Safe control systems with control barrier function. - Chinelato, Caio Igor Gonçalves (2022)
This work presents approaches for the safe control of dynamical systems with control barrier functions (CBFs). The system must satisfy stability/tracking objectives and safety constraints. Stability/tracking objectives can be satisfied through a control Lyapunov function (CLF) or a nominal control law, as described in classical control literature. Safety constraints are specified in terms of a set invariance and verified through CBFs. The existence of a CBF satisfying specific conditions implies in set invariance and system safety. The control framework considered unifies stability/tracking objectives, expressed as a CLF or a nominal control law, and safety constraints, expressed as a CBF, through quadratic programming (QP). If stability/tracking objectives and safety constraints are in conflict, the control framework mediates these requirements, in the sense that safety is always prioritized. Initially, a literature review with works related to the safety of dynamical systems and CBF is presented and the basic formulation of the considered control framework is described by CBFs represented by relative-degree one safety constraints. Posteriorly, advanced topics are presented, such as CBFs represented by high relativedegree safety constraints, robust CBFs, an explicit solution without QP and discrete-time CBFs (DCBFs). The main contributions of this work are new formulations for robust CBFs, where robust exponential control barrier functions (RECBFs) and sliding mode control barrier functions (SMCBFs) are proposed, the experimental application of an explicit solution to deal with high relative-degree and robust safety constraints, and practical applications not explored in the literature so far. The experiments are organized so that all the topics described in the literature review and the work contributions be covered. The results are presented experimentally in a reaction wheel pendulum and a Furuta pendulum, and numerically in a Multiple-Input-Multiple-Output (MIMO) magnetic levitation system (MAGLEV) and adaptive cruise control (ACC) applied to automotive vehicles. In all cases, stability/tracking objectives and safety constraints are satisfied.