Target problems under state constraints for nonlinear controlled impulsive systems
The author investigates target problems for nonlinear control systems with possible jumps (i.e., discontinuity of trajectory). Such impulsive systems have discontinuous trajectories and the value functions are discontinuous in general. The two main results of the article are: -- characterization of the set of all initial conditions from which a given target \(C\) can be reached in finite time, -- characterization of the minimal time to reach \(C\) as a minimal supersolution of some PDE of Hamilton-Jacobi type.
scientific article; zbMATH DE number 1797529