Rao Mease

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 integer control functions exhibits a singular arc.

Mathematical formulation

$\begin{array}{lll}\underset{x,w}{\min }& & \underset{0}{\overset{10}{\int }}(x(t{)}^2+w(t{)}^2)dt\\ \text{subject to}\\ \dot{x}(t)& =& -x(t{)}^3+w(t),\\ x(0)& =& 1,\\ x(10)& =& 1.5\end{array}$

Reference Solutions

Here is one local solution to the above control problem.

• Reference solution plots
• 
  States and measurement control for different choices of $p$.

Miscellaneous and Further Reading

The Toy OED problem was introduced by Sebastian Sager in the paper [Sager2013]Author: Sager, S.
Journal: SIAM Journal on Control and Optimization
Number: 4
Pages: 3181--3207
Title: Sampling Decisions in Optimum Experimental Design in the Light of Pontryagin's Maximum Principle
Url: http://mathopt.de/PUBLICATIONS/Sager2013.pdf
Volume: 51
Year: 2013
, which contains further details.

References

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