Safety Control of Uncertain MIMO Systems Using Dynamic Output Feedback Barrier Pairs

Safety control of dynamical systems using barrier functions relies on knowing the full state information. This article introduces a novel approach for safety control in uncertain multiple-input–muiltiple-output (MIMO) systems with partial state information. The proposed method combines the synthesis of a vector norm barrier function and a dynamic output feedback safety controller to ensure robust safety enforcement. The safety controller guarantees the invariance of the barrier function under uncertain dynamics and disturbances. To address the challenges associated with safety verification using partial state information, a barrier function estimator is developed. This estimator employs an identifier-based state estimator to obtain a state estimate that is affine in the uncertain model parameters of the system. By incorporating a priori knowledge of the limits of the uncertain model parameters and disturbances, the state estimate provides a robust upper bound for the barrier function. Comparative analysis with existing control barrier function-based methods shows the advantage of the proposed approach in enforcing safety constraints under tight input constraints and the utilization of estimated state information.