• What is this?
• Local Installation
• Required Input

• Mathematical Description
• Supported Scenarios
• References

PyDiffGame is a Python package that allows to solve equations arising in models that involve the use of differential games for finding optimal controllers of a multi-objective system with multiple controlled objects.

To clone Git repository locally run this from the command prompt:

git clone https://github.com/krichelj/PyDiffGame.git

The package contains a file named PyDiffGame.py and a class of the same name. An object of the class represents an instance of differential game. Once the object is created, the method that calls for the game to begin is play_the_game. All the constants are defined in the Mathematical Description section. The input parameters to instantiate a PyDiffGame object are:

• A : numpy 2-d array, of shape()

The system dynamics matrix

• B : list of numpy 2-d arrays, of len(), each matrix of shape(),

System input matrices for each control agenda

• Q : list of numpy 2-d arrays, of len(), each matrix of shape(),

Cost function state weights for each control agenda

• R : list of numpy 2-d arrays, of len(), each matrix of shape(),

Cost function input weights for each control agenda

• cl : boolean

Indicates whether to render the closed (True) or open (False) loop behaviour

• T_f : positive float, optional, default = 5

System dynamics horizon. Should be given in the case of finite horizon

• X_0 : numpy 2-d array, of shape(), optional

Initial state vector

• P_f : list of numpy 2-d arrays, of shape(), optional, default = solution of scipy's solve_continuous_are

Final condition for the Riccati equation matrix. Should be given in the case of finite horizon

• data_points : positive int, optional, default = 1000

Number of data points to evaluate the Riccati equation matrix. Should be given in the case of finite horizon

Let us consider the following input parameters for the instantiation of a PyDiffGame object and corresponding call for play_the_game:

import numpy as np
from PyDiffGame import PyDiffGame

A = np.array([[-2, 1],
              [1, 4]])
B = [np.array([[1, 0],
               [0, 1]]),
     np.array([[0],
               [1]]),
     np.array([[1],
               [0]])]
Q = [np.array([[1, 0],
               [0, 1]]),
     np.array([[1, 0],
               [0, 10]]),
     np.array([[10, 0],
               [0, 1]])
     ]
R = [np.array([[100, 0],
               [0, 200]]),
     np.array([[5]]),
     np.array([[7]])]

cl = False
X0 = np.array([10, 20])
T_f = 5
P_f = [np.array([[10, 0],
                 [0, 20]]),
       np.array([[30, 0],
                 [0, 40]]),
       np.array([[50, 0],
                 [0, 60]])]
data_points = 1000
show_legend = True

P = PyDiffGame(A=A, B=B, Q=Q, R=R, cl=cl, X0=X0, P_f =P_f, T_f=T_f, data_points=data_points,
               show_legend=show_legend).play_the_game() # the function returns P

This will result in the following plot for the Riccati equation solution:

and the following state space simulation: