Inverse Optimal Control Via Diagonal Stabilization Applied to Attitude Tracking of a Reusable Launch Vehicle

In this work, a novel strategy for the inverse optimal control of a class of affine nonlinear systems is proposed. The proposed strategy involves translation of the infinite horizon nonlinear optimal control problem into a Diagonal stability problem, followed by the formulation of a set of criteria for the synthesis of a stabilizing feedback control law. Hence, the proposed controller design methodology is refered to as inverse optimal control via diagonal stabilization. Besides providing a closed-form solution, the methodology also possesses the added advantage of inherent robustness, on account of adequate stability margins. Most importantly, the methodology ensures an estimate of the associated domain of attraction, which is a highly desirable feature especially in the case of crucial and stringent aerospace applications. The proposed methodology is applied for the re-entry control of a reusable launch vehicle which provides a full envelope optimality-based design philosophy. For this, the control-oriented attitude model based on the three-degree-of-freedom dynamic model is utilized. The resulting control law possess desirable features of guaranteed estimate of stability domain, assured design flexibility, and inherent robustness. Simulation results verify the validity of these theoretically proven facets in terms of the efficacy and robustness of the proposed controller.