Abstract
This manuscript addresses a new multivariate generalized predictive control strategy using the least squares support vector machine for parabolic distributed parameter systems. First, a set of proper orthogonal decomposition-based spatial basis functions constructed from a carefully selected set of data is used in a Galerkin projection for the building of an approximate low-dimensional lumped parameter systems. Then, the temporal autoregressive exogenous model obtained by the least squares support vector machine is applied in the design of a multivariate generalized predictive control strategy. Finally, the effectiveness of the proposed multivariate generalized predictive control strategy is verified through a numerical simulation study on a typical diffusion-reaction process in radical symmetry.
Highlights
Modeling and control issues in the process industry involving distributed parameter systems (DPSs), which are infinite-dimensional systems, are challenging
We present a new multivariate Generalized predictive control (GPC) strategy used in conjunction with the Proper Orthogonal Decomposition (POD) technique to reduce the model order of weakly nonlinear DPSs of parabolic type
The GPC strategy used in conjunction with POD and recursive least square method has been applied to DPSs [31,32,33]
Summary
Modeling and control issues in the process industry involving distributed parameter systems (DPSs), which are infinite-dimensional systems, are challenging. The K-L expansion combined with the neural network method can be applied to construct a sufficiently accurate approximation for a nonlinear DPS [8,9,10,11,12,13,14]. We present a new multivariate GPC strategy used in conjunction with the POD technique to reduce the model order of weakly nonlinear DPSs of parabolic type. The GPC based on SVM method has been successfully applied to LPSs with nonlinear characteristics [28,29,30]. It is applicable to a wider range of nonlinear DPSs. On the other hand, the GPC strategy used in conjunction with POD and recursive least square method has been applied to DPSs [31,32,33].
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