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Nonlinear Control Allocation: A Learning Based Approach

Hafiz Zeeshan Iqbal Khan, Surrayya Mobeen, Jahanzeb Rajput, Jamshed Riaz

TL;DR

This work tackles nonlinear control allocation for over-actuated aircraft by learning an inverse map of the control-effectiveness function with an artificial neural network (ANN). By training an ANN to map desired moments and state information to actuator commands, the approach avoids online optimization and provides a constrained allocator with stability guarantees, conditioned on a bound on allocation error. The authors introduce performance metrics for allocation quality and propose volume-based approximations to assess coverage, demonstrating that the ANN allocator achieves comparable tracking to a quadratic-programming-based method while offering substantial computational efficiency. The method is validated in a high-fidelity simulation of a tailless flying wing, showing significant speedups (about 0.02 ms per step versus up to ~9 ms) with similar control performance, indicating strong practical potential for real-time embedded flight control. Future work includes improved volume computations for the attainable moment set and domain partitioning for piecewise-linear mappings to further enhance reliability and scalability.

Abstract

Modern aircraft are designed with redundant control effectors to cater for fault tolerance and maneuverability requirements. This leads to aircraft being over-actuated and requires control allocation schemes to distribute the control commands among control effectors. Traditionally, optimization-based control allocation schemes are used; however, for nonlinear allocation problems, these methods require large computational resources. In this work, an artificial neural network (ANN) based nonlinear control allocation scheme is proposed. The proposed scheme is composed of learning the inverse of the control effectiveness map through ANN, and then implementing it as an allocator instead of solving an online optimization problem. Stability conditions are presented for closed-loop systems incorporating the allocator, and computational challenges are explored with piece-wise linear effectiveness functions and ANN-based allocators. To demonstrate the efficacy of the proposed scheme, it is compared with a standard quadratic programming-based method for control allocation.

Nonlinear Control Allocation: A Learning Based Approach

TL;DR

This work tackles nonlinear control allocation for over-actuated aircraft by learning an inverse map of the control-effectiveness function with an artificial neural network (ANN). By training an ANN to map desired moments and state information to actuator commands, the approach avoids online optimization and provides a constrained allocator with stability guarantees, conditioned on a bound on allocation error. The authors introduce performance metrics for allocation quality and propose volume-based approximations to assess coverage, demonstrating that the ANN allocator achieves comparable tracking to a quadratic-programming-based method while offering substantial computational efficiency. The method is validated in a high-fidelity simulation of a tailless flying wing, showing significant speedups (about 0.02 ms per step versus up to ~9 ms) with similar control performance, indicating strong practical potential for real-time embedded flight control. Future work includes improved volume computations for the attainable moment set and domain partitioning for piecewise-linear mappings to further enhance reliability and scalability.

Abstract

Modern aircraft are designed with redundant control effectors to cater for fault tolerance and maneuverability requirements. This leads to aircraft being over-actuated and requires control allocation schemes to distribute the control commands among control effectors. Traditionally, optimization-based control allocation schemes are used; however, for nonlinear allocation problems, these methods require large computational resources. In this work, an artificial neural network (ANN) based nonlinear control allocation scheme is proposed. The proposed scheme is composed of learning the inverse of the control effectiveness map through ANN, and then implementing it as an allocator instead of solving an online optimization problem. Stability conditions are presented for closed-loop systems incorporating the allocator, and computational challenges are explored with piece-wise linear effectiveness functions and ANN-based allocators. To demonstrate the efficacy of the proposed scheme, it is compared with a standard quadratic programming-based method for control allocation.
Paper Structure (12 sections, 3 theorems, 32 equations, 4 figures, 1 table)

This paper contains 12 sections, 3 theorems, 32 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Nonlinear Control Allocation
  4. Artificial Neural Networks (ANNs)
  5. Problem Formulation
  6. ANN-based Constrained Control Allocation
  7. Performance of Control Allocator
  8. Closed Loop Stability Analysis
  9. Aircraft Control Allocation: An Example
  10. Aircraft Specifications
  11. Results & Discussion
  12. Conclusion

Key Result

Lemma 1

Given an unconstrained optimization problem of the following form The optimal solution $x^{*}:\mathcal{Y}\mapsto\mathcal{X}$ can be equivalently considered as the solution of the following problem:

Figures (4)

  • Figure 1: Feedback-loop structure with control allocation
  • Figure 2: Projection Operator: An Illustration
  • Figure 3: ANN Training Architecture
  • Figure 4: Comparison of Performance and Allocation Error

Theorems & Definitions (14)

  • Definition 1
  • Definition 2: Projection Operator
  • Remark 1
  • Lemma 1
  • proof
  • Definition 3
  • Definition 4
  • Definition 5
  • Theorem 1
  • proof
  • ...and 4 more