Barrier Pairs for Safety Control of Uncertain Output Feedback Systems

The barrier function method for safety control typically assumes the availability of full state information. Unfortunately, in many scenarios involving uncertain dynamical systems, full state information is often unavailable. In this paper, we aim to solve the safety control problem for an uncertain single-input single-output system with partial state information. First, we develop a synthesis method that simultaneously creates a barrier function and a dynamic output feedback safety controller. This safety controller guarantees that the unit sub-level set of the barrier function is an invariant set under the uncertain dynamics and disturbances of the system. Then, we build an identifier-based estimator that provides a state estimate affine to the uncertain model parameters of the system. To detect the potential risks of the system, a fault detector uses the state estimate to find an upper bound for the barrier function. The fault detector triggers the safety controller when the system's original action leads to a potential safety issue and resumes the original action when the potential safety issue is resolved by the safety controller.