By Biao Huang

A ordinary layout technique for version predictive keep an eye on or keep an eye on functionality tracking comprises: 1. id of a parametric or nonparametric version; 2. derivation of the output predictor from the version; three. layout of the keep an eye on legislations or calculation of functionality indices in accordance with the predictor.

Both layout difficulties want an particular version shape and either require this three-step layout process. Can this layout method be simplified? Can an particular version be kept away from? With those questions in brain, the authors put off the 1st and moment step of the above layout method, a “data-driven” method within the experience that no conventional parametric types are used; accordingly, the intermediate subspace matrices, that are got from the method information and another way pointed out as a primary step within the subspace id tools, are used without delay for the designs. with out utilizing an particular version, the layout technique is simplified and the modelling errors as a result of parameterization is eliminated.

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**Additional info for Dynamic Modeling, Predictive Control and Performance Monitoring: A Data-driven Subspace Approach**

**Example text**

This assumption holds under the open-loop condition. 61) This result indicates that the column space of ΓN is the same as the column space of Yf /Uf Wp , which can be calculated by the SVD decomposition of Yf /Uf Wp . Similarly, the row space of Yf /Uf Wp is the same as the row space of Xf /Uf Wp , which is the Kalman ﬁlter state solution with Xp /Uf Wp as its initial condition, as has been discussed before. Therefore, the Kalman state sequences can also be calculated from the SVD decomposition of Yf /Uf Wp .

N, θ). , measure of the prediction error. In the stochastic framework, L1 (z −1 ; θ) and L2 (z −1 ; θ) are typically chosen to obtain an optimal predictor, as discussed above. The criterion to measure the prediction error can be chosen in many diﬀerent ways. 27) Given Gp (0; θ) = 0 and Gl (0; θ) = I, which also implies Gp (0; θ0 ) = 0 and Gl (0; θ0 ) = I , it can be veriﬁed that Φu (0; θ, θ0 ) = 0 Φe (0; θ, θ0 ) − I = 0 Namely, both Φu (0; θ, θ0 ) and (Φe (0; θ, θ0 ) − I) have at least one sample time delay.

Because there are fewer parameters to be estimated in the OE model, it is often a good option of model structures in practice. et ut B ( z −1 ) F ( z −1 ) yt Fig. 5. 7 B1 (z −1 ) Bl (z −1 ) u ul,t + . . + 1,t F1 (z −1 ) Fl (z −1 ) C(z −1 ) et i = 1, . . , m + D(z −1 ) State Space Model A state space model is typically identiﬁed through an innovation or Kalman predictor form: xt+1 = A(θ)xt + B(θ)ut + K(θ)et yt = C(θ)xt + et where A, B, C are system matrices, D matrix is commonly omitted owing to zero-order-hold in the sampling (thus one sample delay results), et is called the innovation sequence, and K is the Kalman predictor gain.