A Comparison of Multi-Parametric Programming, Mixed-Integer Programming, Gradient Descent Based, and the Embedding Approach on Four Published Hybrid Optimal Control Examples

Details A Comparison of Multi-Parametric Programming, Mixed-Integer Programming, Gradient Descent Based, and the Embedding Approach on Four Published Hybrid Optimal Control Examples A Comparison of Multi-Parametric Programming, Mixed-Integer Programming, Gradient Descent Based, and the Embedding Approach on Four Published Hybrid Optimal Control Examples

2012-03-15

arxiv.org/abs/1203.3341v1

Mathematics

Optimization and Control

Submitted to 2012 IEEE Conference on Decision and Control

Scientific paper

This paper compares the embedding approach for solving hybrid optimal control problems to multi-parameter programming, mixed-integer programming, and gradient-descent based methods in the context of four published examples. The four examples include a spring-mass system, moving-target tracking for a mobile robot, two-tank filling, and a DC-DC boost converter. Numerical advantages of the embedding approach are set forth and validated for each example: significantly faster solution time, no ad hoc assumptions (such as predetermined mode sequences) or control models, lower performance index costs, and algorithm convergence when other methods fail. Specific (theoretical) advantages of the embedding approach over the other methods are also described: guaranteed existence of a solution under mild conditions, convexity of the embedded optimization problem solvable with traditional techniques such as sequential quadratic programming with no need for any mixed-integer programming, applicability to nonlinear systems, etc. Common misconceptions regarding the embedding approach are addressed including whether or not it results in an average value control model (no), is necessary to "tweak" the algorithm to get bang-bang solutions (no), requires infinite switching (no), has real-time capability (yes), or reduction to a classical nonlinear optimization problem (a desirable yes).

Affiliated with

Also associated with

No associations

Rating

A Comparison of Multi-Parametric Programming, Mixed-Integer Programming, Gradient Descent Based, and the Embedding Approach on Four Published Hybrid Optimal Control Examples does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Comparison of Multi-Parametric Programming, Mixed-Integer Programming, Gradient Descent Based, and the Embedding Approach on Four Published Hybrid Optimal Control Examples, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Comparison of Multi-Parametric Programming, Mixed-Integer Programming, Gradient Descent Based, and the Embedding Approach on Four Published Hybrid Optimal Control Examples will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-30749