Discrete-Time Deterministic (dt-DS)

Functions for computing barrier certificates for discrete-time deterministic systems over an infinite time horizon.

dt_DS

from src.functions.dt_DS import dt_DS

result = dt_DS(b_degree, dim, L_initial, U_initial, L_unsafe, U_unsafe,
               L_space, U_space, x, f, solver="mosek", gam=None, lam=None,
               l_degree=None)

Parameters:

Parameter	Type	Description
b_degree	int	Degree of the barrier polynomial.
dim	int	Dimension of the state space.
L_initial	np.ndarray	Lower bounds of the initial set. Shape: (dim,).
U_initial	np.ndarray	Upper bounds of the initial set. Shape: (dim,).
L_unsafe	np.ndarray	Lower bounds of unsafe set(s). Shape: (n_regions, dim).
U_unsafe	np.ndarray	Upper bounds of unsafe set(s). Shape: (n_regions, dim).
L_space	np.ndarray	Lower bounds of the state space. Shape: (dim,).
U_space	np.ndarray	Upper bounds of the state space. Shape: (dim,).
x	tuple	SymPy symbols for state variables, e.g. sp.symbols('x1:3').
f	np.ndarray	Array of SymPy expressions defining the dynamics \(x_{k+1} = f(x_k)\).
solver	str	"mosek" (default) or "cvxopt".
gam	float or None	Fixed value for \(\gamma\). If None, determined by the solver.
lam	float or None	Fixed value for \(\lambda\). If None, determined by the solver.
l_degree	int or None	Degree of Lagrangian multipliers. Defaults to b_degree.

Returns: dict with keys b_degree, Barrier, gamma, lambda, solver_status, or None if infeasible.

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parallel_dt_DS

from src.functions.parallel_dt_DS import parallel_dt_DS

result = parallel_dt_DS(b_degree, dim, L_initial, U_initial, L_unsafe,
                        U_unsafe, L_space, U_space, x, f, solver="mosek",
                        gam=None, lam=None, l_degree=None)

Searches barrier polynomial degrees 2, 4, …, b_degree in parallel using multiprocessing. Parameters are identical to dt_DS except b_degree is the maximum degree to search.

Note

Must be called inside if __name__ == '__main__': due to Python multiprocessing.

Returns: The result dict from the first successful degree, or None.