Distributed optimal control of the viscous Burgers equation via a Legendre pseudo-spectral approach. (English) Zbl 1344.49053
Summary: This paper presents a computational technique based on the pseudo-spectral method for the solution of a distributed optimal control problem for the viscous Burgers equation. By using a pseudo-spectral method, the problem is converted into a classical optimal control problem governed by a system of ordinary differential equations, which can be solved by well-developed direct or indirect methods. For solving the resulting optimal control problem, we present an indirect method by deriving and numerically solving the first-order optimality conditions. Numerical tests involving both unconstrained and constrained control problems are considered.
MSC:
| 49M30 | Other numerical methods in calculus of variations (MSC2010) |
| 49M37 | Numerical methods based on nonlinear programming |
| 49M05 | Numerical methods based on necessary conditions |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 49K15 | Optimality conditions for problems involving ordinary differential equations |
| 65K10 | Numerical optimization and variational techniques |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
distributed optimal control; viscous Burgers equation; pseudo-spectral method; Pontryagin’s minimum principle; optimality conditionsReferences:
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