A Modular Approach to Adaptive Safety-Critical Control

In the previous chapter, we introduced adaptive control barrier functions (aCBFs) for systems with uncertain parameters. Central to that approach was the construction of a suitable parameter estimation algorithm that continuously reduced the level of uncertainty in the parameter estimates using data collected online. In this chapter, by unifying the concepts of input-to-state stability (ISS) and input-to-state-safety (ISSf), we develop a framework for modular adaptive control that addresses some limitations of that method. Specifically, we show how to allow more freedom in the parameter estimation algorithm, how to relax the required knowledge on the parameter bounds, and how to reduce the redundancy in parameter estimation necessary for safety and stability. In Sect. 6.1, we introduce input-to-state stability (ISS). The concept of modular adaptive stabilization is defined in Sect. 6.2. The ISS concept is extended to input-to-state safety (ISSf) in Sect. 6.3. We include numerical examples in Sect. 6.4 and conclude with final remarks, references, and suggestions for further reading in Sect. 6.5.