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

We propose and analyze a real-time model predictive control (MPC) scheme that utilizes stored data to improve its performance by learning the value function online with stability guarantees. The suboptimality of the applied control input resulting from the real-time requirements is shown to vanish over time as more and more data is collected. For linear and nonlinear systems, a learning method is presented that makes use of basic analytic properties of the cost function and is proven to recover the value function on the limit set of the closed-loop state trajectory. Simulative examples show that existing real-time MPC schemes can be improved by storing data and the proposed learning scheme.