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Approximate Optimal Control for Safety-Critical Systems with Control Barrier Functions

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Document pages: 6 pages

Abstract: Control Barrier Functions (CBFs) have become a popular tool for enforcing setinvariance in safety-critical control systems. While guaranteeing safety, mostCBF approaches are myopic in the sense that they solve an optimization problemat each time step rather than over a long time horizon. This approach may allowa system to get too close to the unsafe set where the optimization problem canbecome infeasible. Some of these issues can be mitigated by introducingrelaxation variables into the optimization problem; however, this compromisesconvergence to the desired equilibrium point. To address these challenges, wedevelop an approximate optimal approach to the safety-critical control problemin which the cost of violating safety constraints is directly embedded withinthe value function. We show that our method is capable of guaranteeing bothsafety and convergence to a desired equilibrium. Finally, we compare theperformance of our method with that of the traditional quadratic programmingapproach through numerical examples.

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