Automated synthesis of provably correct controllers for cyber-physical systems is crucial for deploying these systems in safety-critical scenarios. However, their hybrid features and stochastic or unknown behaviours make this synthesis problem challenging. In this paper, we propose a method for synthesizing controllers for Markov jump linear systems (MJLSs), a particular class of cyber-physical systems, that certifiably satisfy a requirement expressed as a specification in probabilistic computation tree logic (PCTL). An MJLS consists of a finite set of linear dynamics with unknown additive disturbances, where jumps between these modes are governed by a Markov decision process (MDP). We consider both the case where the transition function of this MDP is given by probability intervals or where it is completely unknown. Our approach is based on generating a finite-state abstraction which captures both the discrete and the continuous behaviour of the original system. We formalise such abstraction as an interval Markov decision process (iMDP): intervals of transition probabilities are computed using sampling techniques from the so-called "scenario approach", resulting in a probabilistically sound approximation of the MJLS. This iMDP abstracts both the jump dynamics between modes, as well as the continuous dynamics within the modes. To demonstrate the efficacy of our technique, we apply our method to multiple realistic benchmark problems, in particular, temperature control, and aerial vehicle delivery problems.

Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers. Stochastic noise causes aleatoric uncertainty, whereas imprecise knowledge of model parameters leads to epistemic uncertainty. Several approaches use formal abstractions to synthesize policies that satisfy temporal specifications related to safety and reachability. However, the underlying models exclusively capture aleatoric but not epistemic uncertainty, and thus require that model parameters are known precisely. Our contribution to overcoming this restriction is a novel abstraction-based controller synthesis method for continuous-state models with stochastic noise and uncertain parameters. By sampling techniques and robust analysis, we capture both aleatoric and epistemic uncertainty, with a user-specified confidence level, in the transition probability intervals of a so-called interval Markov decision process (iMDP). We synthesize an optimal policy on this iMDP, which translates (with the specified confidence level) to a feedback controller for the continuous model with the same performance guarantees. Our experimental benchmarks confirm that accounting for epistemic uncertainty leads to controllers that are more robust against variations in parameter values.

在安全关键设置中运行的自治系统的控制器必须考虑随机扰动。这种干扰通常被建模为过程噪声，并且常见的假设是底层分布是已知的和/或高斯的。然而，在实践中，这些假设可能是不现实的并且可以导致真正噪声分布的近似值。我们提出了一种新的规划方法，不依赖于噪声分布的任何明确表示。特别是，我们解决了计算控制器的控制器，该控制器提供了安全地到达目标的概率保证。首先，我们将连续系统摘要进入一个离散状态模型，通过状态之间的概率转换捕获噪声。作为关键贡献，我们根据噪声的有限数量的样本来调整这些过渡概率的方案方法中的工具。我们在所谓的间隔马尔可夫决策过程（IMDP）的转换概率间隔中捕获这些界限。该IMDP在过渡概率中的不确定性稳健，并且可以通过样本的数量来控制概率间隔的紧张性。我们使用最先进的验证技术在IMDP上提供保证，并计算这些保证对自主系统的控制器。即使IMDP有数百万个州或过渡，也表明了我们方法的实际适用性。

我们研究了由测量和过程噪声引起的不确定性的动态系统的规划问题。测量噪声导致系统状态可观察性有限，并且过程噪声在给定控制的结果中导致不确定性。问题是找到一个控制器，保证系统在有限时间内达到所需的目标状态，同时避免障碍物，至少需要一些所需的概率。由于噪音，此问题不承认一般的精确算法或闭合性解决方案。我们的主要贡献是一种新颖的规划方案，采用卡尔曼滤波作为状态估计器，以获得动态系统的有限状态抽象，我们将作为马尔可夫决策过程（MDP）正式化。通过延长概率间隔的MDP，我们可以增强模型对近似过渡概率的数值不精确的鲁棒性。对于这种所谓的间隔MDP（IMDP），我们采用最先进的验证技术来有效地计算最大化目标状态概率的计划。我们展示了抽象的正确性，并提供了几种优化，旨在平衡计划的质量和方法的可扩展性。我们展示我们的方法能够处理具有6维状态的系统，该系统导致具有数万个状态和数百万个过渡的IMDP。

我们在不断变化的环境中提供了一种新的在线学习，特别是专家建议的预测。在非变化环境中，斜视算法的设计至少与其他已知算法相同，在特定情况下，其功能更好。但是，当使用常规的黑盒算法使斜视适合不断变化的环境时，它会失去其有益的特性。因此，我们提供了一种新的算法，即quint-ce，适用于不断变化的环境并保留斜视的特性。