Applying Radial Basis Functions and Partition of Unity for Solving Heating Equations Optimal Control Issues

In this study, we suggest applying the Partition of Unity approach using Radial Basis Functions (RBF-PU) towards the solution of heat equation-governed sparse optimal control issues.An 2 norm is included in the goal function to encourage sparseness in the control equation and quadratic coefficients are used to reduce the deviations from a desired state.Efficient processing of spatially sparse controllers is made possible by this combination, which is crucial for numerous practical uses.By splitting the domain into overlapped subdomains and performing local RBF approximation, which is then integrated utilizing compactly maintained weight functions, the RBF-PU technique offers a versatile and effective strategy.The correctness and effectiveness of the suggested strategy are demonstrated numerically, showing how it can be used to solve intricate optimum control issues with larger dimensions.