Sufficient Conditions for Feasibility of Optimal Control Problems Using Control Barrier Functions
This work addresses a critical bottleneck in control theory for ensuring reliable and safe optimal control in systems like adaptive cruise control, though it is incremental as it builds on existing CBF/CLF frameworks.
The paper tackles the challenge of ensuring feasibility in quadratic programs (QPs) derived from optimal control problems using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs), particularly under tight control bounds and high relative degree safety constraints, by providing sufficient conditions for guaranteed feasibility through an additional CBF constraint that maintains compatibility and increases feasibility.
It has been shown that satisfying state and control constraints while optimizing quadratic costs subject to desired (sets of) state convergence for affine control systems can be reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). One of the main challenges in this approach is ensuring the feasibility of these QPs, especially under tight control bounds and safety constraints of high relative degree. In this paper, we provide sufficient conditions for guranteed feasibility. The sufficient conditions are captured by a single constraint that is enforced by a CBF, which is added to the QPs such that their feasibility is always guaranteed. The additional constraint is designed to be always compatible with the existing constraints, therefore, it cannot make a feasible set of constraints infeasible - it can only increase the overall feasibility. We illustrate the effectiveness of the proposed approach on an adaptive cruise control problem.