Mutational inclusions in a metric space: From $ C_0 $-like semigroups to Filippov's theorem.

Lorenz, Thomas

Mutational inclusions generalize ordinary differential inclusions to states in a metric space, but without using any aspects of a gradient in general. This article specifies more general conditions on the initially chosen class of semidynamical systems (used for first-order approximations in the sense of time derivatives). We discuss all required steps from imitating time derivative of a curve and integration in time up to the celebrated Filippov existence theorem for solutions to inclusions. The touchstone for our new mutational setting is an example motivated by robust control problems. Its states are compact subsets of a Banach space which evolve as closed reachable sets of semilinear evolution inclusions with nonlocal dependencies.

TIME perception; METRIC spaces; BANACH spaces; EXISTENCE theorems; ROBUST control

Mathematical Control & Related Fields, 2024, Vol 14, Issue 4, p1

2156-8472

Academic Journal

10.3934/mcrf.2024047