Solving for Blameless and Optimal Control Under Prioritized Safety Constraints

In many safety‐critical optimal control problems, users may request multiple safety constraints that are jointly infeasible due to external factors such as subsystem failures, unexpected disturbances, or fuel limitations. In this manuscript, we employ the concept of blameless optimality to characterize control actions that (a) satisfy the highest priority safety constraints that are feasible, and (b) remain optimal with respect to a mission objective. For a general optimal control problem with jointly infeasible safety constraints, we prove that there may not be a single optimization problem that solves for a blamelessly optimal controller. Instead, finding blamelessly optimal control actions requires sequentially solving at least two optimal control problems: one to determine the highest priority level of constraints that is feasible and another to determine the optimal control action with respect to these constraints. We show how to formulate two optimal control problems such that the resulting control sequence is guaranteed to be blamelessly optimal. We show that given convex, strictly nested safety constraints, blamelessly optimal control can be found by solving two convex optimization problems. In particular, we outline how to solve for blamelessly optimal control sequences when the prioritized safety sets can be represented by polynomials or hyperspheres. We present the results of numerical examples comparing our proposed algorithm to two alternative algorithms.