A modified backward integration method for optimal control problems with degenerate equilibrium points. (English) Zbl 1484.49054
The article presents a numerical method for autonomous, infinite time horizon optimal control problems whose canonical optimality system is a system of ordinary differential equations with degenerate equilibrium points. Specifically, the authors show for a particular class of degenerate equilibrium points (which they call multiple hyperbolic saddles) how a blow-up technique for vector fields can be combined with a modified backward integration to transform the optimality system (which is a boundary value problem) into an initial value problem that can be handled by standard numerical solvers. To illustrate their approach, the authors consider as a model problem the fight against an invasive species.
Reviewer: Florian Mannel (Graz)
MSC:
| 49M05 | Numerical methods based on necessary conditions |
| 37D05 | Dynamical systems with hyperbolic orbits and sets |
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
Keywords:
optimal control problems; blow-up technique; degenerate singular points; backward integrationReferences:
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