Optimal control of a thermoelastic body with missing initial conditions

ABSTRACT

This paper aims to control the deformation and the temperature of a thermoelastic body by acting on him by an exterior force applied on a part of the body. In this case, all the initial data in the main model are missing values. The incomplete data in the considered model requires the use of the notion of no-regret control introduced by J. L. Lions for optimal control of distributed systems with missing data. An optimality system formed of coupled equations and adjoint coupled equations characterises the optimal pair (control state).

KEYWORDS:

• Optimal control
• incomplete data
• no-regret control
• hyperbolic–parabolic coupled systems
• linear system of thermoelasticity

AMS SUBJECT CLASSIFICATIONS:

• 49J21
• 93C20
• 93C41

Disclosure statement

No potential conflict of interest was reported by the authors.