Code to accompany: Learning Stabilizable Dynamical Systems via Control Contraction Metrics
These instructions will get you a copy of the project up and running on your local machine for development and testing purposes. All code is written in MATLAB.
There are five packages required:
- YALMIP : parsing the learning problems (convex),
- Mosek : SDP solver for the learning problems,
- TOMLAB : parsing the trajectory optimization and CCM controller problems (non-convex),
- SNOPT, NPSOL : solvers for the non-convex problems,
- cvx : auxiliary functions.
YALMIP and cvx are freely available. Mosek is freely available on an academic license. TOMLAB must be purchased (a 21-day trial license is available on their website). Evaluation copies of SNOPT and NPSOL are included with the trial TOMLAB download. In the near future, I will also release open-source alternatives for TOMLAB and SNOPT; additional details below.
Having installed the prerequisites (and adding them to the MATLAB path), download the repo, navigate to the repo in MATLAB, and execute the following in the command window:
run sndl_startup.m
This will add all necessary sub-directories of the repo to the MATLAB path.
This will take you through the various steps involved in reproducing the results in the paper. Currently, only the PVTOL example files are loaded. Additional systems will be uploaded in the near future.
Navigate to the data_gen folder, automated script: generate_PVTOL_data.m. Choose number of trajectories to generate and additional samples for constraint set as indicated within the script. Output files: PVTOL_data_train.mat and PVTOL_data_val.mat.
Navigate to main repo directory, automated script: Main.m. Adjustable parameters:
- Main.m: N_tr: # points to use for training (i.e., included in regression loss). This must be less than N_max (total number of demonstration tuples).
- Main.m: Nc: # points to use for initial constraint set. This constraint set will dynamically change within the algorithm to ensure constraints hold at all points in X.
- load_PVTOL_params.m: Parameter file for PVTOL. See definitions within.
After this, the code enters the script learn_loop.m corresponding to Algorithm 1 in the paper. It will first compute and save two baseline models (unconstrained-unregularized, and unconstrained-l_2 regularized least squares). Following this, the CCM-regularized model will be computed iteratively. Choose max # iterations (max_iter) and termination tolerance (eps_term) within the learn_loop.m script.
All saved functions are stored in learned_functions/ and marked with identifiers 'unconu' and 'uncon' for the two baselines, and 'ccm' for the CCM-regularized model. The additional identifier is the number N_tr. Example solutions are provided.
Navigate to the test folder. In order:
- gen_test_traj_PVTOL.m: Generate test trajectories for the various models. Trajectory optimization uses the Pseudospectral Method with Lagrange interpolating polynomials, CGL nodes, and Clenshaw-Curtis quadrature; see also Fahroo et. al.. Outputs: trajectory datasets PVTOL_test_traj_ with identifiers: model type ('unconu', 'uncon', 'ccm') and training dataset size.
- test_dynamics_PVTOL_bulk.m: Simulate and record data for each model on the generated test trajectories in bulk. Alternatively, load up the trajectory data from any of the generated trajectory datasets, and directly use the simulation functions test_unconu_dynamics_PVTOL, test_uncon_dynamics_PVTOL, or test_CCM_dynamics_PVTOL.
- analyze_PVTOL_results.m: Compare all models with shared (regression) training datasets.
Notes:
- Trajectory optimizer uses TOMLAB and SNOPT. To switch to alternative package, you can still use the same setup functions (constraints, gradients, Hessians, etc) and simply change the optimization call. An example using fmincon will be uploaded soon.
- If using the CCM-LQR hybrid controller when running sims for the CCM model, you will need TOMLAB and NPSOL for solving the geodesic optimization problem. In their absence, given the setup files, you can simply switch to an alternative optimization package.
This project is licensed under the MIT License - see the LICENSE.md file for details