Affine [62–65] Nonlinear Polynomials [66,67] Thin-plate splines (TPS) [29,68,69] B-splines [56] Finite elements (meshes) [70–73] Mesh-free [26,28,74,75] Linear models represent deformation fields u=(u,v)T using linear functions (Section 4.1), while nonlinear models usually use ...
Then, the MPC problem is further solved by the projection neural network with different structures for the control of nonlinear affine systems [122–126], control of nonlinear systems [127–130], tracking control of underactuated vessels [131], synchronous control of barrel temperature for injection...
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Often, it is possible to construct a feasible processing chain with affine mappings which simplifies the calculation for the backtransformation and the interpretation of the result a lot. In this case, the affine backtransformation provides the complete parameterization of the processing chain. This ...
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From Equations (12) and (13) the first affine local model for nominal point (𝑈𝑁1,Ω𝑁1)UN1,ΩN1 (i.e., affine local model for the first rule in Equation (5)) is created: 𝑋(𝑘+1)−𝑋𝑁1=𝑎1(𝑋(𝑘)−𝑋𝑁1)+𝑏1(𝑈(𝑘)−𝑈𝑁1),X(k+1)...