Sensitivity Analysis in Index-1 Differential Algebraic Equations by ESDIRK Methods
| Authors: | Kristensen Morten Rode, Technical University of Denmark, Denmark
Jørgensen John Bagterp, 2-control ApS, Denmark
Thomsen Per Grove, Technical University of Denmark, Denmark
Michelsen Michael Locht, Technical University of Denmark, Denmark
Jørgensen Sten Bay, Technical University of Denmark, Denmark |
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| Topic: | 2.4 Optimal Control |
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| Session: | Optimal Control in Nonlinear Systems II |
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| Keywords: | Differential algebraic equations, sensitivity computation, nonlinear model predictive control, optimal control, parameter estimation |
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Abstract
Dynamic optimization by multiple shooting requires integration and sensitivity calculation. A new semi-implicit Runge-Kutta algorithm for numerical sensitivity calculation of index-1 DAE systems is presented. The algorithm calculates sensitivities with respect to problem parameters and initial conditions, exploiting the special structure of the sensitivity equations. The algorithm is a one-step method which makes it especially efficient compared to multiple-step methods when frequent discontinuities are present. These advantages render the new algorithm particularly suitable for dynamic optimization and nonlinear model predictive control. The algorithm is tested on the Dow Chemicals benchmark problem.
