Non-positive barrier function: a new notion of barrier function for state-safety control of nonlinear dynamical systems

Abstract

The analysis and control of system state safety are a research hotspot in the field of control. This article has thoroughly investigated some issues related to safety criteria with application to the safety analysis, diagnosis, and safety control of a class of dynamical systems with their unique set of available states via a new notion of barrier functions. Inspired by reciprocal barrier functions and zeroing barrier functions, a type of non-positive barrier function (NPBF) is designed and the safety criteria are proposed, guaranteeing that the unique set of available states is forward-invariant to ensure system safety at all times. Then, the control barrier function is established based on NPBFs for a class of dynamical control systems and used to design the safety controller. Conclusively, this is a first-of-its-kind study to apply safety criteria and control barrier functions to safeguard a class of continuously stirred tank reactors.