@article { author = {Nezhadhosein, Saeed}, title = {Haar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems}, journal = {Control and Optimization in Applied Mathematics}, volume = {2}, number = {2}, pages = {1-14}, year = {2017}, publisher = {Payame Noor University (PNU)}, issn = {2383-3130}, eissn = {2538-5615}, doi = {}, abstract = {‎In this paper‎, ‎Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems‎. ‎Firstly‎, ‎using necessary conditions for optimality‎, ‎the problem is changed into a two-boundary value problem (TBVP)‎. ‎Next‎, ‎Haar wavelets are applied for converting the TBVP‎, ‎as a system of differential equations‎, ‎in to a system of matrix algebraic equations‎, ‎as Haar matrix equations using Kronecker product‎. ‎Then the error analysis of the proposed method is presented‎. ‎Some numerical examples are given to demonstrate the efficiency of the method‎. ‎The solutions converge as the number of approximate terms increase.}, keywords = {Time-variant linear-quadratic optimal control problems‎,‎Matrix algebraic equation‎,‎Haar wavelet}, url = {https://mathco.journals.pnu.ac.ir/article_5726.html}, eprint = {https://mathco.journals.pnu.ac.ir/article_5726_39c990da2be15864978cbf6bbbeb5534.pdf} }