Solve a standard Model Predictive Control (MPC) problem written as \begin{eqnarray} \min\limits_{(uk){k\in [0,N-1]}} & \sum\limits_{k=0}^{N_p-1} x_k^T Q xk + \sum\limits{k=0}^{N_t-1} u_k^T T x_k + x_k^T T^T u_k + u_k^T R u_k\ \text{s.t.} & x0 = x{init}\ & x_{k+1} = A x_k + B uk\ & u{min} \leq uk \leq u{max}\ & A_x x_k + A_u \delta u_k \leq b \end{enarray}
where $Q$, $R$, $T$, $f_x$, $fu$ define the cost function. $A$ and $B$ is a state-space representation of the system. $x{init}$ is the initial state. The prediction horizon is denoted as $N_p$ and the control horizon is denoted as $N_t$.
The MPC is implemented to allow for Linear Time-Varying (LTV) systems. However, the size of the problem must not change over time.
The library is build with the CMake build system.
cd buid
cmake ..
makeAn C++\MEX S-function is defined to use the MPC in MATLAB\Simulink. The
S-function is defined in the sfunc directory. Run the MATLAB script
makeSFunction.m to compile the MEX executable.