RK4integrator
implements the classical Runge-Kutta scheme (aka RK4).
Contents
Syntax
Description
This function implements the classical Runge-Kutta scheme and, in addition to solving the initial value problem x_dot = f(x,u,w), x(0) = x0 numerically, can be used for time-discretizing continuous-time dynamical systems, e.g. for reachability analysis using CORA. Both the control input "u" and the disturbance "w" are assumed to be constant during the time step.
Input Arguments
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x0 |
initial state (real array of dimension [nx,1]) |
|
u |
control input (real array of dimension [nu,1]) |
|
w |
disturbance (real array of dimension [nw,1]) |
|
funHandle |
function handle to the dynamics function of the continuous-time system (x_dot = f(x,u,w); |
|
dt |
time step (positive scalar) |
Output Arguments
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xNext |
state at the end of the time interval [0, dt] (real array of dimension [nx,1]) |
See Also
References
[1] W. Kutta, "Beitrag zur näherungsweisen Integration totaler Differentialgleichungen", Zeitschrift für Mathematik und Physik, 46: 435–453, 1901.
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