Convex Optimization in a Nonconvex World: Applications for Aerospace Systems

Abstract

Future aerospace vehicles, and other autonomous systems at large, will operate with higher levels of automation and in more general environments than their predecessors. Counter-intuitively, the sought-after generality of operation of new autonomous systems calls for the consideration of far more constraints during system operation. To name a few examples, these constraints may relate to obstacle avoidance, sensing, or actuator constraints. This future breed of more-constrained autonomous agents calls for the development of new control methods that seamlessly and reliably deal with a host of nonconvex (in other words, difficult) intrinsic and extrinsic constraints. This dissertation makes the basic assumption that, for safety reasons, the control methods are required to be extremely reliable. With this premise in mind, the chapters of this document focus on developing convex optimization-based methods for dealing with nonconvex feedback and feedforward control tasks. The resulting algorithms are applicable to the broad spectrum of aerospace vehicles. The particular cases considered are satellite orbit station-keeping, spacecraft rendezvous and docking, and planetary rocket landing. In each case, it is shown using numerical examples that the algorithms attain levels of performance above the current state-of-the-art. The dissertation is organized into four major parts. In Chapter 3, a robust model predictive feedback controller is presented that is based on convex optimization alone, and that applies to satellite orbit station-keeping. In Chapter 4, an explicit model predictive controller is presented that can be used to precompute optimal control laws for general mixed-integer convex problems, albeit at the price of higher onboard storage memory. In Chapter 6, a novel method is presented for computing feedforward trajectories of hybrid systems using lossless convexification. Applications are shown for spacecraft rendezvous and for rocket landing. Finally, Chapter 7 considers an iterative method to solve even more difficult hybrid system problems. This method is based on the methodologies of sequential convex programming and numerical continuation.