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Distributed_Proportional_Control.py
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Distributed_Proportional_Control.py
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# -*- coding: utf-8 -*-
"""
Created on Thu Mar 8 19:38:16 2018
@author: Andrew
"""
import numpy as np
import matplotlib.pyplot as plt
import copy
class GNode():
def __init__(_self,a,b,ulim,llim,pos):
_self.a = a
_self.b = b
_self.ulim = ulim
_self.llim = llim
_self.umax = (_self.ulim - _self.a)/_self.b
_self.umin = (_self.llim - _self.a)/_self.b
_self.p = 0
_self.lamda = (_self.umax + _self.umin)/2
_self.x = _self.solvex(_self.lamda)
_self.pos = pos
def u(_self, x): #lamda at a given load
u = (x - _self.a)/_self.b
u = np.clip(u,_self.umin,_self.umax)
return(u)
def solvex(_self,lamda):
if lamda < _self.umin:
return(_self.llim)
if lamda >= _self.umax:
return(_self.ulim)
else:
return(_self.a + lamda*_self.b)
def cost(_self,x):
cost = ((x - _self.a)**2)/(2*_self.b)
return(cost)
class SNode():
def __init__(_self,p,pos):
_self.p = p
_self.lamda = 0
_self.x = 0
_self.pos = pos
def solvex(_self, lamda):
return(0)
def consensus(array, W, maxitt = 50000, eps = .0000001):
new = copy.copy(array)
hist = [array[:]]
itt = 0
while itt < maxitt:
old = hist[-1]
for i in np.arange(0,len(array)):
new[i] = np.dot(W[i,:],copy.copy(old))
itt += 1
if np.all(np.abs(new - old) < eps):
return([new,hist])
hist.append(copy.copy(new))
return([new,hist])
def maxconsensus(array,A):
diameter = len(array)
array = copy.copy(array)
for i in np.arange(0,diameter):
array[i] = np.max(A[i,:]*array)
print(array)
return(array[0])
def minconsensus(array,A):
diameter = len(array)
array = copy.copy(array)
for i in np.arange(0,diameter):
array[i] = np.min(A[i,:]*array)
print(array)
return(array[0])
def alpha(t,num = .5, power = .85):
return(num/(t**power))
def beta(t,num = .2, power = .001):
return(num/(t**power))
def lEqual(nodes, eps = .00001):
flag = True
for i in np.arange(0,len(nodes)-1):
for j in np.arange(i+1,len(nodes)):
if abs(nodes[i].lamda - nodes[j].lamda) > eps:
flag = False
return(flag)
return(flag)
def run(y,anum,apow,bnum,bpow):
itt = 1
maxitt = 100000
eps = .00013
lhist = []
xhist = []
x = [node.x for node in generators]
xhist.append(x)
ycurr = y -x
while (abs(np.sum(x) - np.sum(p)) > eps and itt < maxitt) or itt == 1:
xold = copy.copy(xhist[-1])
epsilon = 1/19500
lams = [node.lamda for node in generators]
for node in generators:
node.lamda = np.dot(Rp[node.pos,:],lams) + epsilon*y[node.pos]
node.x = node.solvex(node.lamda)
ycurr[node.pos] = np.dot(Rq[node.pos,:],ycurr) - (node.x - xold[node.pos])
itt += 1
x = [node.x for node in generators]
lams = [node.lamda for node in generators]
xhist.append(x)
lhist.append(lams)
lavg = np.mean(lams)
xtot = np.sum(x)
return((itt,x,lams,xhist,[np.sum(n) - np.sum(p) for n in xhist]))
P = np.array([0,0,0,.5,1.4,1.1,.9,.2])
P_tot = np.sum(P)
Q = np.array([1/3,1/5,0,1/4,0,0,0,0,1/3,1/5,1/5,0,0,1/5,0,1/3,0,1/5,1/5,0,0,1/5,1/3,1/3,1/3,0,0,1/4,1/4,1/5,0,0,0,0,0,1/4,1/4,1/5,1/3,0,0,1/5,1/5,1/4,1/4,1/5,0,0,0,0,1/5,0,1/4,0,1/3,0,0,1/5,1/5,0,0,0,0,1/3])
Q = Q.reshape((8,8))
AQ = Q > 0
Rq = np.array([1/2,1/3,0,1/2,1/3,1/2,0,1/3,1/2]).reshape((3,3))
Rp = np.array([1/2,1/2,0,1/3,1/3,1/3,0,1/2,1/2]).reshape((3,3))
AR = Rq > 0
n1 = GNode(-1,3,2.1,0,0)
n2 = GNode(-1,2,1.0,0,1)
n3 = GNode(-1,2,5.0,0,2)
n4 = SNode(1,3)
n5 = SNode(1.4,4)
n6 = SNode(1.1,5)
n7 = SNode(.9,6)
n8 = SNode(.2,7)
nodes = [n1,n2,n3,n4,n5,n6,n7,n8]
generators = [n1,n2,n3]
lbounds = np.array([node.llim for node in generators])
ubounds = np.array([node.ulim for node in generators])
numnodes = len(nodes)
numgens = len(generators)
eps = .0001
diameter = 2
p = P
ptot = np.sum(p)
[p,phist] = consensus(p,Q)
sold = np.zeros((8,))
for i in np.arange(0,numgens):
sold[i] = p[i]
snew = sold
[snew,hist] = consensus(snew,Q)
ynew = p*p/snew
[y,yhist] = consensus(ynew[0:3],Rq)
for i in np.arange(0,numgens):
generators[i].p = y[i]
(itt,x,lams,xhist,xsums) = run(y,.2,.01,.2,.00001)
plt.plot(xhist)