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as presented in[4]. The limitation of the approach is that the mismatch between
the plant and the model can cause control performance degrading.
The main purpose of this paper is to further expand the application of MPC
in fast dynamic systems. The possible contribution is that a recursive MPC
(RMPC) algorithm is proposed. In traditional MPC, several passes are made
through the data to iteratively improve the optimal result, which is major part
of the computational burden[5]. It is a natural idea to replace the iteration by
recursive method. However, recursive methods can not work here effectively. The
reason is that only the information in the first predictive step can be utilized
to obtain the first term which is actual input in MPC. To solve the problem,
Iterative Learning Control (ILC)[10] is adopted in this paper to use the lim-
ited information sucient to improve the control performance of the first term.
Moreover, the first term obtained from ILC can provide a satisfied start point
for recursive algorithms. Then the recursive Levenberg Marquardt Algorithm
(RLMA) [6] is adopted to obtain other inputs in control horizon.
As the structure of ILC is chosen to be very simple, the amount of computation
in ILC is quite small. Meanwhile, RLMA, which derives input one by one, only
needs short computational time. Therefore, RMPC can reduce the computational
burden of conventional MPC significantly.
2RMPCM thod
In MPC, the controller selects the next input sequence based on the prediction of
the future system state behavior. Precisely speaking, the sequences that optimize
a given cost function is chosen. The controller in RMPC also utilizes the above
strategy.
2.1 Problem Formulation
For convenience to compare, MPC and RMPC use the same plant model:
x ( k +1)= Ax ( k )+ Bu ( k )
y ( k )= Cx ( k )
(1)
A quadratic cost function has been preferred as follows:
P
J =
( e ( k + i ) Qe ( k + i ))
i =1
(2)
y r ( k + i )
e ( k + i )= y ( k + i )
P ,u
M
y
Ψ
Υ
where Q is positive semidefinite matrix to weight the output vector, y r is ref-
erence trajectory. The time interval over which process inputs are computed to
 
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