How to solve a state space model with Odeint?

Question

I am trying to implement a numerical simulation of a state space model using Eigen and Odeint. My trouble is that I need to reference control data U (predefined before integration) in order to properly solve the Ax+Bu part of the state space model. I was trying to accomplish this by using a counter to keep track of the current time step, but for whatever reason, it is reset to zero every time the System Function is called by Odeint.

How would I get around this? Is my approach to modeling the state space system flawed?

My System

struct Eigen_SS_NLTIV_Model
{
    Eigen_SS_NLTIV_Model(matrixXd &ssA, matrixXd &ssB, matrixXd &ssC, 
           matrixXd &ssD, matrixXd &ssU, matrixXd &ssY)
                :A(ssA), B(ssB), C(ssC), D(ssD), U(ssU), Y(ssY)
    {
        Y.resizeLike(U);
        Y.setZero();

        observerStep = 0;
        testPtr = &observerStep;
    }

    /* Observer Function:*/
    void operator()(matrixXd &x, double t)
    {
        Y.col(observerStep) = C*x + D*U.col(observerStep);
        observerStep += 1;
    }

    /* System Function:
     * ONLY the mathematical description of the system dynamics may be placed
     * here. Any data placed in here is destroyed after each iteration of the
     * stepper.
     */
    void operator()(matrixXd &x, matrixXd &dxdt, double t)
    {
        dxdt = A*x + B*U.col(*testPtr);
        //Cannot reference the variable "observerStep" directly as it gets reset 
        //every time this is called. *testPtr doesn't work either.
    }

    int observerStep;
    int *testPtr;
    matrixXd &A, &B, &C, &D, &U, &Y; //Input Vectors
};

My ODE Solver Setup

const double t_end = 3.0;
const double dt = 0.5;
int steps = (int)std::ceil(t_end / dt) + 1;

matrixXd A(2, 2), B(2, 2), C(2, 2), D(2, 2), x(2, 1);
matrixXd U = matrixXd::Constant(2, steps, 1.0);
matrixXd Y;

A << -0.5572, -0.7814, 0.7814, 0.0000;
B << 1.0, -1.0, 0.0, 2.0;
C << 1.9691, 6.4493, 1.9691, 6.4493;
D << 0.0, 0.0, 0.0, 0.0;
x << 0, 0;

Eigen_SS_NLTIV_Model matrixTest(A, B, C, D, U, Y);

odeint::integrate_const(odeint::runge_kutta4<matrixXd, double, matrixXd, double,
    odeint::vector_space_algebra>(),
    matrixTest, x, 0.0, t_end, dt, matrixTest);

//Ignore these two functions. They are there mostly for debugging.
writeCSV<matrixXd>(Y, "Y_OUT.csv");
prettyPrint<matrixXd>(Y, "Out Full");

Answer 1

With classical Runge-Kutta you know that your ODE model function is called 4 times per step with times t, t+h/2, t+h/2, t+h. With other solvers that implement adaptive step size you can not know in advance at what t the ODE model function is called.

You should implement U via some kind of interpolation function, in the most simple case as step function that computes some index from t and returns the U value for that index. Something like

i = (int)(t/U_step)
dxdt = A*x + B*U.col(i);