CONTROL OF SINGULAR DISTRIBUTED SYSTEMS BY CONTROLLABILITY: THE ILL-POSED BACKWARDS HEAT EQUATION
Keywords:
singular distributed systems, optimal control, ill-posed backwards heat equation, controllability, inverse problemDOI:
https://doi.org/10.17654/0972096025005Abstract
To deal with the ill-posed backwards heat equation, we propose the controllability method. The point of view adopted consists in interpreting the state equation as an inverse problem that allows us to obtain a decoupled and strong singular optimality system for the optimal control-state pair. This further permits to propose an existence criterion for a regular solution of the backwards heat equation. It is important to note that the results are obtained without recourse to a Slater-type assumption.
Received: February 15, 2025
Revised: March 17, 2025
Accepted: March 27, 2025
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