Adam Hallmark

Adam Hallmark, Pan Zhao

This paper first demonstrates that applying standard incremental nonlinear dynamic inversion (INDI) with incremental control allocation (ICA) to input nonaffine systems relies on an untenable linear approximation of the actuator model. It then shows that avoiding this issue, while retaining the static control allocation paradigm, generally requires solving a nonlinear programming (NLP) problem. To address the associated online computational challenges, the paper subsequently presents a supervised learning-based approach. Numerical experiments on an example problem validate the identified limitations of standard INDI + ICA for input nonaffine systems, while also demonstrating that the proposed learning-based method provides an effective and computationally tractable alternative.

MD Abul Kashem Niloy, Adam Hallmark, Yikun Cheng et al.

Nonlinear parameter-varying (NPV) systems are a class of nonlinear systems whose dynamics explicitly depend on time-varying external parameters, making them suitable for modeling real-world systems with dynamics variations. Traditional synthesis methods for NPV systems, such as sum-of-squares (SOS) optimization, are only applicable to control-affine systems, face scalability challenges and often lead to conservative results due to structural restrictions. To address these limitations, we propose Neural-NPV, a two-stage learning-based framework that leverages neural networks to jointly synthesize a PD controller and a PD Lyapunov function for an NPV system under input constraints. In the first stage, we utilize a computationally cheap, gradient-based counterexample-guided procedure to synthesize an approximately valid PD Lyapunov function and a PD controller. In the second stage, a level-set guided refinement is then conducted to obtain a valid Lyapunov function and controller while maximizing the robust region of attraction (R-ROA). We demonstrate the advantages of Neural-NPV in terms of applicability, performance, and scalability compared to SOS-based methods through numerical experiments involving an simple inverted pendulum with one scheduling parameter and a quadrotor system with three scheduling parameters.