通过控制架构最大化线性随机系统的可达-避免概率
Maximizing Reach-Avoid Probabilities for Linear Stochastic Systems via Control Architectures
AI总结：
本文提出一种结合马尔可夫决策过程和模型预测控制器的控制架构，用于最大化线性随机系统的可达-避免概率，通过在线更新参考信号实现高效鲁棒控制。
摘要：
随机系统中可达-避免概率的最大化是控制文献中的核心主题。然而，现有的方法要么局限于低维系统，要么存在保守的近似问题。为解决这些限制，我们提出了一种结合马尔可夫决策过程的灵活性和模型预测控制器的可扩展性的控制架构。模型预测控制器跟踪参考信号，同时对随机性和可达-避免目标保持中立。相反，通过在线最优更新控制器的参考来最大化可达-避免概率。为此，由系统和模型预测控制器组成的闭环系统被抽象为一个马尔可夫决策过程，在每个时间步可以选择新的参考。然后通过动态规划计算生成最优参考的反馈策略。如果系统的状态空间是连续的，动态规划算法必须在有限的系统近似上执行。对模型预测控制器的修改使动态规划算法能够高效地对近似误差进行鲁棒化，从而保持所实现的可达-避免概率的界限。该方法在扰动的12维四旋翼模型在杂乱的可达-避免环境中得到验证，证明了其灵活性和可扩展性。
英文摘要：
The maximization of reach-avoid probabilities for stochastic systems is a central topic in the control literature. Yet, the available methods are either restricted to low-dimensional systems or suffer from conservative approximations. To address these limitations, we propose control architectures that combine the flexibility of Markov Decision Processes with the scalability of Model Predictive Controllers. The Model Predictive Controller tracks reference signals while remaining agnostic to the stochasticity and reach-avoid objective. Instead, the reach-avoid probability is maximized by optimally updating the controller's reference online. To achieve this, the closed-loop system, consisting of the system and Model Predictive Controller, is abstracted as a Markov Decision Process in which a new reference can be chosen at every time-step. A feedback policy generating optimal references is then computed via Dynamic Programming. If the state space of the system is continuous, the Dynamic Programming algorithm must be executed on a finite system approximation. Modifications to the Model Predictive Controller enable a computationally efficient robustification of the Dynamic Programming algorithm to approximation errors, preserving bounds on the achieved reach-avoid probability. The approach is validated on a perturbed 12D quadcopter model in cluttered reach-avoid environments proving its flexibility and scalability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
