Haar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems

‎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