Temporal Logic Specifications Research Articles

Mining of extended signal temporal logic specifications with ParetoLib 2.0

Mining of extended signal temporal logic specifications with ParetoLib 2.0

Adaptive Reactive Synthesis for LTL and LTLf Modulo Theories

Reactive synthesis is the process of generate correct con- trollers from temporal logic specifications. Typically, synthesis is restricted to Boolean specifications in LTL. Recently, a Boolean abstraction technique allows to translate LTLT specifications that contain literals in theories into equi-realizable LTL specifications, but no full synthesis procedure exists yet. In synthesis modulo theories, the system receives valuations of environment variables (from a first-order theory T ) and outputs valuations of system variables from T . In this paper, we address how to syntheize a full controller using a combination of the static Boolean controller obtained from the Booleanized LTL specification together with on-the-fly queries to a solver that produces models of satisfiable existential T formulae. This is the first synthesis method for LTL modulo theories. Additionally, our method can produce adaptive responses which increases explainability and can improve runtime properties like performance. Our approach is applicable to both LTL modulo theories and LTLf modulo theories.

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.

On reward distribution in reinforcement learning of multi-agent surveillance systems with temporal logic specifications

In multi-agent systems, it is important to design a reward based on the contribution of each agent for efficient learning. In this paper, we propose a reward distribution method for a surveillance system based on our previously proposed multi-agent reinforcement learning method with an aggregator, in which a control specification is described by a linear temporal logic formula. In this method, the aggregator computes and distributes rewards according to the actions that agents take on the surveillance system. Finally, the effectiveness of the proposed method is presented through a numerical simulation of a surveillance problem addressing a specific type of linear temporal logic specification.

A leader‐follower communication protocol for motion planning in partially known environments under temporal logic specifications

AbstractThis paper considers the problem of communication protocols between leaders and its followers for motion planning in an initially partially known environment. In this setting, the leader observes the environment information to satisfy its own local objective and and the follower completes its own local objective by estimating the states of the leader and communicating with the leader to update its knowledge about the environment when it is necessary, where the local objectives can be expressed in temporal logic. A verifier construction is built first to contain all possible communication protocols between the leaders and the followers. Then, a two‐step synthesis procedure is proposed to capture all feasible communication protocol that satisfy the local objectives for the leader and follower, respectively. In the first step, a sub‐verifier is synthesized to satisfy the objective of the follower. In the second step, based on the obtained sub‐verifier, an iterative algorithm is proposed to extract communication protocols such that the objectives of the leader and follower are satisfied, respectively. A running example is provided to illustrate the proposed procedures.

Dynamic event‐triggered prescribed performance control for nonlinear systems with signal temporal logic

AbstractThis article is concerned with the problem of dynamic event‐triggered prescribed performance control for nonlinear systems under signal temporal logic tasks. By utilizing the method of prescribed performance control, the constrained plant can be transformed into an unconstrained one, and a dynamic event‐triggered feedback control law is generated for the transformed system to ensure that the signal temporal logic specification is satisfied. A dynamic event‐triggered mechanism is designed to guarantee the event‐triggered stability, safety and complex specification. Besides, Zeno phenomenon is definitely avoided. Compared with the continuous‐time feedback controller, the event‐triggered controller has proven to be effective in reducing sensing, communication and computation costs. Finally, two simulations are given to illustrate the effectiveness of theoretical results.

Control/physical systems co-design with spectral temporal logic specifications and its applications to MEMS

‘Co-design’ problems try to simultaneously design the physical and control components to improve the overall system performance. However, existing co-design paradigms cannot deal with complex frequency temporal domain specifications. In this paper, we investigate the co-design problem for a class of linear parameter-varying (LPV) systems with frequency temporal domain specifications. Firstly, the frequency temporal domain specifications are written in a formal language called spectral temporal logic (STL). Secondly, the satisfaction conditions of the spectral temporal logic specifications have been transformed into non-linear matrices inequality forms with necessary and sufficient conditions. Thirdly, the co-design problem is transformed into a non-convex optimisation problem with mixed-integer linear matrix inequalities (MILMIs) constraints, and then an iterative algorithm is proposed to solve the co-design problem with semidefinite programming (SDP). Finally, the performance of the algorithm and the expressiveness of spectral temporal logic are illustrated with the applications to micro-electromechanical systems (MEMS).

Reinforcement Learning for Multi-Agent Systems with Temporal Logic Specifications

Reinforcement Learning for Multi-Agent Systems with Temporal Logic Specifications

Reactive Planner Synthesis Under Temporal Logic Specifications

Reactive Planner Synthesis Under Temporal Logic Specifications

Distributed Model Predictive Control for Probabilistic Signal Temporal Logic Specifications

Distributed Model Predictive Control for Probabilistic Signal Temporal Logic Specifications

Zonotope-based Symbolic Controller Synthesis for Linear Temporal Logic Specifications

Zonotope-based Symbolic Controller Synthesis for Linear Temporal Logic Specifications

Deep Learning-Based Path Planning Under Co-Safe Temporal Logic Specifications

Deep Learning-Based Path Planning Under Co-Safe Temporal Logic Specifications

Continuous-Time Control Synthesis Under Nested Signal Temporal Logic Specifications

Continuous-Time Control Synthesis Under Nested Signal Temporal Logic Specifications

End-to-End Path Planning Under Linear Temporal Logic Specifications

End-to-End Path Planning Under Linear Temporal Logic Specifications

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.

Statistical Verification using Surrogate Models and Conformal Inference and a Comparison with Risk-aware Verification

Uncertainty in safety-critical cyber-physical systems can be modeled using a finite number of parameters or parameterized input signals. Given a system specification in Signal Temporal Logic (STL), we would like to verify that for all (infinite) values of the model parameters/input signals, the system satisfies its specification. Unfortunately, this problem is undecidable in general. Statistical model checking (SMC) offers a solution by providing guarantees on the correctness of CPS models by statistically reasoning on model simulations. We propose a new approach for statistical verification of CPS models for user-provided distribution on the model parameters. Our technique uses model simulations to learn surrogate models , and uses conformal inference to provide probabilistic guarantees on the satisfaction of a given STL property. Additionally, we can provide prediction intervals containing the quantitative satisfaction values of the given STL property for any user-specified confidence level. We compare this prediction interval with the interval we get using risk estimation procedures. We also propose a refinement procedure based on Gaussian Process (GP)-based surrogate models for obtaining fine-grained probabilistic guarantees over sub-regions in the parameter space. This in turn enables the CPS designer to choose assured validity domains in the parameter space for safety-critical applications. Finally, we demonstrate the efficacy of our technique on several CPS models.

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.

A skin microbiome model with AMP interactions and analysis of quasi-stability vs stability in population dynamics

The skin microbiome plays an important role in the maintenance of a healthy skin. It is an ecosystem, composed of several species, competing for resources and interacting with the skin cells. Imbalance in the cutaneous microbiome, also called dysbiosis, has been correlated with several skin conditions, including acne and atopic dermatitis. Generally, dysbiosis is linked to colonization of the skin by a population of opportunistic pathogenic bacteria. Treatments consisting in non-specific elimination of cutaneous microflora have shown conflicting results. In this article, we introduce a mathematical model based on ordinary differential equations, with 2 types of bacteria populations (skin commensals and opportunistic pathogens) and including the production of antimicrobial peptides to study the mechanisms driving the dominance of one population over the other. By using published experimental data, assumed to correspond to the observation of stable states in our model, we reduce the number of parameters of the model from 13 to 5. We then use a formal specification in quantitative temporal logic to calibrate our model by global parameter optimization and perform sensitivity analyses. On the time scale of 2 days of the experiments, the model predicts that certain changes of the environment, like the elevation of skin surface pH, create favorable conditions for the emergence and colonization of the skin by the opportunistic pathogen population, while the production of human AMPs has non-linear effect on the balance between pathogens and commensals. Surprisingly, simulations on longer time scales reveal that the equilibrium reached around 2 days can in fact be a quasi-stable state followed by the reaching of a reversed stable state after 12 days or more. We analyze the conditions of quasi-stability observed in this model using tropical algebraic methods, and show their non-generic character in contrast to slow-fast systems. These conditions are then generalized to a large class of population dynamics models over any number of species.

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.