Utilities

Helper functions and enumerations used across PRoTECT.

generate_polynomial

from src.functions.generate_polynomial import generate_polynomial

polys = generate_polynomial(variables, lower_bounds, upper_bounds)

Creates the set-defining polynomials \(g_i(x) = (x_i - l_i)(u_i - x_i)\) used to represent rectangular regions in the SOS program. A point \(x\) is inside the region when all \(g_i(x) \geq 0\).

Parameters:

Parameter

Type

Description

variables

tuple

SymPy symbols for the state variables.

lower_bounds

np.ndarray

Lower bounds of the region. Shape: (dim,).

upper_bounds

np.ndarray

Upper bounds of the region. Shape: (dim,).

Returns: List of SymPy expressions, one per dimension.

SystemMode

Enumeration of the four supported system types.

from src.utils.system_mode import SystemMode

Member

Value

SystemMode.DT_DS

"discrete_deterministic"

SystemMode.DT_SS

"discrete_stochastic"

SystemMode.CT_DS

"continuous_deterministic"

SystemMode.CT_SS

"continuous_stochastic"

NoiseType

Enumeration of noise distributions for stochastic systems.

from src.utils.noise_type import NoiseType

Member

Value

NoiseType.normal

"Normal"

NoiseType.exponential

"Exponential"

NoiseType.uniform

"Uniform"

doublefactorial / factorial

Mathematical utility functions used internally by the stochastic barrier computations for computing moments of noise distributions.

from src.functions.doublefactorial import doublefactorial
from src.functions.factorial import factorial