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. 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 learn the MPC control law and the value function on the limit set of the closed-loop state trajectory. The main idea is to generate a smart warm start based on historical data that improves future data points and thus future warm starts. We show that these warm starts are asymptotically exact and converge to the solution of the MPC optimization problem. Thereby, the suboptimality of the applied control input resulting from the real-time requirements vanishes over time. Numerical examples show that existing real-time MPC schemes can be improved by storing optimization data and using the proposed learning scheme.

我们提出并分析了实时模型预测控制（MPC）方案，该方案利用存储的数据通过在线学习具有稳定性保证的价值函数来提高其性能。对于线性和非线性系统，提出了一种利用成本函数的基本分析性质的学习方法，并被证明可以学习MPC控制律和闭环状态轨迹极限集上的值函数。主要思想是根据历史数据生成智能热启动，从而改善未来的数据点，从而改善未来的热启动。我们证明这些热启动是渐近精确的，并且收敛于MPC优化问题的解决方案。因此，由实时需求导致的所施加的控制输入的次优性随时间消失。