Bryson Denham: Difference between revisions
RobertLampel (talk | contribs) Created page with "{{Dimensions |nd = 1 |nx = 2 |nw = 1 }} The '''Bryson-Denham problem''' is a two-dimensional toy ODE model. It aims to minimize a quadratic Lagrange term. The optimal integer control functions exhibits a singular arc. == Mathematical formulation == <p> <math> \begin{array}{lll} \displaystyle \min_{u} && \int_0^{1} \frac{1}{2} \cdot w(t)^2 dt \\ \text{subject to} \\ \quad \dot{x}(t)..." |
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<math> | <math> | ||
\begin{array}{lll} | \begin{array}{lll} | ||
\displaystyle \min_{ | \displaystyle \min_{w} && \int_0^{1} \frac{1}{2} \cdot w(t)^2 dt \\ | ||
\text{subject to} \\ | \text{subject to} \\ | ||
\quad \dot{x}(t) & = & v(t),\\ | \quad \dot{x}(t) & = & v(t),\\ | ||
\quad \dot{v}(t) & = & | \quad \dot{v}(t) & = & w(t), \\ | ||
\quad x(0) &=& 0, \\ | \quad x(0) &=& 0, \\ | ||
\quad v(0) &=& 1, \\ | \quad v(0) &=& 1, \\ | ||
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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:Bryson-Denham.png| States and discretized control for a local optimum. | ||
</gallery> | </gallery> | ||
== Miscellaneous and Further Reading == | == Miscellaneous and Further Reading == | ||
The Bryson-Denham problem is a variation of the double integrator problem [[#BH75|[1]]]. This formulation | The Bryson-Denham problem is a variation of the double integrator problem [[#BH75|[1]]]. This formulation can be found in [[#openmdao|[2]]]. | ||
== References == | == References == | ||
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[[Category:MIOCP]] | [[Category:MIOCP]] | ||
[[Category: | [[Category:Path-constrained arcs]] | ||
Latest revision as of 13:47, 28 November 2025
| Bryson Denham | |
|---|---|
| State dimension: | 1 |
| Differential states: | 2 |
| Discrete control functions: | 1 |
The Bryson-Denham problem is a two-dimensional toy ODE model. It aims to minimize a quadratic Lagrange term.
The optimal integer control functions 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 Bryson-Denham problem is a variation of the double integrator problem [1]. This formulation can be found in [2].
References
[1] Arthur E Bryson and Yu-Chi Ho. Applied Optimal Control: Optimization, Estimation and Control. CRC Press, 1975.
[2] Multidisciplinary Optimal Control Library: https://openmdao.org/dymos/docs/latest/examples/bryson_denham/bryson_denham.html