… initialize the algorithm from a robust control invariant set and gradually enlarge it (… approach
is the use of contractive sets. The former is not applicable to our algorithm since the feasible …

… , discretize the dynamics, enforce constraints at nodes of the … The feasible region is in the
circle and below the line. The … linear time-invariant time optimal control problems evolving …

… , determining a control invariant set is a key element for recursively feasible model predictive
… Kashima, Controlled invariant feasibility—A general approach to enforcing strong feasibility …

… that CBFs are a practical method for enforcing complex safety … In Section III, we show that
forward (pre-)invariance of the … set is stronger than required for forward invariance (Theorem 2…

… solution approach. We show how we can find a feasibility constraint for an optimal control
problem … After we find a feasibility constraint, we can enforce it through a CBF and take it as an …

… Remark 2: Note that in the discrete-time setting with dynamics xk+1 = f(xk, uk), a set S is
said to be control invariant if, for each x ∈ S, there exists u ∈ U(x) such that f(x, u) ∈ S holds. …

… and sufficient conditions for control invariance, b) we show … , c) we formulate a recursively
feasible DCBF-based constrained … for control invariance as opposed to the stronger necessary …

… Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled
system, respectively. They are commonly utilized to build constraints that can be incorpo…

… data-driven safe control using notions from set invariance (… λ-contractivity is a stronger property
than asymptotic stability, … is feasible if and only if the modelbased solution is feasible. The …

… and develop a powerful criterion for the connectivity of their feasible regions. An … invariant.
At the end of this section, the difficulties of investigating the connectivity properties for general …