Set-based Optimal, Robust, and Resilient Control with Applications to Autonomous Precision Landing

We present a real-time-capable set-based framework for closed-loop predictive control of autonomous systems using tools from computational geometry, dynamic programming, and convex optimization. The control architecture relies on the offline precomputation of the controllable tube, i.e, a time-indexed sequence of controllable sets. Sets are represented using constrained zonotopes (CZs), which are efficient encodings of convex polytopes that support fast set operations and enable tractable dynamic programming in high dimensions. Online, we obtain a globally optimal control profile by solving a series of one-step optimal control problems. Our key contributions are: (1) free-final-time optimality: we devise an optimal horizon computation algorithm to achieve global optimality; (2) robustness: we handle stochastic uncertainty in both the state and control, with probabilistic guarantees, by constructing bounded disturbance sets; (3) resilience: we develop (i) an optimization-free approach to computing the instantaneous reachable set, i.e., the reachable set from the current state, to enable, for example, large/maximal divert maneuvers, and (ii) an approach to achieving maximal decision-deferral, i.e., maintaining reachability/divert-feasibility to multiple targets for as long as possible. By means of an autonomous precision landing case study, we demonstrate globally optimal free-final-time guidance, robustness to navigation and actuation uncertainties, instantaneous divert envelope computation, and maximal decision-deferral.