Neural Network-Based Lyapunov Stability Verification for Continuous-Time Nonlinear Systems via Mixed Integer Linear Programming

This paper discusses Lyapunov stability verification methods for continuous-time nonlinear systems. Traditional mathematical methods require a lot of manual calculations, which consume a lot of time and energy. To address the problem of the low efficiency in traditional methods, this paper introduces neural networks into the design of the Lyapunov function to achieve independent verification. First, a neural network is used to represent the Lyapunov function. Then, the Lyapunov stability condition is converted into a mixed integer linear programming (MILP) problem, and the solution to the optimization problem is solved through the MILP solver to verify whether the output of the neural network satisfies the Lyapunov stability condition. In addition, this paper gives the training loss function of the Lyapunov neural network, which mainly consists of optimization problems. Finally, a simulation example is given to illustrate the effectiveness of this method.