An Averaging Approach to Optimal Adaptive Control of Large Space Structures

In this paper, averaging methods are applied to analyzing the transient response associated with adaptive control of large space structures. Using a dominant mode approximation to the plant, an analytical bound is found on the envelope of the adaptive response, characterizing many of the features of the response useful for control design (e.g., peak values, quadratic costs, settling times, etc.). An optimal adaptive design problem is then formulated based on minimizing the product of the settling time and peak torque requirement. The resulting nonlinear constrained optimization problem is solved in closed-form and several interesting properties of the optimal adaptive design are discussed.