Real-Time Optimal Gain Scheduling for Nonlinear Dynamic Inversion

Abstract

This paper presents a novel approach to combine trajectory optimization and gain scheduling for a nonlinear dynamic inversion controller, in order to optimize both guidance commands and control response. Therein, the guidance problem is formulated as an optimal control problem that also incorporates inner-loop dynamics based on a nonlinear dynamic inversion control block. At the same time, the gain profile for this control block is incorporated into the optimization problem as additional variables. As a result, the optimization process not only optimizes the required guidance commands based on knowledge of the control response, but also the control response itself. The optimal control problem is transcribed into a nonlinear optimization problem by direct multiple shooting, while the resulting nonlinear program is solved with an sequential quadratic programming method. The optimization procedure is augmented by an ordinary differential equation formulation to obtain the required sensitivity terms, as well as a condensing procedure to decrease the size of the auxiliary quadratic problem within the iterative optimization algorithm. Numerical results are presented that illustrate the feasibility of this approach and that indicate potential benefits.