Dynamics¶

`openscvx.dynamics.Dynamics` `dataclass` ¶

Dataclass to hold a system dynamics function and (optionally) its gradients. This class is intended to be instantiated using the dynamics decorator wrapped around a function defining the system dynamics. Both the dynamics and optional gradients should be composed of jax primitives to enable efficient computation.

Usage examples:

@dynamics
def f(x_, u_):
    return x_ + u_
# f is now a Dynamics object

@dynamics(A=grad_f_x, B=grad_f_u)
def f(x_, u_):
    return x_ + u_

Or, if a more lambda-function-style is desired, the function can be directly wrapped:

dyn = dynamics(lambda x_, u_: x_ + u_)

Using Parameters in Dynamics

You can use symbolic Parameter objects in your dynamics function to represent tunable or environment-dependent values. The argument names for parameters must match the parameter name with an underscore suffix (e.g., I_sp_ for a parameter named I_sp). This is required for the parameter mapping to work correctly.

Example (3DoF rocket landing):

from openscvx.backend.parameter import Parameter
import jax.numpy as jnp

I_sp = Parameter("I_sp")
g = Parameter("g")
theta = Parameter("theta")

@dynamics
def rocket_dynamics(x_, u_, I_sp_, g_, theta_):
    m = x_[6]
    T = u_
    r_dot = x_[3:6]
    g_vec = jnp.array([0, 0, g_])
    v_dot = T/m - g_vec
    m_dot = -jnp.linalg.norm(T) / (I_sp_ * 9.807 * jnp.cos(theta_))
    t_dot = 1
    return jnp.hstack([r_dot, v_dot, m_dot, t_dot])

# Set parameter values before solving
I_sp.value = 225
g.value = 3.7114
theta.value = 27 * jnp.pi / 180

Using Parameters in Nodal Constraints

You can also use symbolic Parameter objects in nodal constraints. As with dynamics, the argument names for parameters in the constraint function must match the parameter name with an underscore suffix (e.g., g_ for a parameter named g).

Example:

from openscvx.backend.parameter import Parameter
from openscvx.constraints import nodal
import jax.numpy as jnp

g = Parameter("g")
g.value = 3.7114

@nodal
def terminal_velocity_constraint(x_, u_, g_):
    # Enforce a terminal velocity constraint using the gravity parameter
    return x_[5] + g_ * x_[7]  # e.g., vz + g * t <= 0 at final node

When building your problem, collect all parameters with Parameter.get_all() and pass them to your problem setup.

Parameters:

Name	Type	Description	Default
`f`	`Callable[[ndarray, ndarray], ndarray]`	Function defining the continuous time nonlinear system dynamics as x_dot = f(x, u, ...params). - x: 1D array (state at a single node), shape (n_x,) - u: 1D array (control at a single node), shape (n_u,) - Additional parameters: passed as keyword arguments with names matching the parameter name plus an underscore (e.g., g_ for Parameter('g')). If you want to use parameters, include them as extra arguments with the underscore naming convention. If you use vectorized integration or batch evaluation, x and u may be 2D arrays (N, n_x) and (N, n_u).	required
`A`	`Optional[Callable[[ndarray, ndarray], ndarray]]`	Jacobian of `f` w.r.t. `x`. If not specified, will be calculated using `jax.jacfwd`.	`None`
`B`	`Optional[Callable[[ndarray, ndarray], ndarray]]`	Jacobian of `f` w.r.t. `u`. If not specified, will be calculated using `jax.jacfwd`.	`None`

Returns:

Name	Type	Description
`Dynamics`		A dataclass bundling the system dynamics function and
		Jacobians.

Dynamics¶

openscvx.dynamics.Dynamics dataclass ¶

`openscvx.dynamics.Dynamics` `dataclass` ¶