Convex Approximation for DeePC

In this project, we introduce a new bi-level optimization formulation and discuss a series of its convex approximations by relaxing some hard constraints. This repository contains the MATLAB scripts for reproducing the experiments in our paper.

Convex Approximations for a Bi-level Formulation of Data-Enabled Predictive Control (DeePC)

Data-EnablEd Predictive Control (DeePC) combines behavioral theory with receding horizon control has received increasing attention. It is first established for LTI systems and has been extended and applied for practical systems beyond LTI settings which has shown promising results. However, the relationship between different DeePC variants, involving regularization and dimension reduction, remains unclear.

In this paper, we introduce a new bi-level formulation incorporating both system ID techniques and predictive control, and discuss how existing and new variants of DeePC can be considered as convex approximations of this bi-level formulation. Notably, a novel variant called DeeP-SVD-Iter has shown remarkable empirical performance on systems beyond deterministic LTI settings.

Schematic of data-driven control

Bi-level Formulation

Dependency

The code requires the installation of Mosek and the plot requires function multiple_boxplot.

Instruction

Non-deterministic LTI System

• The main_linear_100 and main_linear_Hyper can be used to reproduce results for non-deterministic LTI system with different pre-collected trajectories and different hyperparameters. The pre-collected trajectories are in Non_deterministic_LTI\data_100.
• The results for reproducing Fig. 2 are in result_eq_all, result_eq_Hy_SVD and result_eq_Hy_SVD_SPC and the figure is plotted by the plot_traj.
• The results for reproducing Fig. 3 are in results_Hyper and the figure is plotted by the plot_cost.
• The results for reproducing Table 1 and Fig. 4 are in results_100exp and the figure is also plotted by plot_traj.

Nonlinear System:

• The main_Nonlinear_100 and can be used to reproduce results for systems with various of nonlinearity with different pre-collected trajectories. The pre-collected trajectories are in Nonlinear\data_100.
• The results for reproducing Fig. 5 and Fig. 6 are in results_100Exp. The Fig. 5 and Fig. 6 are plotted by plot_avg_cost and plot_avg_cost_var, respectively.

Contact us

To contact us about robust DeeP-LCC, email either Xu Shang or Yang Zheng.