A Data-Driven Autopilot for Fixed-Wing Aircraft Based on Model Predictive Control

TL;DR

The paper tackles autopilot design for fixed-wing aircraft in the absence of reliable aerodynamic models by introducing Predictive Cost Adaptive Control (PCAC), an indirect adaptive control that couples online Recursive Least Squares (RLS) identification with Model Predictive Control (MPC). RLS with variable-rate forgetting updates a linear input-output model on-the-fly, which is then embedded in a Block Observable Canonical Form (BOCF) and used by a receding-horizon MPC to compute controls over a horizon length $\ell$ with weights $Q$, $\bar{Q}$, $\bar{P}$, and $R$. The approach is validated on both a linearized 6DOF AVL aircraft model and a nonlinear 3DOF MATLAB aircraft model, showing effective command following without prior aerodynamic data and without gain scheduling. This data-driven autopilot has potential to reduce wind-tunnel testing needs, eliminate gain scheduling, and accelerate aircraft/autopilot design cycles, with future work focusing on embedded implementations for fixed-wing autonomous aircraft.

Abstract

Autopilots for fixed-wing aircraft are typically designed based on linearized aerodynamic models consisting of stability and control derivatives obtained from wind-tunnel testing. The resulting local controllers are then pieced together using gain scheduling. For applications in which the aerodynamics are unmodeled, the present paper proposes an autopilot based on predictive cost adaptive control (PCAC). As an indirect adaptive control extension of model predictive control, PCAC uses recursive least squares (RLS) with variable-rate forgetting for online, closed-loop system identification. At each time step, RLS-based system identification updates the coefficients of an input-output model whose order is a hyperparameter specified by the user. For MPC, the receding-horizon optimization can be performed by either the backward-propagating Riccati equation or quadratic programming. The present paper investigates the performance of PCAC for fixed-wing aircraft without the use of any aerodynamic modeling or offline/prior data collection.

Figures (16)

• Figure 1: Sampled-data implementation of predictive controller for control of continuous-time system ${\mathcal{M}}.$ All sample-and-hold operations are synchronous. The predictive controller $G_{{\rm c},k}$ generates the requested discrete-time control $u_{{\rm req},k}\in{\mathbb R}^m$ at each step $k$. The implemented discrete-time control is $u_k=\gamma_k(\sigma(u_{{\rm req},k}))$, where $\sigma\colon{\mathbb R}^m\to{\mathbb R}^m$ represents control-magnitude saturation and $\gamma_k \colon{\mathbb R}^m\to{\mathbb R}^m$ represents move-size saturation. The resulting continuous-time control $u(t)$ is generated by applying a zero-order-hold operation to $u_k$. For this work, ${\mathcal{M}}$ represents a fixed-wing aircraft simulation model.
• Figure 2: Command-following block diagram for altitude $h$ and bank angle $\Phi$. This architecture uses two PCAC controllers, namely, PCAC/long for the longitudinal dynamics and PCAC/lat for the lateral dynamics. Note that PCAC/long uses the elevation angle $\Theta$ for system identification.
• Figure 3: Altitude and bank-angle command following. (a) compares the command $h_{\rm cmd}$ and the simulated $h$. (b) compares the command $\Phi_{\rm cmd}$ and the simulated $\Phi$. Note that learning takes place for the longitudinal dynamics for $t\in[0,5]$ s causing the excitation seen in (a).
• Figure 4: Aileron and elevator deflections for altitude and bank-angle command following. (a) shows the elevator deflection $\delta e$ (blue) with the constraints on $\vert \delta e \vert$ (dashed black). (b) shows the aileron deflection $\delta a$ (blue) with the constraints on $\vert \delta a \vert$ (dashed black).
• Figure 5: Estimated coefficient vectors for the altitude command-following loop $\theta_{\rm long}$ (a) and the bank-angle command-following loop $\theta_{\rm lat}$ (b). No prior modeling information is assumed, where $\theta_{\rm long,0} = \theta_{\rm lat,0} = 0.01 \textbf{1}_{36\times 1}$.