Although this could fall under engineering, I thought the Diff Eq forum was the most relevant. Let me know if I should post elsewhere.(adsbygoogle = window.adsbygoogle || []).push({});

I have a fairly basic system for which I'm trying to find a minimum-time optimal control policy. I know there are many ways to do this numerically, but since I'm trying to solve it very rapidly, I'm wondering if there is an analytical solution.

My system is a double integrator in 3-dimensions with the control inputs being acceleration. This system is affine because there is a constant forcing term (gravity - however this acceleration does not appear in the control accelerations). The control constraints are simply that the norm of the acceleration components our bounded above (i.e. there is a maximum total acceleration due to a maximum thrust of the system).

The cost function is just final time. I want to control my system from one state (A) to another (B) in a minimum amount of time while obeying my max acceleration constraint.

It looks very similar to a linear-quadratic regulator, which has an analytical solution. However, it is not a LQR because of the affine term and control constraints.

For those who do not study controls, this may be too esoteric. However for control engineers, there may be a commonly known answer of which I am unaware.

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Optimal Control of Linear-Affine System w/ Constraints

Loading...

Similar Threads for Optimal Control Linear |
---|

I Linear differential equation |

A Pontryagin minimum principle with control constraints |

I Minimizing a non-linear ODE in f, f_t |

I How to find a solution to this linear ODE? |

A Causality in differential equations |

**Physics Forums | Science Articles, Homework Help, Discussion**