Finite Codimensional Controllability for Evolution Equations
Xu Liu, Qi Lu, Xu Zhang
TL;DR
This paper introduces finite codimensional controllability for evolution equations, linking it to optimal control with endpoint constraints and demonstrating its application to wave and heat equations.
Contribution
It defines a new controllability concept and establishes its equivalence to conditions ensuring Pontryagin's maximum principle in infinite-dimensional control problems.
Findings
Finite codimensional controllability is equivalent to the finite codimensionality condition.
Application to wave and heat equations demonstrates the concept's practical relevance.
Connects controllability with optimal control principles in infinite-dimensional systems.
Abstract
Motivated by infinite-dimensional optimal control problems with endpoint state constraints, in this Note, we introduce the notion of finite codimensional exact controllability for evolution equations. It is shown that this new controllability is equivalent to the finite codimensionality condition in the literatures to guarantee Pontryagin's maximum principle. As examples, LQ problems with fixed endpoint state constraints for a wave and a heat equation are analyzed, respectively.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Numerical methods for differential equations · Nonlinear Differential Equations Analysis