Risk-aware stochastic control of a sailboat

This repository contains the source code used to generate all examples presented in "Risk-aware stochastic control of a sailboat" manuscript by MingYi Wang, Natasha Patnaik, Anne Somalwar, Jingyi Wu, and Alexander Vladimirsky.

License

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.

Abstract of our manuscript

Sailboat path-planning is a natural hybrid control problem (due to continuous steering and occasional "tack-switching" maneuvers), with the actual path-to-target greatly affected by stochastically evolving wind conditions. Previous studies have focused on finding risk-neutral policies that minimize the expected time of arrival. In contrast, we present a robust control approach, which maximizes the probability of arriving before a specified deadline/threshold. Our numerical method recovers the optimal risk-aware (and threshold-specific) policies for all initial sailboat positions and a broad range of thresholds simultaneously. This is accomplished by solving two quasi-variational inequalities based on second-order Hamilton-Jacobi-Bellman (HJB) PDEs with degenerate parabolicity. Monte-Carlo simulations show that risk-awareness in sailing is particularly useful when a carefully calculated bet on the evolving wind direction might yield a reduction in the number of tack-switches.

Manuscript

The "Risk-aware stochastic control of a sailboat" manuscript can be found here.

Contributions & Acknowledgements

• The problem statement and the numerical scheme were developed by MingYi Wang, Natasha Patnaik, Anne Somalwar, Jingyi Wu, and Alexander Vladimirsky.
• The implementation was carried out by MingYi Wang, Natasha Patnaik, Anne Somalwar, and Jingyi Wu.
• The manuscript was written by MingYi Wang, Natasha Patnaik, Anne Somalwar, Jingyi Wu, and Alexander Vladimirsky.
• The authors acknowledge Cole Miles, Roberto Ferretti, and Adriano Festa for inspiring our work.

Instructions

Requirements:

• The C++ code requires the users to install the "Boost" library (external).

  • We install it directly under the directory Cpp_code. Please feel free to install it anywhere you want on your end but you would have to modify its path in the Makefile described below.

• The CDFs and the deterministic-optimal policy are generated with Matlab code.

Running the C++ Code:

The following instructions explain how to run the Solver for our risk(threshold)-aware optimal value functions/policies using the Makefile.

To change compilers, edit CC= by putting your desired compiler after the = sign. The default compiler is set to g++.

To update the path/version of the "Boost" library you've installed, edit BOOSTPATH by putting your own path/version after the = sign. The current path/version is ./boost_1_79_0.

To compile the code, type make main in the terminal in this folder.

• Please note that you need to enter the Risk-Neutral folder to run the PDE solver for the risk-neutral value function/policy, and the Risk-Aware folder to run the PDE solver for the risk-aware value function/policy, respectively.
• In either case, after compilation, type ./main to run the respective PDE solver.

To delete the executable and the data files, type make clean.

Running the Matlab Code:

To generate a CDF with risk(threshold)-aware optimal policies:

• Sailing_Risk_Aware_CDF.m
  • Produces a CDF $y(s) = {\mathbb{P}}(T \le s)$ that measures the probability of keeping the accumulative time-to-target $T$ under any threshold value $s$ but maximized at a given initial threshold/budget $\hat{s}$ using threshold-aware policies. It will produce a plot of the CDF and a plot of a sample path at the end of execution.
  • Note: It requires folders containing data matrices of the risk-neutral policy (optimal steering angle/switchgrid) and data matrices of the risk-aware policy (optimal steering angle/switchgrid) as inputs.
    • Please make sure the folder names under the output folder in both cases are the same with the same wind drift and diffusion constants.
    • In the simplest case, you can just run the C++ code without creating another folder under output and just define the argument as DataFile_dir = ''.

To generate a CDF with the risk-neutral policy:

• Sailing_Risk_Neutral_CDF.m
  • Produces a CDF $y(s) = {\mathbb{P}}(T \le s)$ that measures the probability of success where the cumulative time-to-target $T$ is within any positive threshold value $s$ using the risk-neutral policy. It will produce a plot of the CDF and a plot of a sample path at the end of execution.
  • Note: It requires a folder (under output) containing data matrices of the risk-neutral policy (optimal steering angle/switchgrid).
  • In the simplest case, you can just run the C++ code without creating another folder under output and just define the argument as DataFile_dir = ''.

Demonstration:

• demo.m
  • This script is solely for demonstration. The user need to compile and run the C++ code first before running this script. (Please start with a coarse grid.)