Optimal Safety for Constrained Differential Inclusions Using Nonsmooth Control Barrier Functions

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