Non‐recursive Haar Connection Coefficients Based Approach for Linear Optimal Control

In the present paper, two‐fold contributions are made. First, non‐recursive formulations of various Haar operational matrices, such as Haar connection coefficients matrix, backward integral matrix, and product matrix are developed. These non‐recursive formulations result in computationally efficient algorithms, with respect to execution time and stack‐and‐memory overflows in computer implementations, as compared to corresponding recursive formulations. This is demonstrated with the help of MATLAB PROFILER. Later, a unified method is proposed, based on these non‐recursive connection coefficients, for solving linear optimal control problems of all types, irrespective of order and nature of the system. This means that the single method is capable of optimizing both time‐invariant and time‐varying linear systems of any order efficiently; it has not been reported in the literature so far. The proposed method is applied to solve finite horizon LQR problems with final state control. Computational efficiency of the proposed method is established with the help of comparison on computation‐time at different resolutions by taking several illustrative examples.