New efficient algorithm for the minimization of controller fragility using algebraic Riccati equation (ARE) and analyzing the results for different controllers

We present the solution to the problem of fragility minimization using the algebraic Ricatti equation (ARE) from the optimal control arsenal. Fragile controllers are controllers which must be implemented exactly otherwise performance degradation or instability results. Formerly, the gradient flow technique (GFT) was presented as a tool to minimize the controller fragility, but the idea proved to be cumbersome and computationally inefficient. On the other hand, the algorithm using the algebraic Ricatti equation (ARE) brings up the result with less execution time along with ease of understanding. Moreover, the solution to the problem of multiple poles has also been given In this work. Finally, the optimization results obtained from these different controllers have been discussed.