Retrospective and Predictive Cost Adaptive Control of Space Systems

Abstract

As space missions become increasingly complex and autonomous, more advanced control algorithms will be needed to handle the dynamical uncertainty facing these missions. These future missions will experience unknown disturbances, unmodeled nonlinearities, time-varying parameters such as changes in mass due to fuel usage, or unknown changes in the operating environment. In this dissertation, we explore the use of adaptive control to allow for spacecraft to adapt online to reject unknown disturbances and maintain performance under dynamic uncertainty. Specifically, we develop and apply the retrospective cost adaptive control (RCAC) and predictive cost adaptive control (PCAC) algorithms for disturbance rejection of lightly damped systems such as space telescopes and for sample gathering from small celestial bodies such as asteroids. For disturbance rejection of lightly damped systems, RCAC requires several hundred impulse response coefficients for its closed-loop target model. We introduce the idea of using a dereverberated transfer function as the modeling information for RCAC to significantly reduce the order of the target model. The resulting algorithm was successfully implemented on an acoustic disturbance rejection experiment. Next, we consider the model reference adaptive control (MRAC) problem and develop the retrospective cost model reference adaptive control (RC-MRAC) algorithm. MRAC methods allow for robotic systems to adjust to changes while attempting to follow a desired reference trajectory from a predetermined reference model. RC-MRAC enables reference model following of arbitrary linear systems as long as the relative degree, leading numerator coefficient, system order, and nonminimum-phase zeros are known. We then focus on PCAC, which combines online model identification with model predictive control (MPC). For online identification, PCAC relies on a variable-rate forgetting (VRF) factor to track time-varying parameters. We develop a new VRF factor using the F-test that is more robust to noise and provides faster parameter convergence after a system change compared to the standard constant-rate forgetting factor used in practice. The F-test based VRF factor is a variation of the standard VRF factor used in PCAC. We demonstrate the applicability of PCAC for disturbance rejection of large truss structures representative of space telescopes subject to harmonic and broadband disturbances under aliasing and modal folding. Finally, we focus on the small celestial body surface sampling problem, where a spacecraft with a robotic sampling arm descends onto the surface of an asteroid with unknown properties and must maintain a desired contact force to gather a sample before leaving the surface. The contact dynamics of this problem are nonlinear, nonsmooth, and unknown prior to contact. We demonstrate that PCAC can be used to augment a nominal robust controller to improve the overall sampling performance of the spacecraft for a wide variety of surface properties. We then show that the online identification combined with the VRF factor in PCAC can allow the spacecraft to perform multiple sampling maneuvers in regions with different surface properties without loss of performance.