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 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