Adaptive Neural Stochastic Control with Lipschitz Constant Optimization

An adaptive neural stochastic contraction metric with Lipschitz constant optimization (aNSCM-Lip) is proposed for It stochastic systems with unmatched parameter uncertainties. The adaptive law is designed via the certainty equivalence principle with incremental stability guarantee, which is specified by the neural stochastic contraction metric (NSCM). Then, we develop a neural network (NN) based on Lipschitz constant estimation and optimization. Lipschitz optimization and weights training are formulated as optimization problems utilizing the alternating direction method of multipliers (ADMM), which ensures the Lipschitz continuity of the network metric and its derivative. The learning-based controller with a Lipschitz constant optimized network provides stability certificates for the closed-loop system. DC-DC buck vector and single-joint manipulator examples are given to demonstrate the effectiveness and superiority of the proposed control strategy.