RK2integrator

implements the midpoint method for numerically solving ordinary differential equations.

Syntax
Description
Input Arguments
Output Arguments
See Also
References

Syntax

xNext = RK4integrator(x0,u,w,funHandle,dt)

Description

This function implements the midpoint method, a second-order Runge-Kutta method with two stages 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

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

xNext

state at the end of the time interval [0, dt] (real array of dimension [nx,1])

References

[1] W. Kutta, "Beitrag zur näherungsweisen Integration totaler Differentialgleichungen", Zeitschrift für Mathematik und Physik, 46: 435–453, 1901.

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)