Weighted Prioritization of Constraints in Optimization-Based Control

Optimization-based control laws are an effective method for developing controllers that simultaneously accomplish multiple tasks. Inspired by control barrier function methods, we focus on a framework where the control tasks are encoded as state-dependent inequality constraints on the control input and optimal control inputs satisfying the constraints are synthesized at each state. Some applications feature constraints that cannot be simultaneously satisfied at every state, which leads to infeasibilities in optimization-based control laws. Given a prioritized ranking of each control task, this paper develops an optimization-based control law that is always feasible while satisfying a mathematically-defined notion of the best possible combination of constraints based on an exponential weighting of the priority levels. The control law is implemented by solving two optimization problems in sequence, which for most control systems are a mixed integer linear program and a quadratic program.