Data Driven MPC

This project was created by Stephan Rappensberger and Mathias Korte

DDMPC.m - Class

Constructor

The constructer generates the DDMPC-class with user given paramters. These parameters can/must specified:

Necessary:

• matrcies U_d $\in\mathcal{R}^{N\times m}$ and Y_d $\in\mathcal{R}^{N\times p}$ contain the recorded input-output trajectory of length $N$ of a sythem with $u\in\mathcal{R}^{m}$ and $y\in\mathcal{R}^{p}$
• positiv definite cost-matricies Q $\in\mathcal{R}^{m\times m}$ and R $\in\mathcal{R}^{p\times p}$
• postive values for n and L (n is the number of past $u_k$ / $y_k$ considered for including the state information and L is number of steps the opimization problems solves into the future. It follows that complexer systems can only be solved with bigger n and L.)

Optional

• Control variant "ctrl_mode" $\in$ {"nominal"(default), "robust", "nonlinear"}
• Reference trajectory u_ref $\in\mathcal{R}^{m}$ and y_ref $\in\mathcal{R}^{p}$ (by default both are set to 0)
• Any number of input/output constrains: For $d$ input and $f$ output constrains: G_mat_u $\in\mathcal{R}^{d\times m}$, g_vec_u $\in\mathcal{R}^{d}$, G_mat_y $\in\mathcal{R}^{f\times p}$ and g_vec_y $\in\mathcal{R}^{f}$ (emty matrcies by default with $d=f=0$)
• Regularization parameters for Robust/Nonlinear DDMPC: $\lambda\alpha$, $\lambda\sigma$ and $\epsilon$ (default $=1$ for all)

Step function

• function inputs: new measuremnts u_m $\in\mathcal{R}^{m}$ and y_m $\in\mathcal{R}^{p}$
• returns: control input u $\in\mathcal{R}^{m}$

Evalutaion

For purposes of evaluation we included two files for testing our DDMPC:

• dc_motor_example.m: for the linear sysems with state space representation
• four_tank_example.m: for a nonlinear system

Literature

We implemented DDMPC based on this paper: "Data-driven model predictive control: closed-loop guarantees and experimental results" (https://arxiv.org/abs/2107.00966). But the whole idea of Data-driven MPC is first mentioned in "Data-Enabled Predictive Control: In the Shallows of the DeePC" (https://arxiv.org/abs/1811.05890)