On (the existence of) Control Lyapunov Barrier Functions

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Braun, Philipp ; Kellett, Christopher M.:
On (the existence of) Control Lyapunov Barrier Functions.
Newcastle, Australia , 2017 . - 19 S.

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Abstract

Recently, [17] proposed control Lyapunov barrier functions (CLBFs) for the stabilization of nonlinear dynamical systems with state constraints. Under the assumption of the existence of a smooth CLBF, Sontag's universal formula was used to define a continuous feedback ensuring that the constraints are satisfied. However, as we demonstrate in this paper, the above approach neglects the necessity of discontinuous controllers in the case of state constraints. Additionally, we show that the assumption of a smooth CLBF limits the state constraints to those defined by unbounded sets. Consequently, we introduce the notion of nonsmooth complete control Lyapunov functions (CCLFs) and indicate how they may be used for stabilization in the presence of state constraints.