Neural-NPV Control: Learning Parameter-Dependent Controllers and Lyapunov Functions with Neural Networks

A research team including MD Abul Kashem Niloy, Adam Hallmark, Yikun Cheng, and Pan Zhao has introduced Neural-NPV, a novel AI-driven framework for controlling complex nonlinear parameter-varying (NPV) systems. These systems, which include drones, robotic arms, and autonomous vehicles, have dynamics that change with external parameters like wind speed or payload weight. Traditional control synthesis methods like sum-of-squares optimization struggle with scalability and often produce conservative, inefficient controllers. Neural-NPV addresses these limitations by leveraging neural networks to jointly learn both a parameter-dependent controller and a corresponding Lyapunov function—a mathematical certificate proving the system's stability.

The framework operates in two distinct stages. First, it uses a computationally efficient, gradient-based counterexample-guided procedure to synthesize an approximately valid controller and stability certificate. Then, a level-set guided refinement stage optimizes these components to maximize the robust region of attraction—essentially expanding the range of conditions under which the system remains stable. The researchers validated their approach on two benchmark systems: a simple inverted pendulum with one scheduling parameter and a more complex quadrotor (drone) system with three scheduling parameters. In both cases, Neural-NPV demonstrated superior performance and scalability compared to traditional methods, successfully handling the complex, nonlinear dynamics that challenge conventional approaches.