sto_sys = SysDescription((1, 1, 0),
name='Deterministic Storage for PV',
stationnary=False)
sto_sys.dyn = dyn_sto
sto_sys.control_box = admissible_controls
sto_sys.cost = cost_model
sto_sys.print_summary()
### Create the DP solver:
dpsolv = DPSolver(sto_sys)
# discretize the state space
N_E = 50
E_grid = dpsolv.discretize_state(0, E_rated, N_E)[0]
dpsolv.control_steps = (.001, )
dpsolv.print_summary()
J_fin = np.zeros(N_E)
J, pol = dpsolv.bellman_recursion(T_horiz, J_fin)
pol_sto = pol[..., 0]
### Plot the policy
plt.figure('policy')
plt.subplot(111,
title='$P_{grid}(t,E)$ policy',
xlabel='time',
ylabel='$E_{sto}$')
print('Invertory Control with (h={:.1f}, p={:.1f}, c={:.1f})'.format(h, p, c))
### DP Solver ##################################################################
from stodynprog import DPSolver
dpsolv = DPSolver(invsys)
# discretize the state space
xmin, xmax = (-3, 6)
N_x = xmax - xmin + 1 # number of states
dpsolv.discretize_state(xmin, xmax, N_x)
# discretize the perturbation
N_w = len(demand_values)
dpsolv.discretize_perturb(demand_values[0], demand_values[-1], N_w)
# control discretization step:
dpsolv.control_steps = (1, ) #
#dpsolv.print_summary()
### Value iteration
J_0 = np.zeros(N_x)
# first iteration
J, u = dpsolv.value_iteration(J_0)
print(u[..., 0])
# A few more iterations
J, u = dpsolv.value_iteration(J)
print(u[..., 0])
J, u = dpsolv.value_iteration(J)
print(u[..., 0])
J, u = dpsolv.value_iteration(J)
print(u[..., 0])
def optimize(crtReachMovementTask):
minimum_movement_length = crtReachMovementTask.minimum_movement_length
maximum_movement_length = crtReachMovementTask.maximum_movement_length
c = crtReachMovementTask.c
target_position = crtReachMovementTask.target_position
number_of_iterations = crtReachMovementTask.number_of_iterations
#functions defined here inside the optimizer
def dyn_inv(x, u, w):
'dynamical equation of the inventory stock `x`. Returns x(k+1).'
return (x + u + w, )
def op_cost(x, u, w):
'energy cost'
cost = abs(target_position - x) + c * u
#cost = abs(20-x)+c*u
# print(cost)
return cost
def admissible_movements(x):
'interval of allowed orders movements(x_k)'
U1 = (minimum_movement_length, maximum_movement_length)
return (U1, ) # tuple, to support several controls
# Attach it to the system description.
# Attach the dynamical equation to the system description:
movement_sys.dyn = dyn_inv
mov_values = [-6, -4, -2, 0, 2, 4, 6]
mov_proba = [0.1, 0.1, 0.15, 0.3, 0.15, 0.1, 0.1]
demand_law = stats.rv_discrete(values=(mov_values, mov_proba))
demand_law = demand_law.freeze()
demand_law.pmf([0, 3]) # Probality Mass Function
demand_law.rvs(10) # Random Variables generation
movement_sys.perturb_laws = [demand_law
] # a list, to support several perturbations
movement_sys.control_box = admissible_movements
movement_sys.cost = op_cost
print('Movement Control with (c={:.1f})'.format(c))
dpsolv = DPSolver(movement_sys)
# discretize the state space
xmin, xmax = (0, 100)
N_x = xmax - xmin + 1 # number of states
dpsolv.discretize_state(xmin, xmax, N_x)
# discretize the perturbation
N_w = len(mov_values)
dpsolv.discretize_perturb(mov_values[0], mov_values[-1], N_w)
# control discretization step:
dpsolv.control_steps = (1, ) #
#dpsolv.print_summary()
### Value iteration
J_0 = np.zeros(N_x)
# first iteration
J, u = dpsolv.value_iteration(J_0)
print(u[..., 0])
for i in xrange(number_of_iterations):
J, u = dpsolv.value_iteration(J)
# print(u[...,0])
return [movement_sys, dpsolv, u]
print('Invertory Control with (h={:.1f}, p={:.1f}, c={:.1f})'.format(h,p,c))
### DP Solver ##################################################################
from stodynprog import DPSolver
dpsolv = DPSolver(invsys)
# discretize the state space
xmin, xmax = (-3,6)
N_x = xmax-xmin+1 # number of states
dpsolv.discretize_state(xmin, xmax, N_x)
# discretize the perturbation
N_w = len(demand_values)
dpsolv.discretize_perturb(demand_values[0], demand_values[-1], N_w)
# control discretization step:
dpsolv.control_steps=(1,) #
#dpsolv.print_summary()
### Value iteration
J_0 = np.zeros(N_x)
# first iteration
J,u = dpsolv.value_iteration(J_0)
print(u[...,0])
# A few more iterations
J,u = dpsolv.value_iteration(J)
print(u[...,0])
J,u = dpsolv.value_iteration(J)
print(u[...,0])
J,u = dpsolv.value_iteration(J)
print(u[...,0])
### Create the system description:
sto_sys = SysDescription((1,1,0), name='Deterministic Storage', stationnary=False)
sto_sys.dyn = dyn_sto
sto_sys.control_box = admissible_controls
sto_sys.cost = cost_model
sto_sys.print_summary()
### Create the DP solver:
dpsolv = DPSolver(sto_sys)
# discretize the state space
N_E = 100
E_grid = dpsolv.discretize_state(0, p['E_rated'], N_E)[0]
dpsolv.control_steps=(.001,)
dpsolv.print_summary()
if __name__ == '__main__':
### Solve the problem:
# Zero final cost
J_fin = np.zeros(N_E)
# Solve the problem:
J, pol = dpsolv.bellman_recursion(T_horiz, J_fin)
# RMS cost from the cost function:
J_l2_empty = np.sqrt(J[0,0]/T_horiz)
J_l2_mid = np.sqrt(J[0,N_E//2]/T_horiz)
J_l2_full = np.sqrt(J[0,-1]/T_horiz)
print('output RMS deviation from cost function')
