A Theory of Sampling for Continuous-time Metric Temporal Logic

This paper revisits the classical notion of sampling in the setting of real-time temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over continuous-time models and over discrete-time models is studied. It is shown to what extent discrete-time sequences obtained by sampling continuous-time signals capture the semantics of MTL formulas over the two time domains. The main results apply to "flat" formulas that do not nest temporal operators and can be applied to the problem of reducing the verification problem for MTL over continuous-time models to the same problem over discrete-time, resulting in an automated partial practically-efficient discretization technique.Comment: Revised version, 43 pages

On-Line Monitoring for Temporal Logic Robustness

In this paper, we provide a Dynamic Programming algorithm for on-line monitoring of the state robustness of Metric Temporal Logic specifications with past time operators. We compute the robustness of MTL with unbounded past and bounded future temporal operators MTL over sampled traces of Cyber-Physical Systems. We implemented our tool in Matlab as a Simulink block that can be used in any Simulink model. We experimentally demonstrate that the overhead of the MTL robustness monitoring is acceptable for certain classes of practical specifications

Decentralized Abstractions and Timed Constrained Planning of a General Class of Coupled Multi-Agent Systems

This paper presents a fully automated procedure for controller synthesis for a general class of multi-agent systems under coupling constraints. Each agent is modeled with dynamics consisting of two terms: the first one models the coupling constraints and the other one is an additional bounded control input. We aim to design these inputs so that each agent meets an individual high-level specification given as a Metric Interval Temporal Logic (MITL). Furthermore, the connectivity of the initially connected agents, is required to be maintained. First, assuming a polyhedral partition of the workspace, a novel decentralized abstraction that provides controllers for each agent that guarantee the transition between different regions is designed. The controllers are the solution of a Robust Optimal Control Problem (ROCP) for each agent. Second, by utilizing techniques from formal verification, an algorithm that computes the individual runs which provably satisfy the high-level tasks is provided. Finally, simulation results conducted in MATLAB environment verify the performance of the proposed framework

Learning and Designing Stochastic Processes from Logical Constraints

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics must be known exactly. As this is seldom the case, many methods have been devised over the last decade to infer (learn) such parameters from observations of the state of the system. In this paper, we depart from this approach by assuming that our observations are {\it qualitative} properties encoded as satisfaction of linear temporal logic formulae, as opposed to quantitative observations of the state of the system. An important feature of this approach is that it unifies naturally the system identification and the system design problems, where the properties, instead of observations, represent requirements to be satisfied. We develop a principled statistical estimation procedure based on maximising the likelihood of the system's parameters, using recent ideas from statistical machine learning. We demonstrate the efficacy and broad applicability of our method on a range of simple but non-trivial examples, including rumour spreading in social networks and hybrid models of gene regulation

Prescribed Performance Control Guided Policy Improvement for Satisfying Signal Temporal Logic Tasks

Signal temporal logic (STL) provides a user-friendly interface for defining complex tasks for robotic systems. Recent efforts aim at designing control laws or using reinforcement learning methods to find policies which guarantee satisfaction of these tasks. While the former suffer from the trade-off between task specification and computational complexity, the latter encounter difficulties in exploration as the tasks become more complex and challenging to satisfy. This paper proposes to combine the benefits of the two approaches and use an efficient prescribed performance control (PPC) base law to guide exploration within the reinforcement learning algorithm. The potential of the method is demonstrated in a simulated environment through two sample navigational tasks.Comment: This is the extended version of the paper accepted to the 2019 American Control Conference (ACC), Philadelphia (to be published

Active Sampling-based Binary Verification of Dynamical Systems

Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates verification that the system does in fact satisfy those requirements at all possible operating conditions. While analytical proof-based techniques and finite abstractions can be used to provably verify the closed-loop system's response at different operating conditions, they often produce conservative approximations due to restrictive assumptions and are difficult to construct in many applications. In contrast, popular statistical verification techniques relax the restrictions and instead rely upon simulations to construct statistical or probabilistic guarantees. This work presents a data-driven statistical verification procedure that instead constructs statistical learning models from simulated training data to separate the set of possible perturbations into "safe" and "unsafe" subsets. Binary evaluations of closed-loop system requirement satisfaction at various realizations of the uncertainties are obtained through temporal logic robustness metrics, which are then used to construct predictive models of requirement satisfaction over the full set of possible uncertainties. As the accuracy of these predictive statistical models is inherently coupled to the quality of the training data, an active learning algorithm selects additional sample points in order to maximize the expected change in the data-driven model and thus, indirectly, minimize the prediction error. Various case studies demonstrate the closed-loop verification procedure and highlight improvements in prediction error over both existing analytical and statistical verification techniques.Comment: 23 page