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

TL;DR

The paper tackles a priori performance guarantees for nonlinear, potentially nonminimum-phase feedforward control by lifting dynamics to a finite-length trajectory space and deriving an explicit upper bound on tracking error $\frac{1}{N_k^{1/p}} \| R - Y \|_p \le V_{\text{id}}(\cdot) + V_{\text{ff}}(\cdot) + \varepsilon$. It introduces a feedforward control-oriented identification cost $V_{\text{id}}$ and a finite-horizon optimization $V_{\text{ff}}$ to compute the feedforward input, all within lifted representations $Y=\Phi(x_0,R,U_{\text{ff}})$ and $\hat{Y}=\hat{\Phi}(\theta,x_0,R,U_{\text{ff}})$. The framework subsumes inverse-model feedforward and linear ILC as special cases and extends to iterative learning (IL--FHOFC) for repetitive tasks. Validation on a nonlinear PGNN-based mechatronic example shows improved tracking and faster convergence compared to linear ILC, illustrating practical impact for nonlinear, data-driven feedforward control.

Abstract

Feedforward controllers typically rely on accurately identified inverse models of the system dynamics to achieve high reference tracking performance. However, the impact of the (inverse) model identification error on the resulting tracking error is only analyzed a posteriori in experiments. Therefore, in this work, we develop an approach to feedforward control design that aims at minimizing the tracking error a priori. To achieve this, we present a model of the system in a lifted space of trajectories, based on which we derive an upperbound on the reference tracking performance. Minimization of this bound yields a feedforward control-oriented system identification cost function, and a finite-horizon optimization to compute the feedforward control signal. The nonlinear feedforward control design method is validated using physics-guided neural networks on a nonlinear, nonminimum phase mechatronic example, where it outperforms linear ILC.

Figures (6)

• Figure 1: Schematic overview of the control structure.
• Figure 2: Visual representation of the dynamics \ref{['eq:SystemDynamics']} in lifted form \ref{['eq:SystemDynamicsLifted']}.
• Figure 3: Rotating--translating mass with actuation and sensing on opposite sides of the centre of mass.
• Figure 4: Reference $R$ used for performance evaluation.
• Figure 5: Normalized $2$--norm of the identification ($Y^d - \hat{Y}^d$, $N = N_d$), inversion ($R - \hat{Y}$, $N=N_k$) and tracking ($R-Y$, $N = N_k$) error for PGNNs with different number of neurons using $\gamma = 2 \cdot 10^{-4}$ (left window) and $\gamma = 10^{-3}$ (right window).

Theorems & Definitions (11)

• Remark IV.1
• Remark IV.2
• Proposition IV.1
• proof
• Remark IV.3
• Lemma V.1
• proof
• Remark V.1
• Lemma V.2
• proof