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lin_method_mpc.py
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lin_method_mpc.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""Run DAC simulations using various linearisation methods
@author: Bikash Adhikari
@date: 22.02.2024
@license: BSD 3-Clause
"""
import numpy as np
from scipy import linalg , signal
import sys
import random
import gurobipy as gp
from gurobipy import GRB
import tqdm
class MPC:
def __init__(self, Nb, Qstep, QMODEL, A, B, C, D):
"""
Constructor for the Model Predictive Controller.
:param Nb: Number of bits
:param Qstep: Quantizer step size / Least significant bit (LSB)
:param N_PRED: Prediction horizon | int
:param Xcs: Reference/Test signal
:param QL: Quantization levels
:param A, B, C, D: Matrices; state space representation of the reconstruction filter
"""
self.Nb = Nb
self.Qstep = abs(Qstep)
self.QMODEL = QMODEL
self.A = A
self.B = B
self.C = C
self.D = D
def state_prediction(self, st, con):
"""
Predict the state for the given initial condition and control
"""
x_iplus1 = self.A @ st + self.B * con
return x_iplus1
def q_scaling(self, X):
Xs = X.squeeze() /self.Qstep + 2**(self.Nb-1)
return Xs
# def get_codes(self, Xcs, N_PRED, YQns, MLns)
def get_codes(self, N_PRED, Xcs, YQns, MLns ):
# Scale the input to the quantizer levels to run it as an MILP
Xs = Xcs.squeeze()
X = Xs/self.Qstep + 2**(self.Nb-1)
X = self.q_scaling(Xcs)
# Scale ideal levels
# match self.QMODEL:
# case 1:
# QLS = (YQns /self.Qstep ) + 2**(self.Nb-1) -1/2
# QLS = QLS.squeeze()
# case 2:
# QLS = (MLns /self.Qstep ) + 2**(self.Nb-1) -1/2
# QLS = QLS.squeeze()
INL = YQns - MLns
match self.QMODEL:
case 1:
QLS = (YQns /self.Qstep ) + 2**(self.Nb-1) -1/2
QLS = QLS.squeeze()
case 2:
QLS = (YQns /self.Qstep ) + 2**(self.Nb-1) -1/2
QLS = QLS + INL
QLS = QLS.squeeze()
# match self.QMODEL:
# case 1:
# QLS = self.q_scaling(YQns.reshape(1,-1)).squeeze()
# case 2:
# QLS = self.q_scaling(MLns.reshape(1,-1)).squeeze()
# Storage container for code
C = []
# Loop length
len_MPC = X.size - N_PRED
# State dimension
x_dim = int(self.A.shape[0])
# Initial state
init_state = np.zeros(x_dim).reshape(-1,1)
# MPC loop
for j in tqdm.tqdm(range(len_MPC)):
m = gp.Model("MPC- INL")
u = m.addMVar(N_PRED, vtype=GRB.INTEGER, name= "u", lb = 0, ub = 2**self.Nb-1) # control variable
x = m.addMVar((x_dim*(N_PRED+1),1), vtype= GRB.CONTINUOUS, lb = -GRB.INFINITY, ub = GRB.INFINITY, name = "x") # State varible
# Add objective function
Obj = 0
# Set initial constraint
m.addConstr(x[0:x_dim,:] == init_state)
for i in range(N_PRED):
k = x_dim * i
st = x[k:k+x_dim]
con = u[i] - X[j+i]
# Objective update
e_t = self.C @ x[k:k+x_dim] + self.D * con
Obj = Obj + e_t * e_t
# Constraints update
f_value = self.A @ st + self.B * con
st_next = x[k+x_dim:k+2*x_dim]
m.addConstr(st_next == f_value)
# Gurobi model update
m.update
# Set Gurobi objective
m.setObjective(Obj, GRB.MINIMIZE)
# 0 - Supress log output, 1- Print log outputs
m.Params.LogToConsole = 0
# Gurobi setting for precision
# m.Params.IntFeasTol = 1e-9
# m.Params.IntegralityFocus = 1
# Optimization
m.optimize()
# Extract variable values
allvars = m.getVars()
values = m.getAttr("X",allvars)
values = np.array(values)
# Extract only the value of the variable "u", value of the variable "x" are not needed
C_MPC = values[0:N_PRED]
# Ideally they should be integral, but gurobi generally return them in floating point values according to the precision tolorence set: m.Params.IntFeasTol
# Round off to nearest integers
C_MPC = C_MPC.astype(int)
# Store only the first value /code
C.append(C_MPC[0])
# Get DAC level according to the coe
U_opt = QLS[C_MPC[0]]
# State prediction
con = U_opt - X[j]
x0_new = self.state_prediction(init_state, con)
# State update for subsequent prediction horizon
init_state = x0_new
return np.array(C).reshape(1,-1)
# class MPC_BIN:
# def __init__(self, Nb, Qstep, QMODEL, A, B, C, D):
# """
# Constructor for the Model Predictive Controller.
# :param Nb: Number of bits
# :param Qstep: Quantizer step size / Least significant bit (LSB)
# :param N_PRED: Prediction horizon | int
# :param Xcs: Reference/Test signal
# :param QL: Quantization levels
# :param A, B, C, D: Matrices; state space representation of the reconstruction filter
# """
# self.Nb = Nb
# self.Qstep = abs(Qstep)
# # self.N_PRED = N_PRED
# # self.Xcs = Xcs
# # self.QL = QL.reshape(1,-1)
# self.QMODEL = QMODEL
# self.A = A
# self.B = B
# self.C = C
# self.D = D
# # self.x0 = x0
# def state_prediction(self, st, con):
# """
# Predict the state for the given initial condition and control
# """
# x_iplus1 = self.A @ st + self.B * con
# return x_iplus1
# # def get_codes(self, Xcs, N_PRED, YQns, MLns)
# def get_codes(self, N_PRED, Xcs, YQns, MLns ):
# match self.QMODEL:
# case 1:
# QL = YQns
# case 2:
# QL = MLns
# # Storage container for code
# C = []
# # Loop length
# len_MPC = Xcs.size - N_PRED
# # State dimension
# x_dim = int(self.A.shape[0])
# # Initial state
# init_state = np.zeros(x_dim).reshape(-1,1)
# # MPC loop
# for j in tqdm.tqdm(range(len_MPC)):
# m = gp.Model("MPC- INL")
# u = m.addMVar((2**self.Nb, N_PRED), vtype=GRB.BINARY, name= "u") # control variable
# x = m.addMVar((x_dim*(N_PRED+1),1), vtype= GRB.CONTINUOUS, lb = -GRB.INFINITY, ub = GRB.INFINITY, name = "x") # State varible
# # Add objective function
# Obj = 0
# # Set initial constraint
# m.addConstr(x[0:x_dim,:] == init_state)
# for i in range(N_PRED):
# k = x_dim * i
# st = x[k:k+x_dim]
# bin_con = QL.reshape(1,-1) @ u[:,i].reshape(-1,1)
# con = bin_con - Xcs[j+i]
# # Objective update
# e_t = self.C @ x[k:k+x_dim] + self.D * con
# Obj = Obj + e_t * e_t
# # Constraints update
# f_value = self.A @ st + self.B * con
# st_next = x[k+x_dim:k+2*x_dim]
# m.addConstr(st_next == f_value)
# # Binary varialble constraint
# consi = gp.quicksum(u[:,i])
# m.addConstr(consi == 1)
# # m.addConstr(consi >= 0.98)
# # m.addConstr(consi <= 1.02
# # Gurobi model update
# m.update
# # Set Gurobi objective
# m.setObjective(Obj, GRB.MINIMIZE)
# # 0 - Supress log output, 1- Print log outputs
# m.Params.LogToConsole = 0
# # Gurobi setting for precision
# m.Params.IntFeasTol = 1e-9
# m.Params.IntegralityFocus = 1
# # Optimization
# m.optimize()
# # Extract variable values
# allvars = m.getVars()
# values = m.getAttr("X",allvars)
# values = np.array(values)
# # Variable dimension
# nr, nc = u.shape
# u_val = values[0:nr*nc]
# u_val = np.reshape(u_val, (2**self.Nb, N_PRED))
# # Extract Code
# C_MPC = []
# for i in range(N_PRED):
# c1 = np.nonzero(u_val[:,i])[0][0]
# c1 = int(c1)
# C_MPC.append(c1)
# C_MPC = np.array(C_MPC)
# C.append(C_MPC[0])
# U_opt = QL[C_MPC[0]]
# # # Extract only the value of the variable "u", value of the variable "x" are not needed
# # C_MPC = values[0:N_PRED]
# # # Ideally they should be integral, but gurobi generally return them in floating point values according to the precision tolorence set: m.Params.IntFeasTol
# # # Round off to nearest integers
# # C_MPC = C_MPC.astype(int)
# # # Store only the first value /code
# # C.append(C_MPC[0])
# # # Get DAC level according to the coe
# # U_opt = QLS[C_MPC[0]]
# # State prediction
# con = U_opt - Xcs[j]
# x0_new = self.state_prediction(init_state, con)
# # State update for subsequent prediction horizon
# init_state = x0_new
# return np.array(C).reshape(1,-1)