrate the accuracy and effectiveness of the method compared to traditional technique.
