Journal of Optimization, Differential Equations and their Applications (JODEA - Dnipro National Universuty) / Журнал з оптимізації, диференціальних рівнянь та їх застосувань
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Determining the Strength of Structural Materials by Solving Inverse Problems of Thermoelasticity
Get PDFThe paper proposes a method for determining maximum thermoload from the temperature stress measured with a value by solving the inverse problem of thermoelasticity for canonical bodies. Determination of maximum thermoload is of significant practical importance when conducting non-destructive testing. It is important to regulate temperature and force loads, when thermostresses in structural elements will be achieved within permissible limits. For example, the tensile strength of the D16T material is exceeded at a heat flux of 6400 W/m2. This indicates the high heat resistance of the material D16T. To find values, the method of solving inverse problems of thermoelasticity was used. To obtain a stable and accurate solution to the inverse problem of thermoelasticity and thermoconductivity, the numerical finite element method and the Tikhonov method with the search for the regularization parameter are used. The Tikhonov method uses a stabilizing functional with a regularization parameter. The search of the regularizator is carried out using an algorithm for calculating the root of a nonlinear equation, which allows increasing the accuracy of results. The Tikhonov method has an error within 5%. The cost-effectiveness of the method lies in replacing complex and expensive experimental studies of objects with numerical experiments. The proposed methodology allows determining the loads at which it will be destroyed without bringing the object to destruction. Solving internal inverse problems of thermoelasticity is a complex and actual issue, especially in connection with the development of computers. This method applies to energy and aviation engineering facilities under high temperature and force loads
How Can We Manage Repairing a Broken Finite Vibrating String? Solutions to the Problem I
Get PDFThe current research deals with an initial-boundary value problem (IBVP) with the Dirichlet boundary conditions for the 1D homogeneous wave equation with discontinuous piece-wise constant coefficient previously formulated (JODEA, 31 (2) (2023), 89 – 114) to study various methods of solving the conjugate IBVPs for both parts of the string and matching the solutions to the IBVPs (‘repairing’ the string). Solving is based on applying the Laplace Transform, whereas one way of matching utilizes the energy rate equation. It has been shown that the LT inversion inevitably yields to a weak representation of the solution to the IBVP provided the initial and boundary functions of the problem are given in general rather than specific form
Convergence of Adaptive Algorithms for Equilibrium Problems in Hadamard Spaces
Get PDFIn this paper, we consider the equilibrium problems under the setting of Hadamard spaces. For an approximate solution of equilibrium problems, iterative adaptive two-stage proximal algorithms are proposed and studied. At each step of the algorithms, the sequential minimization of two special strongly convex functions should be done. Our self-adaptive algorithms do not calculate bifunction values at additional points and do not require knowledge of the bifunction’s Lipschitz constants. For pseudomonotone bifunctions of the Lipschitz type that are weakly upper semicontinuous in the first variable and convex and lower semicontinuous in the second variable, we prove convergence theorems about sequences generated by proposed algorithms. First, we show weak convergence of generated sequences to a solution of the equilibrium problem. Then we prove strong convergence of Halpern regularization of adaptive extraproximal algorithm. Also it is shown that proposed algorithms are applicable to variational inequalities with Lipschitz-continuous, sequentially weakly continuous and pseudo-monotone operators acting in Hilbert spaces
Global Attractors and Asymptotic Gain Property for Non-Autonomous Inclusion of Reaction–Diffusion Type
Get PDFWe investigate global resolvability and stability of attractors for parabolic inclusion with multi-valued interaction function of reaction-diffusion type and non-autonomous disturbances. For the class of L2-disturbances, we prove existence of global solutions in the phase space L2. In the class of translation-bounded disturbances we prove that obtained global solutions generate the family of multi-valued semiprocesses which possesses a uniform attractor. Finally, for L∞-disturbances we show that the global attractor of unperturbed system is stable w.r.t. disturbances in the asymptotic gain sense
Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors
Get PDFNew types of neural ordinary differential equations (NODE) with power nonlinearities are considered. For these NODE systems, new conditions for the existence of homoclinic and heteroclinic orbits are found. In the future, the implementation of these conditions guarantees the existence of chaotic attractors in the mentioned NODE systems
Drone Swarm Energy Management
Get PDFThis note presents an analytical framework for decision-making in drone swarm systems operating under uncertainty, based on the integration of Partially Observable Markov Decision Processes (POMDP) with Deep Deterministic Policy Gradient (DDPG) reinforcement learning. The proposed approach enables adaptive control and cooperative behavior of unmanned aerial vehicles (UAVs) within a cognitive AI platform, where each agent learns optimal energy management and navigation policies from dynamic environmental states. We extend the standard DDPG architecture with a belief-state representation derived from Bayesian filtering, allowing for robust decision-making in partially observable environments. In this paper, for the Gaussian case, we numerically compare the performance of policies derived from DDPG to optimal policies for discretized versions of the original continuous problem. Simulation results demonstrate that the POMDP-DDPG-based swarm control model significantly improves mission success rates and energy efficiency compared to baseline methods. The developed framework supports distributed learning and decision coordination across multiple agents, providing a foundation for scalable cognitive swarm autonomy. The outcomes of this research contribute to the advancement of energy-aware control algorithms for intelligent multi-agent systems and can be applied in security, environmental monitoring, and infrastructure inspection scenarios. The results were partially supported by the National Research Foundation of Ukraine, grant No. 2025.06/0022 “AI platform with cognitive services for coordinated autonomous navigation of distributed systems consisting of a large number of objects
An Efficient Projection Method for Generalized Variational Inequalities Problem
Get PDFIn this paper, we propose a new version of a projection algorithm for the generalized variational inequalities problem (GVIP) involving a multi-valued mapping. In this work, we introduce a new combination of the main algorithmic steps proposed in projection methods that have been developed previously for classical or generalized variational inequalities problem with the aim of significantly reducing the computational cost. For the convergence, the assumptions required for the underlying mapping are continuity and a condition that is weaker than the pseudo-monotonicity. We show that this method is well-defined and its corresponding algorithm is globally convergent. Preliminary comparative experiments on several test problems to validate the effectiveness of the proposed method
Effect of Functionally Graded Inclusion on Stress Conservation Near a Circular Hole in Thin Plates for Different Boundary Conditions
Get PDFComputer simulation and finite element analysis of stress concentration near a circular hole in thin homogeneous plates with an annular inclusion made of functionally graded material (FGM) under uniaxial and biaxial loads are performed. The influence of boundary conditions on the stress concentration factor is considered. Recommendations on the ways to reduce stress concentration around the hole are presented. Rational geometric and mechanical parameters of FGM inclusions for the considered types of boundary conditions are found, which make it possible to significantly reduce the stress concentration factor. At the same time, a mechanical effect is discovered: the use of an annular FGM inclusion with the proposed law of change in the modulus of elasticity leads to a decrease in the intensity of both stresses and strains around the hole. This study can provide designers with an effective practical way to reduce stress concentration in plate structures with holes, which makes it possible to obtain a smoother stress distribution due to the use of inclusions made of FGM around the hole
Optimal Control for Functional-Differential Equation of Neutral Type in BanachТ‘Т‘ Spaces
No full textThis paper examines an optimal control problem for a class of neutral-type functional-differential equations in Banach spaces, where the control objective relates to the boundary of the domain. Sufficient conditions on the coefficients are established to guarantee the existence of optimal pair
On Chaotic Attractors Whose Basins of Attraction Coincide with the Whole Space
Get PDFA new type of chaotic attractors, whose basin of attraction is the entire phase space, is considered. The main difference between these attractors and the known ones is that any trajectory starting from the basin of attraction first enters a unique transport channel (which is a straight line), and then the trajectory reaches the attractor itself along this channel. For any quadratic dynamic system generating the mentioned attractor, a new concept of a uniquely defined degenerate autonomous quadratic dynamic system with exactly one real double equilibrium point is introduced. It is shown that if the degenerate system exhibits chaotic behavior, then the original (non-degenerate) system also exhibits similar chaotic behavior