Research Article
A Posteriori Error Estimates by FEM for Source Control Problems Governed by a System of Semi-Linear Convection-Diffusion Equations
ChangIl Kim*,
JaYong Ri,
Song Jun Kim
Issue:
Volume 10, Issue 2, June 2025
Pages:
20-35
Received:
24 January 2025
Accepted:
7 August 2025
Published:
23 September 2025
Abstract: In this paper, we consider the optimal source control problem of a system of 2-dimensional semi-linear steady convection-diffusion equations. The problem is modelized from temperature and consistency distribution in the gasification processes, so it is described by 2 non-linear elliptic partial differential equations with Dirichlet boundary condition. The problem is a optimal source control problem that controls the source term necessary to approximate the temperature to a proper target function. First, we derived the optimal condition. Based on setting the approximation problem of a given control problem in a first order polynomial finite element function space and deriving the optimality condition of the approximation problem, we evaluated a priori error between the optimal control, the optimal state, the conjugate state and its finite element approximation functions by using optimal condition of original and approximate problem. And we also evaluated the upper estimate of a posteriori error by finite element method (FEM). We proved the convergence to 0 of a posteriori error indicator (term of the right side of inequality) when division diameter converges to 0. For this, we acquired the lower bound estimation of a posteriori error and proved that a priori error and total variance error converges to 0 when division diameter converges to 0, so that we proved the convergence problem of a posteriori error indicator.
Abstract: In this paper, we consider the optimal source control problem of a system of 2-dimensional semi-linear steady convection-diffusion equations. The problem is modelized from temperature and consistency distribution in the gasification processes, so it is described by 2 non-linear elliptic partial differential equations with Dirichlet boundary conditi...
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Research Article
Pose Control of Omnidirectional Mobile Robot Using Improved Deep Reinforcement Learning
Issue:
Volume 10, Issue 2, June 2025
Pages:
36-43
Received:
2 September 2025
Accepted:
16 September 2025
Published:
9 October 2025
DOI:
10.11648/j.ijimse.20251002.12
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Abstract: Nowadays, mobile robots are being widely applied in various fields such as indoor carrying and check of products and outdoor exploration. One of the most important problems arising in development of mobile robots is to resolve path planning problem. With active studies of implementation of path planning, lots of algorithms have been developed and especially, the dramatic advance in artificial intelligence (AI) led to advent of algorithms using reinforcement learning (RL). Deep reinforcement learning (DRL) has been developed and it uses neural network to approximate parameters of RL algorithm. DDPG is one of deep reinforcement learning (RL) algorithms and is widely used to solve lots of practical issues as it doesn’t need full information of the environment. In other words, path planning with DRL has advantages of possibility for unknown environments in which partial or full information is not given and of direct controllability of the robot. Generally, path planning Up to now, path planning using DRL has considered only position control problem with no consideration of its orientation angle (as the author knows). In this paper, a pose control method using DRL for 3-wheeled omnidirectional mobile robot is proposed. And a method to reduce position error is mentioned. Simulation results show that the proposed method can efficiently solve the control problem of omnidirectional robots.
Abstract: Nowadays, mobile robots are being widely applied in various fields such as indoor carrying and check of products and outdoor exploration. One of the most important problems arising in development of mobile robots is to resolve path planning problem. With active studies of implementation of path planning, lots of algorithms have been developed and e...
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,
Yun Ji Yon
