Optimal Blowup Time for Controlled Ordinary Differential Equations

TL;DR

This paper investigates the optimal timing for blowup in controlled ODEs, establishing existence, maximum principles, and local optimality conditions to better understand control strategies for systems with finite-time singularities.

Contribution

It introduces new existence results and maximum principles for optimal blowup times, leveraging monotonicity to simplify proofs and identify local optimality conditions.

Findings

Established existence of optimal blowup times.

Derived maximum principle for optimal control.

Identified local optimality conditions using system monotonicity.

Abstract

Both the shortest and the longest blowup time for a controlled system are considered. Existence result and maximum principle for optimal triple are established. Thanks to some monotonicity of the controlled system, some kinds of "the front part local optimality" for optimal triple is established. Then proofs of the main results become easy, clear and abundant.