Generalized feedforward control using physics—informed neural networks

Data-driven feedforward control design for nonlinear systems: A control-oriented system identification approach

“…In contrast, for γ = 5•10 −5 the inversion error increases, which limits the achievable performance for n i > 20. Comparing the upperbound (15) with the results in Fig. 4 indicates that ε is small.…”

“…This typically yields a two-step feedforward controller design procedure, consisting of an identification step to fit the model (5) to the data (3), and an inversion step to compute the feedforward input. Although this approach is generally adopted in literature, see, e.g., [3], [15], [16], [18], a quantitative relation between the identification and the tracking error, respectively, is still missing. Hence, the first problem considered in this work is to establish a quantitative relation between the tracking error on one hand, and the identification error and inversion error on the other hand.…”

“…Even when the identification in ( 16) and the FHOFC problem (17) are solved accurately, it is still possible that the tracking error remains too large due to the presence of ε in (15). Options to generate new data and thereby achieve a smaller ε were indicated in Sec.…”

“…Results: Fig. 4 visualizes the 2-norm of the identification, inversion and tracking error in (15) for the reference R in Fig. 3 using different number of neurons n 1 , with γ = 10 −6 (top window) and γ = 5 • 10 −5 (bottom window).…”

“…The aforementioned methods typically assume a known, physics-based model of the system. To account for unknown or complex to model dynamics, data-driven techniques have been explored in combination with artificial intelligence, e.g., neural network (NN) models [14], physics-informed neural networks [15], or physics-guided neural network (PGNN) models [16] and other hybrid model structures [17]. However, due to the non-invertibility of (PG)NN models, these approaches generally adopt an identification of the inverse system directly.…”