Contraction-Based Stochastic Model Predictive Control for Nonlinear Systems With Input Delay Using Multidimensional Taylor Network

For nonlinear systems with stochastic uncertainties and input delay, the existing control approaches based on the robust mechanism are generally conservative in most practical scenarios. Within this context, a stochastic model predictive control (MPC) scheme based on uncertainty contraction is proposed here to reduce conservativeness and improve real-time performance. In terms of the Lyapunov–Razumikhin theorem, a robust variational controller (RVC) is deduced as the primary controller for the variational dynamic with input delay. A variational vector field in Wasserstein metric space is constructed to detect the minimum geodesic between the uncertainty distribution and the desired one. Integrating RVC along the minimum geodesic, the modified auxiliary controller is developed for tracking the nominal trajectory with less conservatism. Subsequently, the chance constraints of stochastic states are transformed into the deterministic quantile constraints of nominal states. The sparse multidimensional Taylor network based on Bayesian compressive sensing is designed to parameterize the ambiguity set in Wasserstein metric space for higher computational efficiency. A tractable MPC scheme is then formulated to achieve the reference index with an improved tradeoff between robustness and real-time performance. The stochastic input-to-state stability of the considered system is verified theoretically by the Lyapunov–Krasovskii theorem. The effectiveness of the proposed scheme is confirmed by a numerical simulation derived from a practical industrial process.