LMI_regulators.py - master - Chronos/Control_lib

LMI_regulators.py
75 строк2 KB
Chronos
Когда всё кончено, всё и начнётся
03 май 2025, 09:43
03 май 2025, 09:43226d6e8
# Проверка D - устойчивости матрицы

import numpy as np
import cvxpy as cp
from scipy.linalg import block_diag

def build_stabilizing_regulator_continuous(A,B):
    Y = cp.Variable((A.shape[0],A.shape[0]),symmetric=True)
    Z = cp.Variable((B.shape[1],A.shape[0]))
    constraints = [
        A@Y+Y@A.T+B@Z+Z.T@B.T  << 0,
        Y >> 0
    ]
    objective = cp.Minimize(0)

    problem = cp.Problem(objective, constraints)
    problem.solve(solver='MOSEK',verbose=False)
    print("Статус решения: ", problem.status)
    theta = Z.value@np.linalg.inv(Y.value)
    print("Регулятор theta: ",theta)
    return theta

def build_stabilizing_regulator_discrete(A,B):
    Y = cp.Variable((A.shape[0],A.shape[0]),symmetric=True)
    Z = cp.Variable((B.shape[1],A.shape[0]))
    constraints = [
        cp.bmat([
            [Y,A@Y+B@Z],
            [(A@Y+B@Z).T,Y]
            ])  >> 0,
        Y >> 0
        ]
    objective = cp.Minimize(0)

    problem = cp.Problem(objective, constraints)
    problem.solve(solver='MOSEK',verbose=False)
    print("Статус решения: ", problem.status)
    theta = Z.value@np.linalg.inv(Y.value)
    print("Регулятор theta: ",theta)
    return theta

def check_matrix_D_stability(A,L,M):
    X = cp.Variable((3,3),symmetric=True)
    constraints = [
        cp.kron(L,X)+cp.kron(M,A@X)+cp.kron(M.T,A.T@X)  << 0,
        X >> 0
    ]

    objective = cp.Minimize(0)

    problem = cp.Problem(objective, constraints)
    problem.solve(solver='MOSEK',verbose=False)
    print("Статус решения:", problem.status)
    return problem.status in ['optimal', 'optimal_inaccurate']

def build_D_stabilizing_regulator(A,B,L,M):
    X = cp.Variable((A.shape[0],A.shape[0]),symmetric=True)
    Z = cp.Variable((B.shape[1],A.shape[0]))


    constraints = [
        cp.kron(L,X)+cp.kron(M,A@X+B@Z)+cp.kron(M.T,(A@X+B@Z).T)  << 0,
        X >> 0
    ]



    objective = cp.Minimize(0)

    problem = cp.Problem(objective, constraints)
    problem.solve(solver='MOSEK',verbose=False)
    print("Статус решения:", problem.status)
    theta = Z.value@np.linalg.inv(X.value)
    print("Регулятор theta: ", theta)
    return theta