Title	Convexified contextual optimization for on-the-fly control of smooth systems
Authors	Abraham P. Vinod, Arie Israel, and Ufuk Topcu
Conference	American Control Conference, 2020

This repository provides codes to reproduce the figures of the paper.

• Correct-by-construction approximation bounds under smoothness, convexity, and monotonicity
  • Figures 1 and 2 are given by Approximation bounds via side information.ipynb
• Empirical comparison of the proposed approach, C2Opt, with SINDYc, CGP-LCB, and the true one-step optimal trajectory
  • Figures 3 and 4 are given by One-step control of unicycle.ipynb
  • You have to change figure_3 = True to figure_3=False in the first cell to obtain Figure 4.

Reproducibility instructions

Use $ conda env create -f conda_env_for_acc2020.yml to get the exact environment used for developing and testing this code. Please perform step 4 below to install coveropt.

Step-by-step guide

1. Create conda environment
   • $ conda create -n acc2020_c2opt python=3.7 scipy matplotlib jupyter tqdm pandas
2. (optional) Install gurobi
   • $ conda install -c gurobi gurobi
   • Availability of gurobi provides for a faster computation. However, its use requires a license (see https://www.gurobi.com/ for more details).
3. Install cvxpy and gpyopt
   • $ pip install cvxpy gpyopt==1.2.5
   • Free software alternative to gurobi (See www.cvxpy.org for more details)
4. Install coveropt (v0.1)
   • $ cd coveropt && pip install -e . && cd ..
5. Run $ jupyter notebook and then open the desired notebook.

Scripts

Notebooks and the associated script files

1. Approximation bounds via side information.ipynb or Approximation bounds via side information.py generates Figures 1 and 2
   • BoundsWithSideInfo.py provides the class that uses coveropt/coveropt/classes/LipSmoothFun.py to implement the correct-by-construction bounds
2. One-step control of unicycle.ipynb or One-step control of unicycle.py generates Figures 3 and 4
   • MyopicDataDrivenControl.py provides the base class for one-step control of unknown dynamics
   • MyopicDataDrivenControlSINDYc.py implements the SINDYc method via LASSO
     • See Kaiser, Eurika, J. Nathan Kutz, and Steven L. Brunton. "Sparse identification of nonlinear dynamics for model predictive control in the low-data limit." Proceedings of the Royal Society A 474.2219 (2018): 20180335 for more details
   • MyopicDataDrivenControlContextGP.py implements the approach utilizing Contextual Gaussian Process optimized via lower confidence bound. This method utilizes gpyopt.
     • See Krause, Andreas, and Cheng S. Ong. "Contextual gaussian process bandit optimization." Advances in neural information processing systems. 2011 and https://github.com/SheffieldML/GPyOpt for more details
   • MyopicDataDrivenControlTrue.py provides a benchmark solution --- the optimal one-step trajectory under the knowledge of the dynamics. It uses scipy.optimize to solve the one-step receding horizon control problem.
   • coveropt/coveropt/classes/applications/C2Opt/ implements the proposed C2Opt method.

Contact

Please contact Abraham Vinod (aby.vinod@gmail.com) for bugs or questions regarding this code.