Rao Mease: Difference between revisions
RobertLampel (talk | contribs) Created page with "{{Dimensions |nd = 1 |nx = 1 |nw = 1 }} The '''Rao Mease problem''' is a very sensitive one-dimensional toy ODE model which is especially suited for multiple shooting solvers. It aims to minimize a quadratic Lagrange term. The optimal integer control functions shows bang bang behavior. == Mathematical formulation == <p> <math> \begin{array}{lll} \displaystyle \min_{x,w} && \int_0^{10} (x(t)^2 + w(..." |
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The '''Rao Mease problem''' is a very sensitive one-dimensional toy [[:Category:ODE model|ODE model]] which is especially suited for multiple shooting solvers. It aims to minimize a quadratic Lagrange term. | The '''Rao Mease problem''' is a very sensitive one-dimensional toy [[:Category:ODE model|ODE model]] which is especially suited for multiple shooting solvers. It aims to minimize a quadratic Lagrange term. | ||
The optimal | The optimal control function exhibits a [[:Category:Sensitivity-seeking arcs|singular arc]]. | ||
== Mathematical formulation == | == Mathematical formulation == | ||
| Line 26: | Line 26: | ||
Here is one local solution to the above control problem. | Here is one local solution to the above control problem. | ||
<gallery caption="Reference solution plots" widths=" | <gallery caption="Reference solution plots" widths="500px" heights="300px" perrow="1"> | ||
Image: | Image:Rao_Mease.png| States and discretized control for a local optimum. | ||
</gallery> | </gallery> | ||
== Miscellaneous and Further Reading == | == Miscellaneous and Further Reading == | ||
The | The problem description and further references can be found in the PhD thesis of Michael Ernst Geiger [[#GeigerPhD|[1]]]. | ||
== References == | == References == | ||
< | <span id="GeigerPhD">[1]</span> "Adaptive Multiple Shooting for Boundary Value Problems and Constrained Parabolic Optimization Problems" by M. E. Geiger <br> | ||
[[Category:MIOCP]] | [[Category:MIOCP]] | ||
[[Category: | [[Category:Sensitivity-seeking arcs]] | ||
Latest revision as of 13:47, 28 November 2025
| Rao Mease | |
|---|---|
| State dimension: | 1 |
| Differential states: | 1 |
| Discrete control functions: | 1 |
The Rao Mease problem is a very sensitive one-dimensional toy ODE model which is especially suited for multiple shooting solvers. It aims to minimize a quadratic Lagrange term.
The optimal control function exhibits a singular arc.
Mathematical formulation
Reference Solutions
Here is one local solution to the above control problem.
- Reference solution plots
-
States and discretized control for a local optimum.
Miscellaneous and Further Reading
The problem description and further references can be found in the PhD thesis of Michael Ernst Geiger [1].
References
[1] "Adaptive Multiple Shooting for Boundary Value Problems and Constrained Parabolic Optimization Problems" by M. E. Geiger