User`s guide

8 Model Analysis
The main difference betw een simulation and predictio n is whether the toolbox
uses measured or computed previous outputs for computing the next output.
Note Output-error m odels, obtained by fixing K to zero for state-space
models and setting
na=nc=nd=0 for p olynomial models, do not u se past
outputs. Therefore, for these models, the simulated and the predicted outputs
are the same for any value of k.
Simulating a model means that you compute the response of a model to
a particular input. Then, the toolbox feeds this computed output into the
differential (continuous-time) or difference (discrete-time) equation for
calculating the nex t output value. In this way, the simulation progresses
usingpreviouslycalculatedoutputsinthedifferenceequationtoproduce
the next output; with an infinite prediction horizon (k=∞), the simulation
has no limit on how far out in time it computes output values. Simulating
models uses the input-data values from the validation data set to compute
the output values.
Simulating models uses only past input values to com pute th e out put va lu es.
If the model-output expression includes past outputs, the toolbox computes
the first output value using the initial conditions and the inputs. Then, the
toolbox feeds this computed output into the difference equation or differential
equation for calculating the next output value. Thus, no past outputs are used
in the computation of output at the current time.
Simulation always uses a discrete model and continuous-time models are
discretized for s imulation purposes. Simulation does not involve the noise
model unless you ex plicitly specify to compute the response to the no ise source
input. During simulation, the toolbox computes the firstoutputvalueusing
the initial conditions and the inputs.
Predicting future outputs of a model from previous d ata o ve r a time horizon of
k samples or kTs time units—where Ts is the sampling interval and k is the
prediction horizon—requires both past inputs and past outputs.
During prediction, the algorithm uses both the measured and the calculated
output data values in the difference equation for computing the next output.
The p redicted value y(t) is com puted from all available inputs u(s),where
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