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Regularization in DDPC: A Convex Relaxation Perspective

In this project, we introduce a novel bi-level optimization formulation based on the trajectory library of the dynamic system and discuss a series of its convex relaxation. This repository contains the MATLAB scripts for reproducing the experiments in our paper.

Convex Relaxation for a Bi-level Formulation of Data-driven Predictive Control (DDPC)

Data-driven Predictive Control (DDPC) 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, its mechanism for nondeterministic and nonlinear systems, and the relationship between different DDPC variants, involving regularization 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 DDPC can be considered as convex relaxations of this bi-level formulation. Notably, a novel variant called O-DDPC has shown remarkable empirical performance on systems beyond deterministic LTI settings.

Schematic of data-driven control

Bi-level Formulation

Inner Problem

Dependency

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

Instruction

Non-deterministic LTI System

  • The main_linear_Diff_Noise can be used to reproduce results for non-deterministic LTI system with different pre-collected trajectories and different controllers. The pre-collected trajectories are in Non_deterministic_LTI\data_100_New.
  • The results for reproducing Fig. 4 are in results_Exp and the figure is plotted by the plot_avg_cost_var.

Nonlinear System:

  • The main_Nonlinear 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_New.
  • The results for reproducing Fig. 5 and Fig. 6 are in results_Nonlinear. The Fig. 5 and Fig. 6 are plotted by plot_avg_cost and plot_avg_cost_var, respectively.

Contact us

To contact us about Regularization in DDPC, email either Xu Shang or Yang Zheng.