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further fixed README.md
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README.md

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@@ -45,34 +45,34 @@ The package was tested for Python >= 3.10, along with the listed packages versio
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The package defines an abstract class [`PyDiffGame.py`](https://github.com/krichelj/PyDiffGame/blob/master/src/PyDiffGame/PyDiffGame.py). An object of this class represents an instance of differential game.
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The input parameters to instantiate a `PyDiffGame` object are:
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* `A` : `np.array` of shape( $n,n$ )
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* `A` : `np.array` of shape $(n,n)$
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>System dynamics matrix
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* `B` : `np.array` of shape( $n,\sum_{i=1}^N m_i$ ), optional
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>Input matrix for all virtual control objectives
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* `Bs` : `Sequence` of `np.array` objects of len( $N$ ), each array $B_i$ of shape( $n,m_i$ ), optional
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* `Bs` : `Sequence` of `np.array` objects of len $(N)$, each array $B_i$ of shape $(n,m_i)$, optional
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>Input matrices for each virtual control objective
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* `Qs` : `Sequence` of `np.array` objects of len( $N$ ), each array $Q_i$ of shape( $n,n$ ), optional
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* `Qs` : `Sequence` of `np.array` objects of len $(N)$, each array $Q_i$ of shape $(n,n)$, optional
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>State weight matrices for each virtual control objective
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* `Rs` : `Sequence` of `np.array` objects of len( $N$ ), each array $R_i$ of shape( $m_i,m_i$ ), optional
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* `Rs` : `Sequence` of `np.array` objects of len $(N)$, each array $R_i$ of shape $(m_i,m_i)$, optional
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>Input weight matrices for each virtual control objective
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* `Ms` : `Sequence` of `np.array` objects of len( $N$ ), each array $M_i$ of shape( $m_i,m$ ), optional
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* `Ms` : `Sequence` of `np.array` objects of len $(N)$, each array $M_i$ of shape $(m_i,m)$, optional
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>Decomposition matrices for each virtual control objective
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* `objectives` : `Sequence` of `Objective` objects of len( $N$ ), each $O_i$ specifying $Q_i, R_i$ and $M_i$, optional
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* `objectives` : `Sequence` of `Objective` objects of len $(N)$, each $O_i$ specifying $Q_i, R_i$ and $M_i$, optional
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>Desired objectives for the game
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* `x_0` : `np.array` of len( $n$ ), optional
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* `x_0` : `np.array` of len $(n)$, optional
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>Initial state vector
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* `x_T` : `np.array` of len( $n$ ), optional
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* `x_T` : `np.array` of len $(n)$, optional
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>Final state vector, in case of signal tracking
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* `T_f` : positive `float`, optional
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>System dynamics horizon. Should be given in the case of finite horizon
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* `P_f` : `list` of `np.array` objects of len( $N$ ), each array $P_{f_i}$ of shape( $n,n$ ), optional, default = uncoupled solution of `scipy's solve_are`
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* `P_f` : `list` of `np.array` objects of len $(N)$, each array $P_{f_i}$ of shape $(n,n)$, optional, default = uncoupled solution of `scipy's solve_are`
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>
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>Final condition for the Riccati equation array. Should be given in the case of finite horizon
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* `state_variables_names` : `Sequence` of `str` objects of len( $N$ ), optional
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* `state_variables_names` : `Sequence` of `str` objects of len $(N)$, optional
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>The state variables' names to display when plotting
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* `show_legend` : `boolean`, optional
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>Indicates whether to display a legend in the plots
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* `state_variables_names` : `Sequence` of `str` objects of len( $n$ ), optional
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* `state_variables_names` : `Sequence` of `str` objects of len $(n)$, optional
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>The state variables' names to display
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* `epsilon_x` : `float` in the interval $(0,1)$, optional
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>Numerical convergence threshold for the state vector of the system

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