Analysis and design of a linear input/output data-based predictive control

In this work, a subspace identification algorithm is reformulated from a control point of view. The proposed algorithm is referred to as an input/output data-based predictive control, in which an explicit model of the system to be controlled is not calculated at any point in the algorithm. First, the state estimation obtained by the subspace identification algorithm is analyzed in comparison with the receding-horizon-based estimation. For the subspace algorithm, it is well-known that a Kalman filter state is calculated by simple linear algebra under specific conditions. In general, however, it is shown that the present state estimation scheme gives a biased state estimate and that it has a structure similar to the best linear unbiased estimation (BLUE) filter obtained by solving the least-squares problem analytically. With such an interpretation of the state estimation, we augment the integrated white noise model to add integral action to a linear input/output data-based predictive controller and use each the BLUE filter and the Kalman filter as a stochastic observer for the unmeasured disturbance. The proposed linear input/ouput data-based predictive controller is applied to the property control of a continuous styrene polymerization reactor to demonstrate its improved performance.