Showing papers presented at "International Conference on Hybrid Systems: computation and control in 2023"

SySCoRe: Synthesis via Stochastic Coupling Relations

Abstract: We present SySCoRe, a MATLAB toolbox that synthesizes controllers for stochastic continuous-state systems to satisfy temporal logic specifications. Starting from a system description and a co-safe temporal logic specification, SySCoRe provides all necessary functions for synthesizing a robust controller and quantifying the associated formal robustness guarantees. It distinguishes itself from other available tools by supporting nonlinear dynamics, complex co-safe temporal logic specifications over infinite horizons and model-order reduction. To achieve this, SySCoRe generates a finite-state abstraction of the provided model and performs probabilistic model checking. Then, it establishes a probabilistic coupling to the original stochastic system encoded in an approximate simulation relation, based on which a lower bound on the satisfaction probability is computed. SySCoRe provides non-trivial lower bounds for infinite-horizon properties and unbounded disturbances since its computed error does not grow linearly in the horizon of the specification. It exploits a tensor representation to facilitate the efficient computation of transition probabilities. We showcase these features on several benchmarks and compare the performance of the tool with existing tools.

Reachability Analysis for Linear Systems with Uncertain Parameters using Polynomial Zonotopes

Abstract: In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast to previous methods, our approach is able to tightly capture the non-convexity of the reachable set. Building up on our main result, we show how our reachability algorithm can be extended to handle linear time-varying systems as well as linear systems with time-varying parameters. Moreover, our approach opens up new possibilities for reachability analysis of linear time-invariant systems, nonlinear systems, and hybrid systems. We compare our approach to other state of the art methods, with superior tightness on two benchmarks including a 9-dimensional vehicle platooning system.

Stealthy attacks formalized as STL formulas for Falsification of CPS Security

Abstract: We propose a framework for security vulnerability analysis for Cyber-Physical Systems (CPS). Our framework imposes only minimal assumptions on the structure of the CPS. Namely, we consider CPS with feedback control loops, state observers, and anomaly detection algorithms. Moreover, our framework does not require any knowledge about the dynamics or the algorithms used in the CPS. Under this common CPS architecture, we develop tools that can identify vulnerabilities in the system and their impact on the functionality of the CPS. We pose the CPS security problem as a falsification (or Search Based Test Generation (SBTG)) problem guided by security requirements expressed in Signal Temporal Logic (STL). We propose two different categories of security requirements encoded in STL: (1) detectability (stealthiness) and (2) effectiveness (impact on the CPS function). Finally, we demonstrate in simulation on an inverted pendulum and on an Unmanned Aerial Vehicle (UAV) that both specifications are falsifiable using our SBTG techniques.

Quantitative Robustness Analysis of Sensor Attacks on Cyber-Physical Systems

Abstract: This paper contributes a formal framework for quantitative analysis of bounded sensor attacks on cyber-physical systems, using the formalism of differential dynamic logic. Given a precondition and postcondition of a system, we formalize two quantitative safety notions, quantitative forward and backward safety, which respectively express (1) how strong the strongest postcondition of the system is with respect to the specified postcondition, and (2) how strong the specified precondition is with respect to the weakest precondition of the system needed to ensure the specified postcondition holds. We introduce two notions, forward and backward robustness, to characterize the robustness of a system against sensor attacks as the loss of safety. Two simulation distances, which respectively characterize upper bounds of the degree of forward and backward safety loss caused by the sensor attacks, are developed to reason with robustness. We verify the two simulation distances by expressing them as formulas of differential dynamic logic. We showcase an example of an autonomous vehicle that needs to avoid a collision.

Quantitative Verification for Neural Networks using ProbStars

Abstract: Most deep neural network (DNN) verification research focuses on qualitative verification, which answers whether or not a DNN violates a safety/robustness property. This paper proposes an approach to convert qualitative verification into quantitative verification for neural networks. The resulting quantitative verification method not only can answer YES or NO questions but also can compute the probability of a property being violated. To do that, we introduce the concept of a probabilistic star (or shortly ProbStar), a new variant of the well-known star set, in which the predicate variables belong to a Gaussian distribution and propose an approach to compute the probability of a probabilistic star in high-dimensional space. Unlike existing works dealing with constrained input sets, our work considers the input set as a truncated multivariate normal (Gaussian) distribution, i.e., besides the constraints on the input variables, the input set has a probability of the constraints being satisfied. The input distribution is represented as a probabilistic star set and is propagated through a network to construct the output reachable set containing multiple ProbStars, which are used to verify the safety or robustness properties of the network. In case of a property is violated, the violation probability can be computed precisely by an exact verification algorithm or approximately by an overapproximate verification algorithm. The proposed approach is implemented in a tool named StarV and is evaluated using the well-known ACASXu networks and a rocket landing benchmark.

Continuity of Thresholded Mode-Switched ODEs and Digital Circuit Delay Models

Abstract: Thresholded mode-switched ODEs are restricted dynamical systems that switch ODEs depending on digital input signals only, and produce a digital output signal by thresholding some internal signal. Such systems arise in recent digital circuit delay models, where the analog signals within a gate are governed by ODEs that change depending on the digital inputs. We prove the continuity of the mapping from digital input signals to digital output signals for a large class of thresholded mode-switched ODEs. This continuity property is known to be instrumental for ensuring the faithfulness of the model w.r.t. propagating short pulses. We apply our result to several instances of such digital delay models, thereby proving them to be faithful.

Poster Abstract: Safety Guaranteed Preference Learning Approach for Autonomous Vehicles

Abstract: In this work, we propose a safety-guaranteed personalization for autonomous vehicles by incorporating Signal Temporal Logic (STL) into preference learning problem. We propose a new variant of STL called Parametric Weighted Signal Temporal Logic with a new quantitative semantics, namely weighted robustness. Given a set of pairwise preferences, and by using gradient-based optimization methods, we learn a set of valuations for weights that reflect preferences such that preferred ones have greater weighted robustness value than their non-preferred matches. Traditional STL formulas fail to incorporate preferences due its complex nature. Our initial results with data from a human-subject on an intersection with stop sign driving scenario, in which the participant is asked their preferred driving behavior from pairs of vehicle trajectories, indicate that we can learn a new weighted STL formula that captures preferences while also encoding correctness.

Fully-Automated Verification of Linear Systems Using Reachability Analysis with Support Functions

Abstract: While reachability analysis is one of the major techniques for formal verification of dynamical systems, the requirement to adequately tune algorithm parameters often prevents its widespread use in practical applications. In this work, we fully automate the verification process for linear time-invariant systems: Based on the computation of tight upper and lower bounds for the support function of the reachable set along a given direction, we present a fully-automated verification algorithm, which is based on iterative refinement of the upper and lower bounds and thus always returns the correct result in decidable cases. While this verification algorithm is particularly well suited for cases where the specifications are represented by halfspace constraints, we extend it to arbitrary convex unsafe sets using the Gilbert-Johnson-Keerthi algorithm. In summary, our automated verifier is applicable to arbitrary convex initial sets, input sets, as well as unsafe sets, can handle time-varying inputs, automatically returns a counterexample in case of a safety violation, and scales to previously unanalyzable high-dimensional state spaces. Our evaluation on several challenging benchmarks shows significant improvements in computational efficiency compared to verification using other state-of-the-art reachability tools.

Poster Abstract: Sampling-based Approach to Robust STL Synthesis for Complex Systems under Uncertainty

Abstract: ACM Reference Format: Qi Heng Ho, Roland B. Ilyes, Zachary Sunberg, and Morteza Lahijanian. 2023. Poster Abstract: Sampling-based Approach to Robust STL Synthesis for Complex Systems under Uncertainty. In Proceedings of the 26th ACM International Conference on Hybrid Systems: Computation and Control (HSCC ’23), May 9–12, 2023, San Antonio, TX, USA. ACM, New York, NY, USA, 2 pages. https://doi.org/10.1145/3575870.3589551

Poster Abstract: Towards Seamless Reactivity of Hybrid Control

Abstract: This poster presents a new technique to synthesize a reactive hybrid controller which actuates a non-linear control system in response to external logical inputs to fulfill an omega-regular specification over a finite set of logical input and observation predicates.

Poster Abstract: Permissiveness for Strategy Adaptation

Abstract: This paper presents a new method to automatically compute permissive strategies and permissive assumptions in ω -regular two-player games on graphs to enable strategy adaptation both during synthesis and execution of distributed symbolic controllers.

Lazy Synthesis of Symbolic Output-Feedback Controllers for State-Based Safety Specifications

Abstract: This short paper presents a lazy symbolic output-feedback controller synthesis algorithm for state-based safety specifications over large transition systems. The novel idea of our approach is to integrate an iterative algorithm for observer design with an online adaptable safety controller synthesis algorithm. This allows us to iteratively update the safety controller to observer refinements and to guide these refinements by the existing controller. This results in efficient lazy synthesis of a safety controller whose domain increases with the time spent in synthesis. We present simulation results for a synthetic robot motion planning example showing the benefits of our algorithm compared to the standard approach.

Mixed Integer Linear Programming Approach for Control Synthesis with Weighted Signal Temporal Logic

Abstract: This work presents an optimization-based control synthesis approach for an extension of Signal Temporal Logic (STL) called weighted Signal Temporal Logic (wSTL). wSTL was proposed to accommodate user preferences for importance and priorities over concurrent and sequential tasks as well as satisfaction times denoted by weights over the logical and temporal operators, respectively. We propose a Mixed Integer Linear Programming (MILP) based approach for synthesis with wSTL specifications. These specifications have the same qualitative semantics as STL but differ in their quantitative semantics, which is recursively modulated with weights. Additionally, we extend the formal definition of wSTL to include the semantics for until and release temporal operators and present an efficient encoding for these operators in the MILP formulation. As opposed to the original implementation of wSTL, where the arithmetic-geometric mean robustness was used with gradient-based methods prone to local optima, our encoding allows the use of a weighted version of traditional robustness and efficient global MILP solvers. We demonstrate the operational performance of the proposed formulation using multiple case studies, showcasing the distinct functionalities over Boolean and temporal operators. Moreover, we elaborate on multiple case studies for synthesizing controllers for an agent navigating a non-convex environment under different constraints highlighting the difference in synthesized control plans for STL and wSTL. Finally, we compare the time and complexity performance of encodings for STL and wSTL.

Poster Abstract: A Toolchain for Accelerated Symbolic Control

Abstract: We present a flexible and efficient toolchain to symbolically solve (standard) Rabin games, fair-adversarial Rabin games, and 21/2-player Rabin games. To our best knowledge, our tools are the first ones to be able to solve these problems. Furthermore, using the optimized game solvers as back-end, we implement a tool for computing correct-by-construction controllers for stochastic dynamical systems with LTL specifications. An important feature of our toolchain is the flexibility created through two programming abstractions: one separates the symbolic fixpoint computations from the predecessor calculations, and the other one allows effortless switching between different BDD libraries. We empirically compare the benefits of using the CUDD and Sylvan BDD libraries, and report substantial computational savings of our tool compared to the state-of-the-art.

Poster: Convex Scenario Optimisation for ReLU Networks

Abstract: No abstract available.

Characterization of the ordering of path-complete stability certificates with addition-closed templates

Abstract: As part of the development of Lyapunov techniques for cyber-physical systems, we study and compare graph-based stability certificates with respect to their conservatism. Previous work have highlighted the dependence of this ordering with respect to the properties of the chosen template of candidate Lyapunov functions. We extend here previous results from the literature to the case of templates closed under addition, as for instance the set of quadratic functions. In this context, we provide a characterization of the ordering, using an approach based on abstract operations on graphs, called lifts, which encode in a combinatorial way the algebraic properties of the chosen template. We finally provide a numerical method to algorithmically check the ordering relation.

Demo Abstract: Analysing CPS Security with Falsification on the Microsoft Flight Simulator

Abstract: In the paper titled " Stealthy attacks formalized as STL formulas for Falsification of CPS Security", we investigate a broad class of attacks on the sensor and actuation blocks in the form of additive perturbation that impacts the measurement and control, respectively. In this demo, we demonstrate the usage of our framework and the underlying technologies along with a case study on aviation systems using Microsoft Flight Simulator (MSFS).

Verification of Recurrent Neural Networks with Star Reachability

Abstract: The paper extends the recent star reachability method to verify the robustness of recurrent neural networks (RNNs) for use in safety-critical applications. RNNs are a popular machine learning method for various applications, but they are vulnerable to adversarial attacks, where slightly perturbing the input sequence can lead to an unexpected result. Recent notable techniques for verifying RNNs include unrolling, and invariant inference approaches. The first method has scaling issues since unrolling an RNN creates a large feedforward neural network. The second method, using invariant sets, has better scalability but can produce unknown results due to the accumulation of overapproximation errors over time. This paper introduces a complementary verification method for RNNs that is both sound and complete. A relaxation parameter can be used to convert the method into a fast overapproximation method that still provides soundness guarantees. The method is designed to be used with NNV, a tool for verifying deep neural networks and learning-enabled cyber-physical systems. Compared to state-of-the-art methods, the extended exact reachability method is 10 × faster, and the overapproximation method is 100 × to 5000 × faster.

Pattern Matching and Parameter Identification for Parametric Timed Regular Expressions

Abstract: Timed formalisms such as Timed Automata (TA), Signal Temporal Logic (STL) and Timed Regular expressions (TRE) have been previously applied as behaviour specifications for monitoring or runtime verification, in particular, under the form of pattern-matching, i.e. computing the set of all the segments of a given system run that satisfy the specification. In this work, timed regular expressions with parameters (for timing delays and for signal values) are considered. We define several classes of parametric expressions (based on Boolean or real-valued signals and discrete events), and tackle the problem of computing a parametric match-set, i.e. the parameter values and time segments of data that give a match for a given expression. We propose efficient data structures for representing match-sets (combining zones and polytopes), and devise pattern-matching algorithms. All these different types and algorithms are combined into a single implementation under a tool named parameTRE. We illustrate the approach on several examples, from electrocardiograms to driving patterns.

Safe Self-Triggered Control Based on Precomputed Reachability Sequences

Abstract: Self-triggered controllers have the potential to improve the state-of-the-art of Cyber-Physical Systems (CPSs) by enhancing the performance of the underlying closed-loop control systems. However, a major concern in deploying a self-triggered controller in a safety-critical CPS is that the stabilizing self-triggered controller may not always guarantee the satisfaction of the safety constraints. We propose a self-triggered control scheme that deals with the safe scheduling of control tasks for uncertain continuous-time linear systems. We derive a computationally efficient scheduling function that computes an upper bound on the next sampling period as a function of the current state in the presence of additive disturbance. To reduce the computational complexity of online reachability analysis and increase accuracy, we compute a large sequence of reachable sets offline and use these precomputed sets to derive a low-complexity online scheduling function that computes sufficiently large bounds in real time. We evaluate our algorithm on three high-dimensional benchmark control systems, where two of the examples have a twelve-dimensional joint state plus feedback input. Experimental results demonstrate that our self-triggered control algorithm guarantees the safety of the closed-loop control system through negligible online computation, establishing the feasibility of its practical implementation.

Automatic Abstraction Refinement in Neural Network Verification using Sensitivity Analysis

Abstract: The formal verification of neural networks is essential for their application in safety-critical environments. However, the set-based verification of neural networks using linear approximations often obtains overly conservative results, while nonlinear approximations quickly become computationally infeasible in deep neural networks. We address this issue for the first time by automatically balancing between precision and computation time without splitting the propagated set. Our work introduces a novel automatic abstraction refinement approach using sensitivity analysis to iteratively reduce the abstraction error at the neuron level until either the specifications are met or a maximum number of iterations is reached. Our evaluation shows that we can tightly over-approximate the output sets of deep neural networks and that our approach is up to a thousand times faster than a naive approach. We further demonstrate the applicability of our approach in closed-loop settings.

Wordgen : a Timed word Generation Tool

Abstract: Sampling timed words out of a timed language described as a timed automaton may seem a simple task: start from the initial state, choose a transition and a delay and repeat until an accepting state is reached. Unfortunately, simple approach based on local, on-the-fly rules produces timed words from distributions that are biased in some unpredictable ways. For this reason, approaches have been developed to guarantee that the sampling follows a more desirable distribution defined over the timed language and not over the automaton. One such distribution is the maximal entropy distribution, whose implementation requires several non-trivial computational steps. In this paper, we present Wordgen which combines those different necessary steps into a lightweight standalone tool. The resulting timed words can be mapped to signals used for model-based testing and falsification of cyber-physical systems thanks to a simple interface with the Breach tool.