Derivation of Necessary Conditions for Optimal Control of the Implicit Burgers’ Equation Using the Variational Principle

Hashimoto, Tomoaki

Control Systems and Optimization Letters
Vol 3, No 3 (2025)

Controlling fluid dynamics is a challenging problem that arises in many fields including aeronautical, biological and chemical engineering. Burgers’ equation is used to describe fundamental flow phenomena. Implicit systems belong to a more generalized class of systems than a class of explicit systems, because they can additionally contain algebraic constraints. Although the optimal control problem of the explicit form of Burgers' equation has been already explored in many papers, the optimal control problem of implicit form of Burgers’ equation is still an open problem as far as general classes of systems are concerned. In this paper, necessary conditions for an evaluation function to be optimized are derived on the basis of the variational principle for the optimal control problem of the implicit form of Burgers’ equation.