Neural-NPV Control: Learning Parameter-Dependent Controllers and Lyapunov Functions with Neural Networks
This work addresses control synthesis for real-world systems with dynamics variations, offering a more scalable and less conservative alternative to traditional methods, though it appears incremental as it builds on existing learning-based and counterexample-guided approaches.
The authors tackled the limitations of traditional synthesis methods for nonlinear parameter-varying (NPV) systems, such as scalability and conservatism, by proposing Neural-NPV, a learning-based framework that jointly synthesizes parameter-dependent controllers and Lyapunov functions, demonstrating advantages in applicability, performance, and scalability through numerical experiments on systems like an inverted pendulum and quadrotor.
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.