Signal Temporal Logic Specifications Research Articles

Mining of extended signal temporal logic specifications with ParetoLib 2.0

Cyber-physical systems are complex environments that combine physical devices (i.e., sensors and actuators) with a software controller. The ubiquity of these systems and dangers associated with their failure require the implementation of mechanisms to monitor, verify and guarantee their correct behaviour. This paper presents ParetoLib 2.0, a Python tool for offline monitoring and specification mining of cyber-physical systems. ParetoLib 2.0 uses signal temporal logic (STL) as the formalism for specifying properties on time series. ParetoLib 2.0 builds upon other tools for evaluating and mining STL expressions, and extends them with new functionalities. ParetoLib 2.0 implements a set of new quantitative operators for trace analysis in STL, a novel mining algorithm and an original graphical user interface. Additionally, the performance is optimised with respect to previous releases of the tool via data-type annotations and multi core support. ParetoLib 2.0 allows the offline verification of STL properties as well as the specification mining of parametric STL templates. Thanks to the implementation of the new quantitative operators for STL, the tool outperforms the expressiveness and capabilities of similar runtime monitors.

Sequential control barrier functions for mobile robots with dynamic temporal logic specifications

We address a motion planning and control problem for mobile robots to satisfy rich, time-varying tasks expressed as Signal Temporal Logic (STL) specifications. The specifications may include tasks with nested temporal operators or time-conflicting requirements (e.g., achieving periodic tasks or tasks defined within the same time interval). Moreover, the tasks can be defined in locations changing with time (i.e., dynamic targets), and their future motions are not known a priori. This unpredictability requires an online control approach which motivates us to investigate the use of control barrier functions (CBFs). The proposed CBFs take into account the actuation limits of the robots and a feasible sequence of STL tasks. They define time-varying feasible sets of states the system must always stay inside. We show the feasible sequence generation process that even includes the decomposition of periodic tasks and alternative scenarios due to disjunction operators. The sequence is used to define CBFs, ensuring STL satisfaction. We also show some theoretical results on the correctness of the proposed method. We illustrate the benefits of the proposed method and analyze its performance via simulations and experiments with aerial robots.

BUSTLE: a Versatile Tool for the Evolutionary Learning of STL Specifications from Data.

Describing the properties of complex systems that evolve over time is a crucial requirement for monitoring and understanding them. Signal Temporal Logic (STL) is a framework that proved to be effective for this aim because it is expressive and allows state properties as human-readable formulae. Crafting STL formulae that fit a particular system is, however, a difficult task. For this reason, a few approaches have been proposed recently for the automatic learning of STL formulae starting from observations of the system. In this paper, we propose BUSTLE (Bi-level Universal STL Evolver), an approach based on evolutionary computation for learning STL formulae from data. BUSTLE advances the state-of-the-art because it (i) applies to a broader class of problems, in terms of what is known about the state of the system during its observation, and (ii) generates both the structure and the values of the parameters of the formulae employing a bi-level search mechanism (global for the structure, local for the parameters). We consider two cases where (a) observations of the system in both anomalous and regular state are available, or (b) only observations of regular state are available. We experimentally evaluate BUSTLE on problem instances corresponding to the two cases and compare it against previous approaches. We show that the evolved STL formulae are effective and human-readable: the versatility of BUSTLE does not come at the cost of lower effectiveness.

Distributed Model Predictive Control for Probabilistic Signal Temporal Logic Specifications

Distributed Model Predictive Control for Probabilistic Signal Temporal Logic Specifications

Continuous-Time Control Synthesis Under Nested Signal Temporal Logic Specifications

Continuous-Time Control Synthesis Under Nested Signal Temporal Logic Specifications

Hybrid Knowledge and Data Driven Synthesis of Runtime Monitors for Cyber-Physical Systems

Recent advances in sensing and computing technology have led to the proliferation of Cyber-Physical Systems (CPS) in safety-critical domains. However, the increasing device complexity, shrinking technology sizes, and shorter time to market have resulted in significant challenges in ensuring the reliability, safety, and security of CPS. This paper presents a hybrid knowledge and data-driven approach for designing run-time context-aware safety monitors that can detect early signs of hazards and mitigate them in CPS. We propose a framework for formal specification of unsafe system context using Signal Temporal Logic (STL) combined with two optimization approaches for scenario-specific refinement and integration of STL specifications using data collected from closed-loop CPS simulations. We demonstrate the effectiveness of our approach in simulation using an autonomous driving system (ADS) and two closed-loop artificial pancreas systems (APS) as well as a publicly-available clinical trial dataset. The results show that a safety monitor developed with the proposed approaches demonstrates up to 4.7 times increase in average prediction accuracy (F1 score) over several well-designed baseline monitors while reducing both false-positive and false-negative rates in most scenarios.

Online control synthesis for uncertain systems under signal temporal logic specifications

Signal temporal logic (STL) formulas have been widely used as a formal language to express complex robotic specifications, thanks to their rich expressiveness and explicit time semantics. Existing approaches for STL control synthesis suffer from limited scalability with respect to the task complexity and lack of robustness against the uncertainty, for example, external disturbances. In this paper, we study the online control synthesis problem for uncertain discrete-time systems subject to STL specifications. Different from existing techniques, we propose an approach based on STL, reachability analysis, and temporal logic trees. First, based on a real-time version of STL semantics, we develop the notion of tube-based temporal logic tree (tTLT) and its recursive (offline) construction algorithm. We show that the tTLT is an under-approximation of the STL formula, in the sense that a trajectory satisfying a tTLT also satisfies the corresponding STL formula. Then, an online control synthesis algorithm is designed using the constructed tTLT. It is shown that when the STL formula is robustly satisfiable and the initial state of the system belongs to the initial root node of the tTLT, it is guaranteed that the trajectory generated by the control synthesis algorithm satisfies the STL formula. We validate the effectiveness of the proposed approach by several simulation examples and further demonstrate its practical usability on a hardware experiment. These results show that our approach is able to handle complex STL formulas with long horizons and ensure the robustness against the disturbances, which is beyond the scope of the state-of-the-art STL control synthesis approaches.

Model predictive monitoring of dynamical systems for signal temporal logic specifications

Online monitoring aims to evaluate or to predict, at runtime, whether or not the behaviors of a system satisfy some desired specification. It plays a key role in safety-critical cyber–physical systems. In this work, we propose a new monitoring approach, called model predictive monitoring, for specifications described by Signal Temporal Logic (STL) formulae. Specifically, we assume that the observed state traces are generated by an underlying dynamical system whose model is known but the control law is unknown. The main idea is to use the dynamic of the system to predict future states when evaluating the satisfaction of the STL formulae. To this end, effective approaches for the computation of feasible sets of STL formulae are provided. We show that, by explicitly utilizing the model information of the dynamical system, the proposed online monitoring algorithm can falsify or certify of the specification in advance compared with existing algorithms, where no model information is used. We also demonstrate the proposed monitoring algorithm by several real world case studies.

Multitask Synthesis of Hybrid Systems via Temporal Logic

In this note, we propose a unified framework for the study of hybrid systems, where the tasks of the systems are encoded as signal temporal logic (STL) specifications. First, we establish the mathematical expression of a class of hybrid systems consisting of continuous and logical parts. Then, we introduce the concept of locally finite time interval dwell (LFTID), which matches the conditions to satisfy such the STL specifications. After that, combining the semi-tensor product (STP) and Lyapunov-like methods, we obtain the sufficient conditions to satisfy the given STL specifications. This approach can be used to study temporal tasks and properties of hybrid systems, such as practical stability, finite-time stability, etc. Furthermore, we consider a special class of hybrid systems with control. Based on the theoretical analysis, a controller design algorithm that enables the system to fulfill the most tasks is provided. Finally, the effectiveness of the method is illustrated by an example.

Mining Hyperproperties using Temporal Logics

Formal specifications are essential to express precisely systems, but they are often difficult to define or unavailable. Specification mining aims to automatically infer specifications from system executions. The existing literature mainly focuses on learning properties defined on single system executions. However, many system characteristics, such as security policies and robustness, require relating two or more executions, and hence cannot be captured by properties. Hyperproperties address this limitation by allowing simultaneous reasoning about multiple executions with quantification over system traces. In this paper, we propose an effective approach for mining Hyper Signal Temporal Logic (HyperSTL) specifications. Our approach is based on the syntax-guided synthesis framework and allows users to control the amount of prior knowledge embedded in the mining procedure. To the best of our knowledge, this is the first mining method for hyperproperties that does not require a pre-defined template as input and allows for quantifier alternation. We implemented our approach and demonstrated its applicability and versatility in several case studies where we showed that we can use the same method to mine specifications both with and without templates, but also to infer subsets of HyperSTL, including STL, HyperLTL, LTL and non-temporal specifications.

Two-Phase Motion Planning Under Signal Temporal Logic Specifications in Partially Unknown Environments

This paper studies the planning problem for robot residing in partially unknown environments under signal temporal logic (STL) specifications, where most existing planning methods using STL rely on a fully known environment. In many practical scenarios, however, robots do not have prior information of all obstacles. In this paper, a novel two-phase planning method, i.e., offline exploration followed by online planning, is proposed to efficiently synthesize paths that satisfy STL tasks. In the offline exploration phase, a Rapidly Exploring Random Tree* (RRT*) is grown from task regions under the guidance of timed transducers, which guarantees that the resultant paths satisfy the task specifications. In the online phase, the path with minimum cost in RRT* is determined when an initial configuration is assigned. This path is then set as the reference of the time elastic band algorithm, which modifies the path until it has no collisions with obstacles. It is shown that the online computational burden is reduced and collisions with unknown obstacles are avoided by using the proposed planning framework. The effectiveness and superiority of the proposed method are demonstrated in simulations and real-world experiments.

Receding Horizon Control With Online Barrier Function Design Under Signal Temporal Logic Specifications

Receding Horizon Control With Online Barrier Function Design Under Signal Temporal Logic Specifications

Distributed Control of Coupled Leader-follower Multi-agent Systems under Spatiotemporal Logic Tasks

This paper addresses the problem of cooperative control of leader-follower multi-agent systems under local signal temporal logic (STL) tasks in a distributed fashion, where the overall system is composed of several leader-follower subsystems with coupled dynamics. In this work, only the leaders know the related STL specifications and are designed to drive the followers in a way such that the STL specifications are globally satisfied. Under the local feasibility assumption, we propose a funnel-based control approach for each leader-follower subsystem such that the local STL specifications are achieved, which further implies the global satisfaction of all STL specifications. In order to enforce the satisfaction of the STL formulas, the funnel parameters are appropriately designed to prescribe certain transient behavior that constrains the closed-loop trajectories. The proposed approach is illustrated by a simulation example.

Dynamic Quantization based Control Synthesis for Signal Temporal Logics Specifications

For dynamical systems under temporal logic tasks, the control objective is mainly to propose control methods for temporal logic tasks. Existing methods are based on the assumption where temporal logic tasks are realizable, which is not always valid and results in the separation between the realizability verification and the controller design. In this paper, we apply dynamic quantization techniques to propose a framework to combine the verification of signal temporal logic (STL) specifications and the controller design. In particular, a sequence of quantization regions is generated to show the realizability of the STL formula, and results in the decomposition of the global STL formula into finite local ones. All local STL formulas are formulated into optimization problems, which are solved iteratively and result in local controllers, whose combination gives the global controller for the satisfaction of the STL formula. Finally, a numerical example is presented to illustrate the proposed approach.

Combined Left and Right Temporal Robustness for Control Under STL Specifications

Many modern autonomous systems, particularly multi-agent systems, are time-critical and need to be robust against timing uncertainties. Previous works have studied left and right time robustness of signal temporal logic specifications by considering time shifts in the predicates that are either only to the left or only to the right. We propose a combined notion of temporal robustness which simultaneously considers left and right time shifts. For instance, in a scenario where a robot plans a trajectory around a pedestrian, this combined notion can now capture uncertainty of the pedestrian arriving earlier or later than anticipated. We first derive desirable properties of this new notion with respect to left and right time shifts and then design control laws for linear systems that maximize temporal robustness using mixed-integer linear programming. Finally, we present two case studies to illustrate how the proposed temporal robustness accounts for timing uncertainties.

Survey on mining signal temporal logic specifications

Formal specifications play an essential role in the life-cycle of modern systems, both at the time of their design and during their operation. Despite their importance, formal specifications are only partially (if at all) available. Specification mining is the process of learning likely system properties from the observation of its behavior and its interaction with the environment. Signal temporal logic (STL) is a popular formalism for expressing properties of cyber-physical systems (CPS). In the last decade, the introduction of first methods for mining STL specifications from time series generated by CPS led to a new vivid area of research.This survey paper overviews methods for mining STL specifications from CPS behaviors, sketches different approaches found in the literature and presents them in an intuitive and didactic manner. It aims at presenting the most influential techniques and covers most important aspects of specification mining: template-based vs. template-free, model-based vs. model-free, passive vs. active, and supervised vs. unsupervised learning.

Backpropagation through signal temporal logic specifications: Infusing logical structure into gradient-based methods

This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into robotics problems that benefit from gradient-based solutions. Specifically, STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems. The quantitative semantics of STL provide a robustness metric, that is, how much a signal satisfies or violates an STL specification. In this work, we devise a systematic methodology for translating STL robustness formulas into computation graphs. With this representation, and by leveraging off-the-shelf automatic differentiation tools, we are able to efficiently backpropagate through STL robustness formulas and hence enable a natural and easy-to-use integration of STL specifications with many gradient-based approaches used in robotics. Through a number of examples stemming from various robotics applications, we demonstrate that STLCG is versatile, computationally efficient, and capable of incorporating human-domain knowledge into the problem formulation.

STL2vec: Signal Temporal Logic Embeddings for Control Synthesis With Recurrent Neural Networks

In this letter, a method for learning a recurrent neural network (RNN) controller that maximizes the robustness of signal temporal logic (STL) specifications is presented. In contrast to previous methods, we consider synthesizing the RNN controller for which the user is able to select an STL specification arbitrarily from multiple STL specifications. To obtain such a controller, we propose a novel notion called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">STL2vec</i> , which represents a vector representation of the STL specifications and exhibits their similarities. The construction of the STL2vec is useful since it allows us to enhance the efficiency and performance of the controller. We validate our proposed method through the examples of the path planning problem.

Multi-Agent Motion Planning From Signal Temporal Logic Specifications

We tackle the challenging problem of multi-agent cooperative motion planning for complex tasks described using signal temporal logic (STL), where robots can have nonlinear and nonholonomic dynamics. Existing methods in multi-agent motion planning, especially those based on discrete abstractions and model predictive control (MPC), suffer from limited scalability with respect to the complexity of the task, the size of the workspace, and the planning horizon. We present a method based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">timed waypoints</i> to address this issue. We show that timed waypoints can help abstract nonlinear behaviors of the system as safety envelopes around the reference path defined by those waypoints. Then the search for waypoints satisfying the STL specifications can be inductively encoded as a mixed-integer linear program. The agents following the synthesized timed waypoints have their tasks automatically allocated, and are guaranteed to satisfy the STL specifications while avoiding collisions. We evaluate the algorithm on a wide variety of benchmarks. Results show that it supports multi-agent planning from complex specification over long planning horizons, and significantly outperforms state-of-the-art abstraction-based and MPC-based motion planning methods. The implementation is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/sundw2014/STLPlanning</uri> .

Recurrent Neural Network Controllers for Signal Temporal Logic Specifications Subject to Safety Constraints

We propose a framework based on Recurrent Neural Networks (RNNs) to determine an optimal control strategy for a discrete-time system that is required to satisfy specifications given as Signal Temporal Logic (STL) formulae. RNNs can store information of a system over time, thus, enable us to determine satisfaction of the dynamic temporal requirements specified in STL formulae. Given a STL formula, a dataset of satisfying system executions and corresponding control policies, we can use RNNs to predict a control policy at each time based on the current and previous states of system. We use Control Barrier Functions (CBFs) to guarantee the safety of the predicted control policy. We validate our theoretical formulation and demonstrate its performance in an optimal control problem subject to partially unknown safety constraints through simulations.