Title: Predictive Control with Learning-Based Terminal Costs Using Approximate Value Iteration Show Chinese title

Title: 基于学习的终端成本预测控制使用近似值迭代

Abstract: Stability under model predictive control (MPC) schemes is frequently ensured by terminal ingredients. Employing a (control) Lyapunov function as the terminal cost constitutes a common choice. Learning-based methods may be used to construct the terminal cost by relating it to, for instance, an infinite-horizon optimal control problem in which the optimal cost is a Lyapunov function. Value iteration, an approximate dynamic programming (ADP) approach, refers to one particular cost approximation technique. In this work, we merge the results of terminally unconstrained predictive control and approximate value iteration to draw benefits from both fields. A prediction horizon is derived in dependence on different factors such as approximation-related errors to render the closed-loop asymptotically stable further allowing a suboptimality estimate in comparison to an infinite horizon optimal cost. The result extends recent studies on predictive control with ADP-based terminal costs, not requiring a local initial stabilizing controller. We compare this controller in simulation with other terminal cost options to show that the proposed approach leads to a shorter minimal horizon in comparison to previous results. Show Chinese abstract

Abstract: 模型预测控制（MPC）方案下的稳定性通常通过终端成分来保证。采用（控制）李雅普诺夫函数作为终端成本是一种常见选择。基于学习的方法可以用来通过将其与无限时域最优控制问题联系起来构建终端成本，在这种情况下，最优成本是一个李雅普诺夫函数。值迭代是一种近似动态规划（ADP）方法，指的是特定的成本近似技术。在这项工作中，我们将终端无约束预测控制的结果和近似值迭代结合起来，以从这两个领域中获得好处。根据不同的因素（如与逼近相关的误差）推导出预测时域，以使闭环渐近稳定，并允许与无限时域最优成本相比的次优性估计。该结果扩展了最近关于具有基于ADP终端成本的预测控制的研究，且不需要局部初始稳定控制器。我们在仿真中将此控制器与其他终端成本选项进行比较，以表明所提出的方法比先前的结果能实现更短的最小时域。