# economic mpc controller
ctrls = {}
sys = tuner.sys
ctrls['economic'] = tuner.create_mpc('economic',N = N)
# normal tracking mpc controller
tuningTn = {'H': [np.diag([10.0, 10.0, 0.1, 0.1])], 'q': S['q']}
ctrls['tracking'] = tuner.create_mpc('tracking',N = N, tuning = tuningTn)
# tuned tracking mpc controller
ctrls['tuned'] = tuner.create_mpc('tuned',N = N)
# check feedback policy equivalence
alpha = np.linspace(0.0, 1.0, 10) # sweep factor
dP2 = 1.0 # initial state perturbation
log = clt.check_equivalence(ctrls, objective(x,u,data), sys['h'], wsol['x',0], ca.vertcat(0.0, dP2), alpha)
# plot feedback controls to check equivalence
ctrl_name = u.keys()
for name in list(ctrls.keys()):
for i in range(nu):
plt.figure(i)
plt.plot([
a*dP2 for a in alpha],
[log[j]['u'][name][0][i] - log[j]['u']['economic'][0][i] \
for j in range(len(alpha))])
plt.legend(list(ctrls.keys()))
plt.xlabel('dP2')
plt.ylabel('u0 - u0_economic: {}'.format(ctrl_name[i]))
plt.title('Feedback policy deviation')
plt.grid(True)
alpha = np.linspace(-1.0, 1.0, alpha_steps + 1) # deviation sweep grid
dz = 8 # max. deviation
x0 = wsol['x', 0]
tgrid = [1 / user_input['p'] * i for i in range(Nmpc)]
tgridx = tgrid + [tgrid[-1] + 1 / user_input['p']]
# open loop simulation
import copy
log = []
for alph in alpha:
x_init = copy.deepcopy(x0)
x_init[2] = x_init[2] + alph * dz
x_init[0] = np.sqrt(-x_init[2]**2 - x_init[1]**2 + (l_t)**2)
x_init[5] = -(x_init[0] * x_init[3] + x_init[1] * x_init[4]) / x_init[2]
log.append(
clt.check_equivalence(ctrls, user_input['l'], user_input['h'], x0,
x_init - x0, [1.0])[-1])
for name in list(ctrls.keys()):
ctrls[name].reset()
# optimal stage cost and constraints for comparison
lOpt, hOpt = [], []
for k in range(Nmpc):
lOpt.append(user_input['l'](wsol['x', k % user_input['p']],
wsol['u', k % user_input['p']]).full()[0][0])
hOpt.append(user_input['h'](wsol['x', k % user_input['p']],
wsol['u', k % user_input['p']]).full())
# plotting options
alpha_plot = -1
lw = 2
ctrls_colors = {
lOpt, hOpt = [], []
for k in range(Nmpc):
lOpt.append(user_input['l'](sol['wsol']['x', k%user_input['p']], sol['wsol']['u',k%user_input['p']]).full()[0][0])
hOpt.append(user_input['h'](sol['wsol']['x', k%user_input['p']], sol['wsol']['u',k%user_input['p']]).full())
# open loop simulation
import copy
log = []
log_acados = []
for alph in alpha:
x_init = copy.deepcopy(x0)
x_init[2] = x_init[2] + alph*dz
x_init[0] = np.sqrt(-x_init[2]**2-x_init[1]**2+(l_t)**2)
x_init[5] = -(x_init[0]*x_init[3] + x_init[1]*x_init[4]) / x_init[2]
if TUNEMPC_SIM:
log.append(clt.check_equivalence(ctrls, user_input['l'], user_input['h'], x0, x_init-x0, [1.0])[-1])
if ACADOS_SIM:
log_acados.append(clt.check_equivalence(
ctrls_acados,
user_input['l'],
user_input['h'],
x0,
x_init-x0,
[1.0],
flag = 'acados')[-1])
for name in list(ctrls.keys()):
ctrls[name].reset()
# plotting options
alpha_plot = -1
lw = 2
ctrls_acados = {'tuned_acados': ctrls['tuned']}
# check equivalence
alpha = np.linspace(-0.1, 1.0, 10)
x0 = wsol['x', 0]
dx_diehl = np.array([1.0, 0.5, 100.0, 100.0]) - wsol['x', 0]
# compute open-loop prediction for list of deviations in different state directions
log = []
log_acados = []
for dist in [0]:
dx = np.zeros((nx, 1))
dx[dist] = dx_diehl[dist]
log.append(
clt.check_equivalence(ctrls, cost, tuner.sys['h'], x0, dx, alpha))
if ACADOS_CODEGENERATE:
log_acados.append(
clt.check_equivalence(ctrls_acados,
cost,
tuner.sys['h'],
x0,
dx,
alpha,
flag='acados'))
fig_num = 1
alpha_plot = -1 # alpha value of interest
dx_plot = 0 # state direction of interest
ctrl_list = list(ctrls.keys())
# nmpc horizon length
N = 200
# gradient
[H, q, _, _, _] = tuner.pocp.get_sensitivities()
# economic mpc controller
ctrls = {}
sys = tuner.sys
ctrls['economic'] = tuner.create_mpc('economic',N = N)
# normal tracking mpc controller
tuningTn = {'H': [np.diag([10.0, 10.0, 0.1, 0.1])], 'q': q}
ctrls['tracking'] = tuner.create_mpc('tracking',N = N, tuning = tuningTn)
# tuned tracking mpc controller
ctrls['tuned'] = tuner.create_mpc('tuned',N = N)
alpha = [0.1, 0.5, 1.0]
log = clt.check_equivalence(ctrls, objective(x,u,data), sys['h'], wsol['x',0], ca.vertcat(0.0, 10.0), alpha)
# plot feedback controls to check equivalence
for name in list(ctrls.keys()):
for i in range(nu):
plt.figure(i)
plt.plot(alpha, [log[j]['u'][name][0][i] for j in range(len(alpha))])
plt.legend(list(ctrls.keys()))
plt.show()
# tuned tracking mpc controller
ctrls['tuned'] = tuner.create_mpc('tuned', N, opts=opts)
# check equivalence
alpha = np.linspace(-0.1, 1.0, 2)
x0 = wsol['x', 0]
dx_diehl = np.array([1.0, 0.5, 100.0, 100.0]) - wsol['x', 0]
# compute open-loop prediction for list of deviations in different state directions
log = []
for dist in [0]:
dx = np.zeros((nx, 1))
dx[dist] = dx_diehl[dist]
log.append(
clt.check_equivalence(ctrls, cost, tuner.sys['h'], x0, dx, alpha))
fig_num = 1
alpha_plot = -1 # alpha value of interest
dx_plot = 0 # state direction of interest
for name in list(ctrls.keys()):
# plot controls
plt.figure(fig_num)
for i in range(nu):
plt.subplot(nu, 1, i + 1)
plt.step(tgrid, [
log[dx_plot][alpha_plot]['u'][name][j][i]
for j in range(len(tgrid))
],
where='post')
sol['wsol']['u',
k % user_input['p']]).full()[0][0])
hOpt.append(user_input['h'](sol['wsol']['x', k % user_input['p']],
sol['wsol']['u', k % user_input['p']]).full())
# open loop simulation
import copy
log = []
log_acados = []
for alph in alpha:
x_init = copy.deepcopy(x0)
x_init[2] = x_init[2] + alph * dz
x_init[0] = np.sqrt(-x_init[2]**2 - x_init[1]**2 + (l_t)**2)
x_init[5] = -(x_init[0] * x_init[3] + x_init[1] * x_init[4]) / x_init[2]
log.append(
clt.check_equivalence(ctrls, user_input['l'], user_input['h'], x0,
x_init - x0, [1.0])[-1])
if ACADOS_CODEGENERATE:
log_acados.append(
clt.check_equivalence({'TUNEMPC_ACADOS': ctrls['TUNEMPC']},
user_input['l'],
user_input['h'],
x0,
x_init - x0, [1.0],
flag='acados')[-1])
for name in list(ctrls.keys()):
ctrls[name].reset()
# plotting options
alpha_plot = -1
lw = 2
ctrls_colors = {