By Kohei Ohtsu, Hui Peng, Genshiro Kitagawa
This booklet offers multivariate time sequence equipment for the research and optimum keep an eye on of suggestions structures. even supposing ships’ autopilot platforms are thought of in the course of the whole booklet, the tools set forth during this booklet should be utilized to many different complex, huge, or noisy suggestions regulate platforms for which it really is tough to derive a version of the full procedure according to idea in that topic quarter. the fundamental types utilized in this system are the multivariate autoregressive version with exogenous variables (ARX) version and the radial bases functionality net-type coefficients ARX version. The noise contribution research can then be played in the course of the envisioned autoregressive (AR) version and numerous varieties of autopilot platforms may be designed during the state–space illustration of the types. The marine autopilot structures addressed during this e-book comprise optimum controllers for course-keeping movement, rolling aid controllers with rudder movement, engine governor controllers, noise adaptive autopilots, route-tracking controllers through direct guidance, and the reference course-setting strategy. The tools provided listed below are exemplified with genuine information research and experiments on genuine ships. This ebook is extremely instructed to readers who're attracted to designing optimum or adaptive controllers not just of ships but in addition of the other complex platforms lower than noisy disturbance conditions.
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Additional info for Time Series Modeling for Analysis and Control: Advanced Autopilot and Monitoring Systems
Example text
1999), which has the advantages of both the state-dependent AR models in the description of nonlinear dynamics and of RBF networks in function approximation. A natural extension of the ideas behind RBF-AR modeling leads us to the RBFARX model (RBF-AR model with eXogenous variables) (Peng et al. 2003, 2004, 2009). 8 RBF-ARX Modeling for a Nonlinear System 43 network model. The RBF-ARX model is actually a hybrid pseudo-linear model constructed based on the Gaussian RBF networks and linear ARX model structure, which was proposed in order to characterize nonlinear systems having dynamic features that depend on time-varying working-points and which may be locally linearized at each working point.
AIC P (M), and find the minimum AIC order AIC P = min j AIC P ( j). Under the assumption that the time series on the entire interval [n k0 , n k1 + L] is stationary, the model is referred to as the pooled model. 4. Judge the homogeneity of data: In order to judge the homogeneity of the two subintervals, compare the values of AIC D and AIC P . Switch to the new model: If AIC D < AIC P , it is judged that the divided model is better. In this case, n k1 + 1 becomes the initial point of the current subinterval, and we put k ≡ k + 1, n k0 ≡ n k−1,1 + 1, n k1 = n k−1,1 + L, Nk = L, and AIC0 = AIC D .
In this method, it is implicitly assumed that the AR coefficients am (i, j) have common orders for all i and j. Using the least squares method based on the Householder transformation, it is possible to determine the AIC best order for each pair of (i, j) (Kitagawa 2010). Furthermore, applying this method, it is possible to determine the best order without explicitly obtaining the AR coefficient matrices. The FORTRAN program MULMAR in the program package TIMSAC-78 (Akaike et al. 1979) can be used for this purpose.
