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Optimal Safety for Constrained Differential Inclusions using Nonsmooth Control Barrier Functions
For a broad class of nonlinear systems, we formulate the problem of
guaranteeing safety with optimality under constraints. Specifically, we define
controlled safety for differential inclusions with constraints on the states
and the inputs. Through the use of nonsmooth analysis tools, we show that a
continuous optimal control law can be selected from a set-valued constraint
capturing the system constraints and conditions guaranteeing safety using
control barrier functions. Our results guarantee optimality and safety via a
continuous state-feedback law designed using nonsmooth control barrier
functions. An example pertaining to obstacle avoidance with a target
illustrates our results and the associated benefits of using nonsmooth control
barrier functions.Comment: Submitted to LCS