For most systems, the integration must be performed numerically. A
system simulator based on numerical integration can be constructed by
breaking into smaller intervals and iterating classical methods
for computing numerical solutions to differential equations. The
Euler method is the simplest of these methods. Let
denote
a small time interval over which the approximation will be made. This
can be considered as an internal parameter of the system simulator.
In practice, this
is usually much smaller than the
used in the discrete-time model of Section 14.2.2.
Suppose that
and
are given and the task is to estimate
.
By performing integration over time, the state transition equation can
be used to determine the state after some fixed amount of time
has passed. For example, if
is given and
is known over the interval
,
then the state at time
can be determined as
Using the fact that
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(14.15) |
Steven M LaValle 2020-08-14