Additional documentation on OSQP MPC example

[alexr...@gmail.com]

Having had experience in optimization and control, but being fairly new to the area of model predictive control, I was wondering if there are any links or papers with additional information/documentation on the quadrotor MPC example that was solved by OSQP (http://osqp.readthedocs.io/en/latest/examples/mpc.html). In particular, I'm hoping to understand what dynamic equations were linearized to produce the state transition matrix A, and control matrix B, and how the parameter values were chosen.

As an aside, I'm extremely excited to have found OSQP. I was amazed at its performance against stalwarts like MOSEK, Gurobi and even CVXGEN, and it's code generation capabilities seem extremely simple to implement. To the OSQP team, thanks for making this happen.

[Paul Goulart]

Thanks for your interest in our solver.   The origin of this example turns out to be a little difficult to track down.    Working backwards….

We took the problem data from this library of MPC benchmark problems : https://github.com/ferreau/mpcBenchmarking.   The paper describing that collection of benchmarks is here: https://ieeexplore.ieee.org/document/7330931/

Unfortunately, either of the above links gives much information about the origin of the particular problem.   I believe (but am not certain) that the problem description is the same as the one described in section 5.4 of this master’s thesis, which is reference [28] in the paper above.    The thesis says that the problem data came from an example from the EU HYCON project, and cites this link : http://control.ee.ethz.ch/~mpt/3/Main/BenchmarkExamples.   Unfortunately, the link doesn’t provide much detail either.

At a guess, I would assume that the origin of the paper (given the authors cited in the MPT3 link) is this paper, but I didn’t compare the problem there in detail with the one in the OSQP examples.

I hope that the above is at least marginally useful.

On 22 Apr 2018, at 03:37, <alexr...@gmail.com> <alexr...@gmail.com> wrote:

Having had experience in optimization and control, but being fairly new to the area of model predictive control, I was wondering if there are any links or papers with additional information/documentation on the quadrotor MPC example that was solved by OSQP (http://osqp.readthedocs.io/en/latest/examples/mpc.html). In particular, I'm hoping to understand what dynamic equations were linearized to produce the state transition matrix A, and control matrix B, and how the parameter values were chosen.

As an aside, I'm extremely excited to have found OSQP. I was amazed at its performance against stalwarts like MOSEK, Gurobi and even CVXGEN, and it's code generation capabilities seem extremely simple to implement. To the OSQP team, thanks for making this happen.

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