Abstract
This paper considers ℓ
1 optimal control problems with full state feedback. In contrast to
H
∞ optimal control, previous work has shown that linear ℓ
1 optimal controllers can be dynamic and arbitrarily high order. However, this paper shows that continuous memoryless
nonlinear state feedback perform as well as dynamic linear state feedback. The derivation, which is nonconstructive, relies on concepts from viability theory.