CASL-HJX

A C++ library for solving Hamilton-Jacobi-Bellman equations in 2D, with specific applications for Linear Quadratic Regulator (LQR) and other control problems.

Features

• 2D Hamilton-Jacobi-Bellman equation solver
• Linear Quadratic Regulator (LQR) implementation
• Laplacian solver with dimensional reduction
• MATLAB export capabilities
• Flexible grid management system
• Configurable solver options

Project Structure

CASL-HJBX/                  
├── CMakeLists.txt          # Main CMake configuration
├── CASLCommonLibrary/      # Core library components
│   ├── CASLArray2D.cpp     # 2D array implementation
│   ├── CaslGrid2D.h        # Grid management
│   ├── CaslOptions.h       # Configuration options
│   ├── CASLCppToMatlab2D.cpp     # MATLAB export utilities
│   ├── CASLHamiltonian2D.cpp     # 2D Hamiltonian solver
│   ├── CASLHamiltonJacobi.cpp    # Hamilton-Jacobi solver
│   ├── CASLHamiltonJacobi2D.cpp  # 2D HJB implementation
│   ├── CASLRK4.cpp               # Runge-Kutta 4th order implementation
│   └── CASLSecondOrderDerivative2D_1D.cpp  # Second order derivative calculator
└── CASLProjects/           # Project implementations
    ├── projectLQR2D/       # Linear Quadratic Regulator
    │   ├── CMakeLists.txt
    │   ├── main.cpp
    │   ├── __Output/              # Generated output directory
    │   │   ├── LQR2D_32/         # Results for 32x32 grid
    │   │   │   └── phi/          # Value function results
    │   │   ├── LQR2D_64/         # Results for 64x64 grid
    │   │   │   └── phi/          # Value function results
    │   │   └── LQR2D_128/        # Results for 128x128 grid
    │   │       └── phi/          # Value function results
    │   └── projectLQR2D_lib/
    │       ├── CaslHamiltonianLQR2D.cpp    
    │       ├── CaslHamiltonianLQR2D.h
    │       ├── CaslLQRSystemDynamics.cpp   
    │       └── CaslLQRSystemDynamics.h
    ├── projectLaplacian2D_1D/     # 2D to 1D Laplacian solver
    │   ├── CMakeLists.txt
    │   ├── main.cpp
    │   ├── __Output/              # Generated output directory
    │   │   ├── phi/              # Solution profiles
    │   │   └── uStar/            # Control profiles
    │   └── projectLaplacian2D_1D_lib/
    │       ├── CaslHamiltonianDiffusion2D.cpp
    │       ├── CaslHamiltonianDiffusion2D.h
    │       ├── CaslInitialProfiles2D.cpp    
    │       └── CaslInitialProfiles2D.h
    ├── projectStochasticHH2D/     # Stochastic Hodgkin-Huxley Model
    │   ├── CMakeLists.txt
    │   ├── main.cpp
    │   ├── __Output/              # Generated output directory
    │   │   ├── phi/              # Value function results
    │   │   └── uStar/            # Optimal control results
    │   └── projectStochasticHH2D_lib/
    │       ├── CaslHHNeuronModel.cpp       
    │       ├── CaslHHNeuronModel.h
    │       ├── CaslHamiltonianHHModel.cpp  
    │       └── CaslHamiltonianHHModel.h
    └── projectDeterministicHH2D/  # Deterministic Hodgkin-Huxley Model
        ├── CMakeLists.txt
        ├── main.cpp
        ├── __Output/              # Generated output directory
        │   ├── phi/              # Value function results
        │   └── uStar/            # Optimal control results
        └── projectDeterministicHH2D_lib/
            ├── CaslHHSingleNeuronModel.cpp 
            ├── CaslHHSingleNeuronModel.h
            ├── CaslHHWholeSystemModel.cpp  
            ├── CaslHHWholeSystemModel.h
            ├── CaslHamiltonianHHModel.cpp  
            └── CaslHamiltonianHHModel.h

Prerequisites

• CMake 3.15 or higher
• C++17 compatible compiler
• For macOS: LLVM/Clang

Installation

macOS

1. Install required dependencies:

brew install llvm cmake

2. Clone and build the project:

git clone https://github.com/yourusername/CASL-HJX.git
cd CASL-HJX
mkdir build && cd build
cmake ..
make

Usage

Running Projects

Each project in the CASLProjects directory can be built and run independently:

cd build/CASLProjects/projectLQR2D
./projectLQR2D

Output Structure

Project outputs are organized as follows:

projectLQR2D/
└── __Output/
    └── LQR2D_[gridsize]/
        └── phi/

Components

Core Library (CASLCommonLibrary)

• CASLArray2D: Efficient 2D array implementation
• CaslGrid2D: Advanced grid management system
• CASLHamiltonJacobi2D: HJB equation solver
• CASLCppToMatlab2D: MATLAB integration utilities

Projects

1. projectLQR2D

   • Implements Linear Quadratic Regulator in 2D
   • Includes system dynamics and Hamiltonian solvers
   • Optimized for control problems

2. projectLaplacian2D_1D

   • Handles 2D to 1D dimensional reduction
   • Implements various boundary conditions
   • Efficient Laplacian solving algorithms

3. projectStochasticHH2D (In Development)

   • Will implement stochastic Hamilton-Jacobi equations
   • Planned support for uncertainty handling

4. projectDeterministicHH2D (In Development)

   • Will implement deterministic Hamilton-Jacobi equations
   • Focus on precise control solutions

Contributing

1. Fork the repository
2. Create your feature branch (git checkout -b feature/AmazingFeature)
3. Commit your changes (git commit -m 'Add some AmazingFeature')
4. Push to the branch (git push origin feature/AmazingFeature)
5. Open a Pull Request

License

This project is licensed under the MIT License - see the LICENSE file for details.

Author

• Faranak Rajabi
• Jacob Fingerman
• Andrew Wang
• Frederic Gibou

Contact

For questions and support, please open an issue in the GitHub repository.