Feasibility Guarantees for CBF-Based Optimal Control

Abstract

In this chapter, we address the crucial issue of whether feasible solutions can be found for the CBF/HOCBF-based optimization in OCP-CBF (2.20), as first discussed in Sect. 2.5.2. At the heart of this problem is preventing the possibility that the control limitations (2.19) conflict with the HOCBF constraint (3.8). Clearly, this depends on whether HOCBFs, as defined in Definition 3.3, can be found in the presence of control limitations (2.19). We describe several methods to accomplish this. First, in Sect. 4.1, we present a method based on assigning weights (penalties) to the functions from the definition of the HOCBF. Then, in Sect. 4.2, we describe an analytical approach based on the idea of designing an additional CBF, which leads to a sufficient condition for feasibility. A simulation example illustrating the use of a sufficient condition for feasibility is provided in Sect. 4.3.