Stl Integer Variable

Simple example using ox.stl.IntegerVariable to enforce discrete-valued states.

This example sets up a 1D integrator where a second "gear" state must always take one of three discrete values {-1, 0, 1}. The control drives the position state x, while the gear state g is itself a continuous variable that is penalized whenever it deviates from the allowed discrete set.

• State x: position, driven by control u
• State g: gear-like variable constrained to {-1, 0, 1} at every node
• u also acts as the rate of change for g (both share the same control)
• The IntegerVariable STL constraint is enforced over the full horizon

Run it directly to solve and print the resulting trajectory.

File: examples/abstract/stl_integer_variable.py

import os
import sys

import numpy as np

import openscvx as ox
from openscvx import Problem

current_dir = os.path.dirname(os.path.abspath(__file__))
project_root = os.path.dirname(os.path.dirname(current_dir))
if project_root not in sys.path:
    sys.path.append(project_root)


# Discretization parameters
N = 10
total_time = 10.0

# Scalar position state
x = ox.State("x", shape=(1,))
x.min = np.array([0.0])
x.max = np.array([5.0])
x.initial = np.array([0.0])
x.final = [5.0]


# Control: drives position; gear integrates toward chosen discrete level
u = ox.Control("u", shape=(1,), parameterization="ZOH")
u.min = np.array([0.0])
u.max = np.array([10.0])
u.guess = np.ones((N, 1)) * 8.0

states = [x]
controls = [u]

# Dynamics: x_dot = u, g_dot = v
dynamics = {
    "x": u,
}

# Box constraints on states and controls
constraints = []
for state in states:
    constraints.extend(
        [
            ox.ctcs(state <= state.max),
            ox.ctcs(state.min <= state),
        ]
    )

# IntegerVariable: g must equal one of the allowed levels at every node
allowed_levels = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]
levels = ox.stl.IntegerVariable(u, allowed_levels, c=1e-8)
constraints.append(levels.over((0, N - 1)))


# Time configuration
time = ox.Time(
    initial=0.0,
    final=ox.Minimize(total_time),
    min=0.0,
    max=total_time,
    uniform_time_grid=True,
    time_dilation_min=0.2,
    time_dilation_max=2.0,
)

problem = Problem(
    dynamics=dynamics,
    constraints=constraints,
    states=states,
    controls=controls,
    N=N,
    time=time,
    algorithm={"autotuner": ox.ConstantProximalWeight(), "ep_vc": 1e-3, "lam_cost": 1e0},
    float_dtype="float64",
)

problem.settings.prp.dt = 0.001


if __name__ == "__main__":
    problem.initialize()
    results = problem.solve()
    results = problem.post_process()