Invariance Entropy of Hyperbolic Control Sets

TL;DR

This paper advances the understanding of invariance entropy in nonlinear control systems by deriving bounds based on Lyapunov exponents for hyperbolic sets, and unifies these bounds into a formula under mild conditions.

Contribution

It provides new bounds for invariance entropy in hyperbolic control sets and merges these bounds into a unified formula under mild assumptions.

Findings

Upper bound for invariance entropy in controllability sets

Lower bound for invariance entropy in hyperbolic sets

Unified formula for invariance entropy in hyperbolic chain control sets

Abstract

In this paper, we improve the known estimates for the invariance entropy of a nonlinear control system. For sets of complete approximate controllability we derive an upper bound in terms of Lyapunov exponents and for uniformly hyperbolic sets we obtain a similar lower bound. Both estimates can be applied to hyperbolic chain control sets, and we prove that under mild assumptions they can be merged into a formula.