IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Robust Safety Critical Control Under Multiple State and Input Constraints: Volume Control Barrier Function Method Jinyang Dong, Shizhen Wu, Rui Liu, Xiao Liang, Senior Member, IEEE, Biao Lu, Member, IEEE, and Y ongchun Fang, Senior Member, IEEE Abstract --In this paper, the safety-critical control problem for uncertain systems under multiple control barrier function (CBF) constraints and input constraints is investigated. A novel framework is proposed to generate a safety filter that minimizes changes to reference inputs when safety risks arise, ensuring a balance between safety and performance. A nonlinear disturbance observer (DOB) based on the robust integral of the sign of the error (RISE) is used to estimate system uncertainties, ensuring that the estimation error converges to zero exponentially. This error bound is integrated into the safety-critical controller to reduce conservativeness while ensuring safety. To further address the challenges arising from multiple CBF and input constraints, a novel Volume CBF (VCBF) is proposed by analyzing the feasible space of the quadratic programming (QP) problem. To ensure that the feasible space does not vanish under disturbances, a DOB-VCBF-based method is introduced, ensuring system safety while maintaining the feasibility of the resulting QP . Subsequently, several groups of simulation and experimental results are provided to validate the effectiveness of the proposed controller. I NTRODUCTION A S automation systems have become integral to our daily lives, the development of safe and high-performance controllers for these systems is of paramount importance. To meet this need, the Control Barrier Function (CBF) is a powerful tool to ensure the safety of control systems [1].

Identifying and suppressing unknown disturbances to dynamical systems is a problem with applications in many different fields. In this Letter, we present a model-free method to identify and suppress an unknown disturbance to an unknown system based only on previous observations of the system under the influence of a known forcing function. We find that, under very mild restrictions on the training function, our method is able to robustly identify and suppress a large class of unknown disturbances. We illustrate our scheme with the identification of unknown forcings to an analog electric chaotic circuit and with a numerical example where a chaotic disturbance to the Lorenz system is identified and suppressed.

Identifying disturbances in network-coupled dynamical systems without knowledge of the disturbances or underlying dynamics is a problem with a wide range of applications. For example, one might want to know which nodes in the network are being disturbed and identify the type of disturbance. Here we present a model-free method based on machine learning to identify such unknown disturbances based only on prior observations of the system when forced by a known training function. We find that this method is able to identify the locations and properties of many different types of unknown disturbances using a variety of known forcing functions. We illustrate our results both with linear and nonlinear disturbances using food web and neuronal activity models. Finally, we discuss how to scale our method to large networks.

We developed a robust control policy design method in high-dimensional state space by using differential dynamic programming with a minimax criterion. As an example, we applied our method to a simulated five link biped robot. The results show lower joint torques from the optimal con- trol policy compared to a hand-tuned PD servo controller. Results also show that the simulated biped robot can successfully walk with unknown disturbances that cause controllers generated by standard differential dy- namic programming and the hand-tuned PD servo to fail. Learning to compensate for modeling error and previously unknown disturbances in conjunction with robust control design is also demonstrated.

In this paper, we tackle the problem of flying a quadrotor using time-optimal control policies that can be replanned online when the environment changes or when encountering unknown disturbances. This problem is challenging as the time-optimal trajectories that consider the full quadrotor dynamics are computationally expensive to generate (order of minutes or even hours). We introduce a sampling-based method for efficient generation of time-optimal paths of a point-mass model. These paths are then tracked using a Model Predictive Contouring Control approach that considers the full quadrotor dynamics and the single rotor thrust limits. Our combined approach is able to run in real-time, being the first time-optimal method that is able to adapt to changes on-the-fly. We showcase our approach's adaption capabilities by flying a quadrotor at more than 60 km/h in a racing track where gates are moving. Additionally, we show that our online replanning approach can cope with strong disturbances caused by winds of up to 68 km/h.