Abstract We address the finite horizon control of a discrete time piecewise affine (PWA) system, which is affected by an additive bounded disturbance. The goal is to robustly drive the state of the system to some target region, while satisfying state and actuation constraints. This problem is challenging due to the mixed discrete and continuous dynamics, requiring the exploration of many mode sequences. We address this problem by proposing a two-step approach which is based on designing a reference trajectory followed by a feedback controller that tries to make all solutions adhere to the reference mode sequence. As a result, the number of considered mode sequences can be drastically reduced. Termination is guaranteed since the time horizon and the number of modes are finite. Key to the computational efficiency of this procedure is the choice of the reference trajectory, which should be designed to avoid the branching of mode sequences from the reference sequence. The resulting set-based feedback control law is simple and easy to implement. Due to the use of reachability analysis, our results are formally correct. A quadruple-tank benchmark example shows the effectiveness of our approach.

中文翻译：

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具有状态和驱动约束的扰动分段仿射系统的基于集合的控制

摘要 我们解决了离散时间分段仿射 (PWA) 系统的有限水平控制问题，该系统受加性有界扰动的影响。目标是将系统状态稳健地驱动到某个目标区域，同时满足状态和驱动约束。由于离散和连续动力学的混合，这个问题具有挑战性，需要探索许多模式序列。我们通过提出一种两步方法来解决这个问题，该方法基于设计参考轨迹，然后是反馈控制器，试图使所有解决方案都遵循参考模式序列。结果，可以大大减少所考虑的模式序列的数量。由于时间范围和模式数量是有限的，因此可以保证终止。该过程计算效率的关键是参考轨迹的选择，其设计应避免模式序列从参考序列的分支。由此产生的基于集合的反馈控制律简单易行。由于使用了可达性分析，我们的结果在形式上是正确的。四缸基准示例显示了我们方法的有效性。