Final LDRD report human interaction with complex systems: advances in hybrid reachability and control.

This document describes new advances in hybrid reachability techniques accomplished during the course of a one-year Truman Postdoctoral Fellowship. These techniques provide guarantees of safety in complex systems, which is especially important in high-risk, expensive, or safety-critical systems. My work focused on new approaches to two specific problems motivated by real-world issues in complex systems: (1) multi-objective controller synthesis, and (2) control for recovery from error. Regarding the first problem, a novel application of reachability analysis allowed controller synthesis in a single step to achieve (a) safety, (b) stability, and (c) prevent input saturation. By extending the state to include the input parameters, constraints for stability, saturation, and envelope protection are incorporated into a single reachability analysis. Regarding the second problem, a new approach to the problem of recovery provides (a) states from which recovery is possible, and (b) controllers to guide the system during a recovery maneuver from an error state to a safe state in minimal time. Results are computed in both problems on nonlinear models of single longitudinal aircraft dynamics and two-aircraft lateral collision avoidance dynamics