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We propose and analyze a real-time model predictive control (MPC) scheme thatutilizes stored data to improve its performance by learning the value functiononline with stability guarantees. For linear and nonlinear systems, a learningmethod is presented that makes use of basic analytic properties of the costfunction and is proven to learn the MPC control law and the value function onthe limit set of the closed-loop state trajectory. The main idea is to generatea smart warm start based on historical data that improves future data pointsand thus future warm starts. We show that these warm starts are asymptoticallyexact and converge to the solution of the MPC optimization problem. Thereby,the suboptimality of the applied control input resulting from the real-timerequirements vanishes over time. Simulative examples show that existingreal-time MPC schemes can be improved by storing data and the proposed learningscheme.

Online learning with stability guarantees: A memory-based real-time model predictive controller