PDE Backstepping

PDE backstepping is a control design method for partial differential equations (PDEs) aiming to stabilize systems by transforming a difficult-to-control PDE into a simpler, target system. Current research heavily emphasizes using neural operators, such as DeepONets and Fourier Neural Operators, to approximate the computationally expensive gain kernels generated by the backstepping transformation, significantly accelerating real-time control implementation. This approach enables faster and more efficient control of PDEs in various applications, including adaptive control and gain scheduling, improving the feasibility of real-time control for complex systems modeled by PDEs.