Since, in the presence of actuatorĭynamics, at the boundary of the Stefan system, this system's main CBF is of Sets that are infinite-dimensional as well. Infinite-dimensional (including one control barrier "functional") and with safe Theįamiliar QP design is employed to ensure safety but with CBFs that are Moves due to a liquid-solid phase change - the so-called Stefan model. Physically-relevant model of thermal dynamics where the boundary of the PDE Generalization of this concept for PDE control, treating a specific, Prominent role in automotive safety and in robotics. High-relative-degree control barrier functions (hi-rel-deg CBFs) play a Subjects: Optimization and Control (math.OC) Systems and Control (eess.SY) Computer simulations provide striking numerical evidence that anĪdopted adaptive HHO algorithm can overcome the Lavrentiev gap phenomenon even Singular minimizers and improved convergence rates for higher polynomialĭegrees. Numerical experiments illustrate an efficient approximation of Under further convexity properties, of the approximations of the primal resp.ĭual variable. The main results imply the convergence of the energy and, Into simplices or in the space of piecewise polynomials with stabilization on Raviart-Thomas finite element functions without stabilization on triangulations High-order method utilizes a gradient reconstruction in the space of piecewise Topology optimization, and the convexified double-well problem. Examples include the p-Laplacian, an optimal design problem in Hybrid high-order method in convex minimization problems with two-sided This paper proposes two convergent adaptive mesh-refining algorithms for the