通过多面体李雅普诺夫函数进行区间马尔可夫决策过程的策略合成
Policy Synthesis for Interval MDPs via Polyhedral Lyapunov Functions
AI总结：
本文提出利用多面体李雅普诺夫函数进行区间马尔可夫决策过程的策略合成，通过构建吸引不变集确保收敛性并减少不确定性影响，通过回收机器人和电动汽车电池案例验证了方法的有效性。
摘要：
在许多安全关键应用中，不确定性下的决策是核心问题，其中决策必须由概率建模形式引导。本文介绍了一种新的方法，用于在多目标区间马尔可夫决策过程中使用多面体李雅普诺夫函数进行策略合成。与以往依赖二次函数的李雅普诺夫方法不同，我们的方法利用多面体函数来提高在动态规划值迭代中管理不确定性的准确性。我们将值迭代算法重新表述为具有区间不确定性的切换仿射系统，并应用控制理论的稳定性原理，以合成引导系统向目标集的策略。通过构建一个吸引不变集，我们确保合成的策略在保证收敛的同时，最小化底层模型转换不确定性的影响。我们的方法通过直接确定一个策略，使目标值在指定范围内，从而消除了对计算密集型帕累托曲线计算的需要。我们通过数值案例研究验证了我们的方法，包括回收机器人和电动汽车电池，展示了其在不确定性下的策略合成有效性。
英文摘要：
Decision-making under uncertainty is central to many safety-critical applications, where decisions must be guided by probabilistic modeling formalisms. This paper introduces a novel approach to policy synthesis in multi-objective interval Markov decision processes using polyhedral Lyapunov functions. Unlike previous Lyapunov-based methods that mainly rely on quadratic functions, our method utilizes polyhedral functions to enhance accuracy in managing uncertainties within value iteration of dynamic programming. We reformulate the value iteration algorithm as a switched affine system with interval uncertainties and apply control-theoretic stability principles to synthesize policies that guide the system toward a desired target set. By constructing an invariant set of attraction, we ensure that the synthesized policies provide convergence guarantees while minimizing the impact of transition uncertainty in the underlying model. Our methodology removes the need for computationally intensive Pareto curve computations by directly determining a policy that brings objectives within a specified range of their target values. We validate our approach through numerical case studies, including a recycling robot and an electric vehicle battery, demonstrating its effectiveness in achieving policy synthesis under uncertainty.
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