Constraint handling during tracking operations is at the core of many real-world control implementations and is well understood when dynamic models of the underlying system exist, yet becomes more challenging when data-driven models are used to describe the nonlinear system at hand. We seek to combine the nonlinear modeling capabilities of a wide class of neural networks with the constraint-handling guarantees of model predictive control (MPC) in a rigorous and online computationally tractable framework. The class of networks considered can be captured using Koopman operators, and are integrated into a Koopman-based tracking MPC (KTMPC) for nonlinear systems to track piecewise constant references. The effect of model mismatch between original nonlinear dynamics and its trained Koopman linear model is handled by using a constraint tightening approach in the proposed tracking MPC strategy. By choosing two Lyapunov functions, we prove that solution is recursively feasible and input-to-state stable to a neighborhood of both online and offline optimal reachable steady outputs in the presence of bounded modeling errors under mild assumptions. Finally, we demonstrate the results on a numerical example, before applying the proposed approach to the problem of reference tracking by an autonomous ground vehicle.

翻译：在跟踪操作过程中处理约束是许多实际控制实现的核心，当存在底层系统的动态模型时，这一过程已得到充分理解，但当使用数据驱动模型描述所涉及的非线性系统时则更具挑战性。我们旨在将各类神经网络的非线性建模能力与模型预测控制（MPC）的约束处理保障相结合，构建一个严谨且在线计算可行的框架。所考虑的神经网络类别可通过Koopman算子进行描述，并集成到基于Koopman的跟踪MPC（KTMPC）中，用于非线性系统以跟踪分段恒定参考值。原始非线性动力学与其训练的Koopman线性模型之间的模型失配效应，通过在所提出的跟踪MPC策略中采用约束收紧方法进行处理。通过选择两个Lyapunov函数，我们证明在温和假设下，当存在有界建模误差时，该解在递归上可行且输入到状态稳定于在线和离线最优可达稳态输出的邻域内。最后，我们通过数值示例展示结果，并将所提方法应用于自主地面车辆的参考跟踪问题。