High Order Control Lyapunov-Barrier Functions for Temporal Logic Specifications
This work addresses safety and temporal logic satisfaction in control systems, representing an incremental advancement in control theory.
The paper tackles the problem of controlling systems with constraints of arbitrary relative degree and initial states that violate constraints by generalizing High Order Control Barrier Functions to High Order Control Lyapunov-Barrier Functions (HOCLBFs), and demonstrates its application to a unicycle safety-critical optimal control problem.
Recent work has shown that stabilizing an affine control system to a desired state while optimizing a quadratic cost subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). In our own recent work, we defined High Order CBFs (HOCBFs) for systems and constraints with arbitrary relative degrees. In this paper, in order to accommodate initial states that do not satisfy the state constraints and constraints with arbitrary relative degree, we generalize HOCBFs to High Order Control Lyapunov-Barrier Functions (HOCLBFs). We also show that the proposed HOCLBFs can be used to guarantee the Boolean satisfaction of Signal Temporal Logic (STL) formulae over the state of the system. We illustrate our approach on a safety-critical optimal control problem (OCP) for a unicycle.