Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine

Open access
Date
2014-03-25Type
- Journal Article
Abstract
The numerical solution of optimal control problems by direct collocation is a widely used approach. Quasi-Newton approximations of the Hessian of the Lagrangian of the resulting nonlinear program are also common practice. We illustrate that the transcribed problem is separable with respect to the primal variables and propose the application of dense quasi-Newton updates to the small diagonal blocks of the Hessian. This approach resolves memory limitations, preserves the correct sparsity pattern, and generates more accurate curvature information. The effectiveness of this improvement when applied to engineering problems is demonstrated. As an example, the fuel-optimal and emission-constrained control of a turbocharged diesel engine is considered. First results indicate a significantly faster convergence of the nonlinear program solver when the method proposed is used instead of the standard quasi-Newton approximation. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000083128Publication status
publishedExternal links
Journal / series
Journal of Applied MathematicsVolume
Pages / Article No.
Publisher
HindawiMore
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