Analytic algebraic Riccati solution for a robust control system: application to 2-DOF arm robot

Abstract

An analytic solution to the Riccati algebraic equation has been investigated by employing eigenvalue–eigenvector techniques combined with the Gram–Schmidt orthogonality process. An analytic solution to the Riccati algebraic equation has been investigated by employing eigenvalue–eigenvector techniques combined with the Gram–Schmidt orthogonalization process. The applied method is used to improve robust control of second and third-order state-dependent systems by handling nonlinearities. An H∞ controller is designed in this context via backstepping technique to enhance robustness and reduce computational effort. The effectiveness of this method has been demonstrated on a two-degree-of-freedom (2-DOF) robotic manipulator arm. Simulation results validate the performance of the controller, showing improved tracking accuracy, disturbance rejection, and overall system stability, thereby confirming the efficiency and applicability of the combined analytic Riccati algebraic equation and H∞ backstepping approach for nonlinear robotic systems.