Neural-network-based iterative learning control of nonlinear systems

Novel Nonlinear Hypothesis for the Delta Parallel Robot Modeling

“…Figure 8 shows the ELP obtained with equation (20). Before the training with equations (4), (6), and α = 1, the initial parameters for the NH are in equation 21 Before the training with equations (7), (9), (10), and α = 1, the initial parameters for the SONH of this document are in equation 22, rand is a random number with values between 0 and 1. a = [rand, rand, rand, rand, rand, rand, rand] T b = [rand, rand, rand, rand, rand, rand, rand] T c = [rand, rand, rand, rand, rand, rand, rand] T (22) Before the training with equations (11), (13), (14), (15), (16), (17), (18), (19), and α = 1, the initial parameters for the NNH of this document are in equation 23, rand is a random number with values between 0 and 1. a = [rand, rand, rand, rand, rand, rand, rand, rand, rand, rand, rand, rand] T b = [rand, rand, rand, rand, rand, rand, rand, rand, rand, rand, rand, rand] T c = [rand, rand, rand, rand, rand, rand, rand, rand, rand, rand, rand, rand] T (23) Table 1 shows the cost functions J (a) of (5), J (b) of (8), J (c) of (12) for the modeling of θ i 1 , θ i 2 , θ i 3 in an ELP during the training.…”

“…A linear hypothesis is described as the combination of the first order terms and it is detailed as the sum of multiplication of the first order modeling parameters with the first order inputs [7], [8], [15], [16]. A linear hypothesis is described to relate the input variable of the end-effector (…”

“…are modeling parameters to be updated, j = 0, 1, 2, 3. The goal is to find the modeling parameters Figure 1 shows the structure of the linear hypothesis for the output θ i 1 , it is similar for the outputs θ i 1 , θ i membership maps of [7], [8], or the linear activation maps of [15], [16]. Nonlinear hypothesis are described as the combination of the first order terms and it is detailed as the sum of the multiplication of the first order modeling parameters with the first order inputs, and after of the mentioned combination, one bounded map like the sigmoid [19], [20], hyperbolic tangent [21], [22], Gaussian [13], [14], or other is applied to alter the result.…”

“…This document proposes two nonlinear hypothesis which use different structures instead of using the linear bounded maps. They are termed as novel nonlinear hypothesis of equations (11), (13), (14), (15), (16), (17), (18), (19) and second order nonlinear hypothesis of equations (11), (13), (14), (15), (16), (17), (18), (19) and their goal is to improve the second order processes modeling.…”

“…In [13], [14], authors use hypothesis containing Gaussian membership maps. In [15], [16], authors use hypothesis containing linear activation maps. In [17], [18], authors use hypothesis containing discontinuous activation maps.…”