mpcinterface

Given an MPC problem of the form

$$ \begin{align} min_{x_{1:H},u_{1:H-1}} ~\sum_{k=1}^{H-1}\left(\frac{1}{2}x_k^\top Q_k x_k + \frac{1}{2}u_k^\top R_k u_k\right) + x_H^\top P_H x_H \\ s.t.~~ x_{k+1} = A_k x_k + B_k u_k \\ x_{min} \leq x_k \leq x_{max} \\ u_{min} \leq u_k \leq u_{max} \\ \end{align} $$

this package re-formulates the MPC problem into a canonical Quadratic Program of the form

$$ \begin{align} min_z \frac{1}{2} z^\top \bar{P} z + \bar{q}^\top z \\ s.t.~~ \bar{l} \leq \bar{A}z \leq \bar{u} \\ \end{align} $$

where $$z = [x_1, u_1, x_2, u_2, \dots, u_{H-1}, x_H] ^\top $$

More specifically, this package returns the $\bar{P}, \bar{q}, \bar{l}, \bar{u}$ and $\bar{A}$ matrices for your QP MPC problem. These matrices can then be directly passed to off-the-shelf QP solvers like OSQP.

Installation

This package is compiled using the Bazel build system. Install Bazel by following the installation instructions here

The only other dependency of this package is Eigen. This package however automatically downloads its own copy of Eigen during compilation so it doesn't matter whether or not you already have Eigen installed on your local system.

Usage

See the test files for usage examples.