Abstract
In this chapter, we introduce Control Barrier Functions (CBFs) in the context of control systems. We start by tracing back the history of CBFs to the barrier functions used in classical mathematical optimization (Sect. 2.1) and then show how they can be extended to Lyapunov-like barrier functions (Sect. 2.2). We explain in Sects. 2.3 and 2.4 how these have been adapted to the control of dynamical systems in the presence of constraints. In Sect. 2.5, we describe how to combine CBFs with constrained optimal control problems as introduced in Chap. 1 and outline a general-purpose solution methodology for such problems.
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© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
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Xiao, W., Cassandras, C.G., Belta, C. (2023). Control Barrier Functions. In: Safe Autonomy with Control Barrier Functions. Synthesis Lectures on Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-031-27576-0_2
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DOI: https://doi.org/10.1007/978-3-031-27576-0_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-031-27575-3
Online ISBN: 978-3-031-27576-0
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