Neural Lyapunov Differentiable Predictive Control
This work addresses the challenge of ensuring stability in learning-based control for applications like robotics or aerospace, though it appears incremental by combining differentiable programming with Lyapunov methods.
The authors tackled the problem of learning-based predictive control with stability guarantees by introducing Neural Lyapunov Differentiable Predictive Control (NLDPC), which jointly learns a control policy and a Lyapunov function to certify stable regions, resulting in a computationally efficient alternative to classical methods as demonstrated in simulations on a double integrator and aircraft model.
We present a learning-based predictive control methodology using the differentiable programming framework with probabilistic Lyapunov-based stability guarantees. The neural Lyapunov differentiable predictive control (NLDPC) learns the policy by constructing a computational graph encompassing the system dynamics, state and input constraints, and the necessary Lyapunov certification constraints, and thereafter using the automatic differentiation to update the neural policy parameters. In conjunction, our approach jointly learns a Lyapunov function that certifies the regions of state-space with stable dynamics. We also provide a sampling-based statistical guarantee for the training of NLDPC from the distribution of initial conditions. Our offline training approach provides a computationally efficient and scalable alternative to classical explicit model predictive control solutions. We substantiate the advantages of the proposed approach with simulations to stabilize the double integrator model and on an example of controlling an aircraft model.