Control models#

This section contains documentation of selected control models. It is only intended to use as reference material.

class irlc.ex04.model_pendulum.SinCosPendulumModel(l=1.0, m=0.8, friction=0.0, max_torque=6.0, transform_coordinates=False)[source]#

phi_x(x)[source]#

Coordinate transformation of the state when the model is discretized.

This function specifies the coordinate transformation $x_k={\mathrm{\Phi }}_x(x(t_k))$ which is applied to the environment when it is discretized. It should accept a list of symbols, corresponding to $x$, and return a new list of symbols corresponding to the (discrete) coordinates.

Parameters:

x – A list of symbols [x0, x1, ..., xn] corresponding to $\mathbf{x}(t)$

Returns:

A new list of symbols corresponding to the discrete coordinates ${\mathbf{x}}_k$.

phi_x_inv(x)[source]#

Inverse of coordinate transformation for the state.

This function should specify the inverse of the coordinate transformation ${\mathrm{\Phi }}_x$, i.e. ${\mathrm{\Phi }}_x^{-1}$. In other words, it has to map from the discrete coordinates to the continuous-time coordinates: $x(t)={\mathrm{\Phi }}_x^{-1}(x_k)$.

Parameters:

x – A list of symbols [x0, x1, ..., xn] corresponding to ${\mathbf{x}}_k$

Returns:

A new list of symbols corresponding to the continuous-time coordinates $\mathbf{x}(t)$.

phi_u(u)[source]#

Coordinate transformation of the action when the model is discretized.

This function specifies the coordinate transformation $x_k={\mathrm{\Phi }}_x(x(t_k))$ which is applied to the environment when it is discretized. It should accept a list of symbols, corresponding to $x$, and return a new list of symbols corresponding to the (discrete) coordinates.

Parameters:

x – A list of symbols [x0, x1, ..., xn] corresponding to $\mathbf{x}(t)$

Returns:

A new list of symbols corresponding to the discrete coordinates ${\mathbf{x}}_k$.

phi_u_inv(u)[source]#

Inverse of coordinate transformation for the action.

This function should specify the inverse of the coordinate transformation ${\mathrm{\Phi }}_u$, i.e. ${\mathrm{\Phi }}_u^{-1}$. In other words, it has to map from the discrete coordinates to the continuous-time coordinates: $u(t)={\mathrm{\Phi }}_u^{-1}(u_k)$.

Parameters:

x – A list of symbols [u0, u1, ..., ud] corresponding to ${\mathbf{u}}_k$

Returns:

A new list of symbols corresponding to the continuous-time coordinates $\mathbf{u}(t)$.

u_bound()[source]#

The bound on the terminal state $\mathbf{u}(t)$.

Return type:

Box

Returns:

An appropriate gymnasium Box instance.