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Add Superlinear Homotopy Update #2

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Dec 8, 2022
Merged

Add Superlinear Homotopy Update #2

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eef833e
add superlinear update rule
apozharski Dec 8, 2022
0566abc
add update rule test to test_ocp
apozharski Dec 8, 2022
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2 changes: 1 addition & 1 deletion nosnoc/__init__.py
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
from .nosnoc import NosnocSolver, NosnocModel, NosnocOcp
from .nosnoc_settings import NosnocSettings, MpccMode, IRKSchemes, StepEquilibrationMode, CrossComplementarityMode, IrkRepresentation, PssMode, IrkRepresentation
from .nosnoc_settings import NosnocSettings, MpccMode, IRKSchemes, StepEquilibrationMode, CrossComplementarityMode, IrkRepresentation, PssMode, IrkRepresentation, HomotopyUpdateRule
from .helpers import NosnocSimLooper
from .utils import casadi_length
from .plot_utils import plot_timings, latexify_plot
16 changes: 12 additions & 4 deletions nosnoc/nosnoc.py
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Original file line number Diff line number Diff line change
Expand Up @@ -6,13 +6,13 @@
import numpy as np
from casadi import SX, vertcat, horzcat, sum1, inf, Function, diag, nlpsol, fabs, tanh, mmin, transpose, fmax, fmin

from nosnoc.nosnoc_settings import NosnocSettings, MpccMode, InitializationStrategy, CrossComplementarityMode, StepEquilibrationMode, PssMode, IrkRepresentation
from nosnoc.nosnoc_settings import NosnocSettings, MpccMode, InitializationStrategy, CrossComplementarityMode, StepEquilibrationMode, PssMode, IrkRepresentation, HomotopyUpdateRule
from nosnoc.utils import casadi_length, print_casadi_vector, casadi_vertcat_list, casadi_sum_vectors, generate_butcher_tableu, generate_butcher_tableu_integral, flatten_layer, flatten, increment_indices, validate


@dataclass
class NosnocModel:
"""
r"""
\dot{x} \in f_i(x, u) if x(t) in R_i \subset \R^{n_x}

with R_i = {x \in \R^{n_x} | diag(S_i,\dot) * c(x) > 0}
Expand Down Expand Up @@ -834,7 +834,7 @@ def solve(self):
print('sigma \t\t compl_res \t CPU time \t iter \t status')

w0 = self.w0
sigma_k = settings.sigma_0 / settings.homotopy_update_slope
sigma_k = settings.sigma_0

# lambda00 initialization
x0 = w0[self.ind_x[0]]
Expand All @@ -843,7 +843,6 @@ def solve(self):

# homotopy loop
for ii in range(settings.max_iter_homotopy):
sigma_k = settings.homotopy_update_slope * sigma_k
p_val[0] = sigma_k

# solve NLP
Expand Down Expand Up @@ -879,6 +878,15 @@ def solve(self):
if complementarity_residual < settings.comp_tol:
break

if sigma_k <= settings.sigma_N:
break

# Update the homotopy parameter.
if settings.homotopy_update_rule == HomotopyUpdateRule.LINEAR:
sigma_k = settings.homotopy_update_slope * sigma_k
elif settings.homotopy_update_rule == HomotopyUpdateRule.SUPERLINEAR:
sigma_k = max(settings.sigma_N, min(settings.homotopy_update_slope * sigma_k, sigma_k**settings.homotopy_update_exponent))

# collect results
results = dict()
results["x_out"] = w_opt[self.ind_x[-1][-1]]
Expand Down
10 changes: 9 additions & 1 deletion nosnoc/nosnoc_settings.py
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Expand Up @@ -43,6 +43,10 @@ class IrkRepresentation(Enum):
# NOTE: tested in test_ocp


class HomotopyUpdateRule(Enum):
LINEAR = 0
SUPERLINEAR = 1

class PssMode(Enum):
# NOTE: tested in simple_sim_tests
STEWART = 0
Expand Down Expand Up @@ -74,7 +78,7 @@ class NosnocSettings:
max_iter_homotopy: int = 0

initialization_strategy: InitializationStrategy = InitializationStrategy.ALL_XCURRENT_W0_START
homotopy_update_slope: float = 0.1

irk_representation: IrkRepresentation = IrkRepresentation.INTEGRAL

# IRK and FESD Settings
Expand Down Expand Up @@ -104,6 +108,10 @@ class NosnocSettings:
# MPCC and Homotopy Settings
comp_tol: float = 1e-8
sigma_0: float = 1.0
sigma_N: float = 1e-8
homotopy_update_slope: float = 0.1
homotopy_update_exponent: float = 1.5
homotopy_update_rule: HomotopyUpdateRule = HomotopyUpdateRule.LINEAR

# step equilibration
step_equilibration: StepEquilibrationMode = StepEquilibrationMode.HEURISTIC_DELTA
Expand Down
48 changes: 25 additions & 23 deletions test/test_ocp.py
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Expand Up @@ -25,29 +25,31 @@ def test_loop():
for irk_representation in nosnoc.IrkRepresentation:
for irk_scheme in nosnoc.IRKSchemes:
for pss_mode in PSS_MODES:
settings = get_default_settings()
settings.comp_tol = 1e-5
settings.N_stages = 5
settings.N_finite_elements = 2
settings.equidistant_control_grid = equidistant_control_grid
settings.step_equilibration = step_equilibration
settings.irk_representation = irk_representation
settings.irk_scheme = irk_scheme
settings.pss_mode = pss_mode

print(f"test setting: {settings}")
results = solve_ocp(settings)

x_traj = results["x_traj"]
u_traj = results["u_traj"]
t_grid = results["t_grid"]

np.allclose(x_traj[0], X0, atol=1e-4)
np.allclose(x_traj[-1][:2], X_TARGET, atol=1e-4)
np.allclose(t_grid[-1], TERMINAL_TIME, atol=1e-6)
np.allclose(t_grid[0], 0.0, atol=1e-6)
np.alltrue(u_traj < UBU)
np.alltrue(u_traj > LBU)
for homotopy_update_rule in nosnoc.HomotopyUpdateRule:
settings = get_default_settings()
settings.comp_tol = 1e-5
settings.N_stages = 5
settings.N_finite_elements = 2
settings.equidistant_control_grid = equidistant_control_grid
settings.step_equilibration = step_equilibration
settings.irk_representation = irk_representation
settings.irk_scheme = irk_scheme
settings.pss_mode = pss_mode
settings.homotopy_update_rule = homotopy_update_rule

print(f"test setting: {settings}")
results = solve_ocp(settings)

x_traj = results["x_traj"]
u_traj = results["u_traj"]
t_grid = results["t_grid"]

np.allclose(x_traj[0], X0, atol=1e-4)
np.allclose(x_traj[-1][:2], X_TARGET, atol=1e-4)
np.allclose(t_grid[-1], TERMINAL_TIME, atol=1e-6)
np.allclose(t_grid[0], 0.0, atol=1e-6)
np.alltrue(u_traj < UBU)
np.alltrue(u_traj > LBU)


if __name__ == "__main__":
Expand Down