Maximum under continuous-discrete-time dynamic with target and viability constraints

Abstract

The viable maximum of of a continuous function L ∈ ℒ¹(ℝ^2m+1, ℝ⁺) under a dynamic x′(t) ∈ F(x(t)) under constraint x(t) ∈ K where K is closed is obtained on the boundary of the capture-viability kernel in the direction of high y of the target K × {0} viable in K × ℝ⁺ under the extended dynamic (x′(t), y′(t)) ∈ (F(x(t)), −L(x(t), u(t))). The result holds true with discrete-continuous-time measurable controls. Example and application to hybrid dynamics under viability constraints and target are given.

Keywords:

• viability
• target
• maximum