arXiv subjects

Abolfazl Lavaei

Publications and source records attributed to Abolfazl Lavaei.

At least 55 records · Page 3Linked to original sources

arXiv2024

Rare Collision Risk Estimation of Autonomous Vehicles with Multi-Agent Situation Awareness

This paper offers a formal framework for the rare collision risk estimation of autonomous vehicles (AVs) with multi-agent situation awareness, affected by different sources of noise in a complex dynamic environment. In our proposed setting, the situation awareness is considered for one of the ego vehicles by aggregating a range of diverse information gathered from other vehicles into a vector. We model AVs equipped with the situation awareness as general stochastic hybrid systems (GSHS) and assess the probability of collision in a lane-change scenario where two self-driving vehicles simultaneously intend to switch lanes into a shared one, while utilizing the time-to-collision measure for decision-making as required. Due to the substantial data requirements of simulation-based methods for the rare collision risk estimation, we leverage a multi-level importance splitting technique, known as interacting particle system-based estimation with fixed assignment splitting (IPS-FAS). This approach allows us to estimate the probability of a rare event by employing a group of interacting particles. Specifically, each particle embodies a system trajectory and engages with others through resampling and branching, focusing computational resources on trajectories with the highest probability of encountering the rare event. The effectiveness of our proposed approach is demonstrated through an extensive simulation of a lane-change scenario.

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arXiv2024

IMPaCT: Interval MDP Parallel Construction for Controller Synthesis of Large-Scale Stochastic Systems

This paper is concerned with developing a software tool, called IMPaCT, for the parallelized verification and controller synthesis of large-scale stochastic systems using interval Markov chains (IMCs) and interval Markov decision processes (IMDPs), respectively. The tool serves to (i) construct IMCs/IMDPs as finite abstractions of underlying original systems, and (ii) leverage interval iteration algorithms for formal verification and controller synthesis over infinite-horizon properties, including safety, reachability, and reach-avoid, while offering convergence guarantees. IMPaCT is developed in C++ and designed using AdaptiveCpp, an independent open-source implementation of SYCL, for adaptive parallelism over CPUs and GPUs of all hardware vendors, including Intel and NVIDIA. IMPaCT stands as the first software tool for the parallel construction of IMCs/IMDPs, empowered with the capability to leverage high-performance computing platforms and cloud computing services. Specifically, parallelism offered by IMPaCT effectively addresses the challenges arising from the state-explosion problem inherent in discretization-based techniques applied to large-scale stochastic systems. We benchmark IMPaCT on several physical case studies, adopted from the ARCH tool competition for stochastic models, including a 2-dimensional robot, a 3-dimensional autonomous vehicle, a 5-dimensional room temperature system, and a 7-dimensional building automation system. To show the scalability of our tool, we also employ IMPaCT for the formal analysis of a 14-dimensional case study.

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arXiv2023

Symbolic Abstractions with Guarantees: A Data-Driven Divide-and-Conquer Strategy

This article is concerned with a data-driven divide-and-conquer strategy to construct symbolic abstractions for interconnected control networks with unknown mathematical models. We employ a notion of alternating bisimulation functions (ABF) to quantify the closeness between state trajectories of an interconnected network and its symbolic abstraction. Consequently, the constructed symbolic abstraction can be leveraged as a beneficial substitute for the formal verification and controller synthesis over the interconnected network. In our data-driven framework, we first establish a relation between each unknown subsystem and its data-driven symbolic abstraction, so-called alternating pseudo-bisimulation function (APBF), with a guaranteed probabilistic confidence. We then provide compositional conditions based on max-type small-gain techniques to construct an ABF for an unknown interconnected network using APBF of its individual subsystems, constructed from data. We demonstrate the efficacy of our data-driven approach over a room temperature network composing 100 rooms with unknown models. We construct a symbolic abstraction from data for each room as an appropriate substitute of original system and compositionally synthesize controllers regulating the temperature of each room within a safe zone with some guaranteed probabilistic confidence.

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arXiv2023

MDP Abstractions from Data: Large-Scale Stochastic Networks

This work proposes a compositional data-driven technique for the construction of finite Markov decision processes (MDPs) for large-scale stochastic networks with unknown mathematical models. Our proposed framework leverages dissipativity properties of subsystems and their finite MDPs using a notion of stochastic storage functions (SStF). In our data-driven scheme, we first build an SStF between each unknown subsystem and its data-driven finite MDP with a certified probabilistic confidence. We then derive dissipativity-type compositional conditions to construct a stochastic bisimulation function (SBF) between an interconnected network and its finite MDP using data-driven SStF of subsystems. Accordingly, we formally quantify the probabilistic distance between trajectories of an unknown large-scale stochastic network and those of its finite MDP with a guaranteed confidence. We illustrate the efficacy of our data-driven results over a room temperature network composing 100 rooms with unknown models.

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arXiv2023

Safety Barrier Certificates for Stochastic Control Systems with Wireless Communication Networks

This work is concerned with a formal approach for safety controller synthesis of stochastic control systems with both process and measurement noises while considering wireless communication networks between sensors, controllers, and actuators. The proposed scheme is based on control barrier certificates (CBC), which allows us to provide safety certifications for wirelessly-connected stochastic control systems. Despite the available literature on designing control barrier certificates, there has been unfortunately no consideration of wireless communication networks to capture potential packet losses and end-to-end delays, which is absolutely crucial in safety-critical real-world applications. In our proposed setting, the key objective is to construct a control barrier certificate together with a safety controller while providing a lower bound on the satisfaction probability of the safety property over a finite time horizon. We propose a systematic approach in the form of sum-of-squares optimization and matrix inequalities for the synthesis of CBC and its associated controller. We demonstrate the efficacy of our approach on a permanent magnet synchronous motor. For the application of automotive electric steering under a wireless communication network, we design a CBC together with a safety controller to maintain the electrical current of the motor in a safe set within a finite time horizon while providing a formal probabilistic guarantee.

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arXiv2023

Data-driven verification and synthesis of stochastic systems via barrier certificates

In this work, we study verification and synthesis problems for safety specifications over unknown discrete-time stochastic systems. When a model of the system is available, barrier certificates have been successfully applied for ensuring the satisfaction of safety specifications. In this work, we formulate the computation of barrier certificates as a robust convex program (RCP). Solving the acquired RCP is hard in general because the model of the system that appears in one of the constraints of the RCP is unknown. We propose a data-driven approach that replaces the uncountable number of constraints in the RCP with a finite number of constraints by taking finitely many random samples from the trajectories of the system. We thus replace the original RCP with a scenario convex program (SCP) and show how to relate their optimizers. We guarantee that the solution of the SCP is a solution of the RCP with a priori guaranteed confidence when the number of samples is larger than a pre-computed value. This provides a lower bound on the safety probability of the original unknown system together with a controller in the case of synthesis. We also discuss an extension of our verification approach to a case where the associated robust program is non-convex and show how a similar methodology can be applied. Finally, the applicability of our proposed approach is illustrated through three case studies.

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arXiv2023

Formal Control of New England 39-Bus Test System: An Assume-Guarantee Approach

This work is concerned with an assume-guarantee approach to compositionally control a New England 39-bus Test System (NETS). The proposed scheme is based on the new notion of robust simulation functions with disturbance refinement alongside the composition of multiple subsystems to tackle the difficulties associated with scalability, also known as the curse of dimensionality. In our proposed setting, we approximate concrete subsystems with abstractions that have lower dimensions (a.k.a. reduced-order models) while providing mathematical guarantees on controller synthesis through the quantification of an upper bound on the closeness between output trajectories of original systems and their abstractions. We propose two control methods to provide guarantees for NETS: one using the principle of interconnected synchronous machines and another considering the power flows in the network between neighbouring subsystems.

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arXiv2022

Automata-based Controller Synthesis for Stochastic Systems: A Game Framework via Approximate Probabilistic Relations

In this work, we propose an abstraction and refinement methodology for the controller synthesis of discrete-time stochastic systems to enforce complex logical properties expressed by deterministic finite automata (a.k.a. DFA). Our proposed scheme is based on a notion of so-called $(ε,δ)$-approximate probabilistic relations, allowing one to quantify the similarity between stochastic systems modeled by discrete-time stochastic games and their corresponding finite abstractions. Leveraging this type of relations, the lower bound for the probability of satisfying the desired specifications can be well ensured by refining controllers synthesized over abstract systems to the original games. Moreover, we propose an algorithmic procedure to construct such a relation for a particular class of nonlinear stochastic systems with slope restrictions on the nonlinearity. The proposed methods are demonstrated on a quadrotor example, and the results indicate that the desired lower bound for the probability of satisfaction is guaranteed.

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arXiv2022

Compositional Controller Synthesis for Interconnected Stochastic Systems with Markovian Switching

In this work, we propose a compositional scheme for the safety controller synthesis of interconnected discrete-time stochastic systems with Markovian switching signals. Our proposed approach is based on a notion of so-called control storage certificates computed for individual subsystems, by leveraging which, one can synthesize state-feedback controllers for interconnected systems to enforce safety specifications over finite time horizons. To do so, we employ a sum-of-squares (SOS) optimization approach to search for multiple storage certificates of each switching subsystem while synthesizing its corresponding safety controller. We then utilize dissipativity theory to compositionally construct barrier certificates for interconnected systems based on storage certificates of individual subsystems. The proposed dissipativity-type compositional conditions can leverage the structure of the interconnection topology and be fulfilled independently of the number or gains of subsystems. We eventually employ the constructed barrier certificate and quantify upper bounds on the probability that the interconnected system reaches certain unsafe regions in a finite time horizon. We apply our results to a room temperature network of 200 rooms with Markovian switching signals while accepting multiple storage certificates. We compositionally synthesize safety controllers to maintain the temperature of each room in a comfort zone for a bounded time horizon.

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arXiv2022

Safety Barrier Certificates for Stochastic Hybrid Systems

This work is concerned with the safety controller synthesis of stochastic hybrid systems, in which continuous evolutions are described by stochastic differential equations with both Brownian motions and Poisson processes, and instantaneous jumps are governed by stochastic difference equations with additive noises. Our proposed framework leverages the notion of control barrier certificates (CBC), as a discretization-free approach, to synthesize safety controllers for stochastic hybrid systems while providing safety guarantees in finite time horizons. In our proposed scheme, we first provide an augmented framework to characterize each stochastic hybrid system containing continuous evolutions and instantaneous jumps with a unified system covering both scenarios. We then introduce an augmented control barrier certificate (ACBC) for augmented systems and propose sufficient conditions to construct an ACBC based on CBC of original hybrid systems. By utilizing the constructed ACBC, we quantify upper bounds on the probability that the stochastic hybrid system reaches certain unsafe regions in a finite time horizon. The proposed approach is verified over a nonlinear case study.

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arXiv2022

Compositional Reinforcement Learning for Discrete-Time Stochastic Control Systems

We propose a compositional approach to synthesize policies for networks of continuous-space stochastic control systems with unknown dynamics using model-free reinforcement learning (RL). The approach is based on implicitly abstracting each subsystem in the network with a finite Markov decision process with unknown transition probabilities, synthesizing a strategy for each abstract model in an assume-guarantee fashion using RL, and then mapping the results back over the original network with approximate optimality guarantees. We provide lower bounds on the satisfaction probability of the overall network based on those over individual subsystems. A key contribution is to leverage the convergence results for adversarial RL (minimax Q-learning) on finite stochastic arenas to provide control strategies maximizing the probability of satisfaction over the network of continuous-space systems. We consider finite-horizon properties expressed in the syntactically co-safe fragment of linear temporal logic. These properties can readily be converted into automata-based reward functions, providing scalar reward signals suitable for RL. Since such reward functions are often sparse, we supply a potential-based reward shaping technique to accelerate learning by producing dense rewards. The effectiveness of the proposed approaches is demonstrated via two physical benchmarks including regulation of a room temperature network and control of a road traffic network.

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arXiv2022

Formal Estimation of Collision Risks for Autonomous Vehicles: A Compositional Data-Driven Approach

In this work, we propose a compositional data-driven approach for the formal estimation of collision risks for autonomous vehicles (AVs) while acting in a stochastic multi-agent framework. The proposed approach is based on the construction of sub-barrier certificates for each stochastic agent via a set of data collected from its trajectories while providing an a-priori guaranteed confidence on the data-driven estimation. In our proposed setting, we first cast the original collision risk problem for each agent as a robust optimization program (ROP). Solving the acquired ROP is not tractable due to an unknown model that appears in one of its constraints. To tackle this difficulty, we collect finite numbers of data from trajectories of each agent and provide a scenario optimization program (SOP) corresponding to the original ROP. We then establish a probabilistic bridge between the optimal value of SOP and that of ROP, and accordingly, we formally construct the sub-barrier certificate for each unknown agent based on the number of data and a required level of confidence. We then propose a compositional technique based on small-gain reasoning to quantify the collision risk for multi-agent AVs with some desirable confidence based on sub-barrier certificates of individual agents constructed from data. For the case that the proposed compositionality conditions are not satisfied, we provide a relaxed version of compositional results without requiring any compositionality conditions but at the cost of providing a potentially conservative collision risk. Eventually, we also present our approaches for non-stochastic multi-agent AVs. We demonstrate the effectiveness of our proposed results by applying them to a vehicle platooning consisting of 100 vehicles with 1 leader and 99 followers. We formally estimate the collision risk by collecting data from trajectories of each agent.

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arXiv2022

Compositional Synthesis of Control Barrier Certificates for Networks of Stochastic Systems against $ω$-Regular Specifications

This paper is concerned with a compositional scheme for the construction of control barrier certificates for interconnected discrete-time stochastic systems. The main objective is to synthesize switching control policies against $ω$-regular properties that can be described by accepting languages of deterministic Streett automata (DSA) along with providing probabilistic guarantees for the satisfaction of such specifications. The proposed framework leverages the interconnection topology and a notion of so-called \emph{control sub-barrier certificates} of subsystems, which are used to compositionally construct control barrier certificates of interconnected systems by imposing some dissipativity-type compositionality conditions. We propose a systematic approach to decompose high-level $ω$-regular specifications into simpler tasks by utilizing the automata corresponding to the specifications. In addition, we formulate an alternating direction method of multipliers (ADMM) optimization problem in order to obtain suitable control sub-barrier certificates of subsystems while satisfying compositionality conditions. For systems with polynomial dynamics, we provide a sum-of-squares (SOS) optimization problem for the computation of control sub-barrier certificates and local control policies of subsystems. Finally, we demonstrate the effectiveness of our proposed approaches by applying them to a physical case study.

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arXiv2022

Constructing MDP Abstractions Using Data with Formal Guarantees

This paper is concerned with a data-driven technique for constructing finite Markov decision processes (MDPs) as finite abstractions of discrete-time stochastic control systems with unknown dynamics while providing formal closeness guarantees. The proposed scheme is based on notions of stochastic bisimulation functions (SBF) to capture the probabilistic distance between state trajectories of an unknown stochastic system and those of finite MDP. In our proposed setting, we first reformulate corresponding conditions of SBF as a robust convex program (RCP). We then propose a scenario convex program (SCP) associated to the original RCP by collecting a finite number of data from trajectories of the system. We ultimately construct an SBF between the data-driven finite MDP and the unknown stochastic system with a given confidence level by establishing a probabilistic relation between optimal values of the SCP and the RCP. We also propose two different approaches for the construction of finite MDPs from data. We illustrate the efficacy of our results over a nonlinear jet engine compressor with unknown dynamics. We construct a data-driven finite MDP as a suitable substitute of the original system to synthesize controllers maintaining the system in a safe set with some probability of satisfaction and a desirable confidence level.

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arXiv2022

From Small-Gain Theory to Compositional Construction of Barrier Certificates for Large-Scale Stochastic Systems

This paper is concerned with a compositional approach for the construction of control barrier certificates for large-scale interconnected stochastic systems while synthesizing hybrid controllers against high-level logic properties. Our proposed methodology involves decomposition of interconnected systems into smaller subsystems and leverages the notion of control sub-barrier certificates of subsystems, enabling one to construct control barrier certificates of interconnected systems by employing some max-type small-gain conditions. The main goal is to synthesize hybrid controllers enforcing complex logic properties including the ones represented by the accepting language of deterministic finite automata, while providing probabilistic guarantees on the satisfaction of given specifications in bounded-time horizons. To do so, we propose a systematic approach to first decompose high-level specifications into simple reachability tasks by utilizing automata corresponding to the complement of specifications. We then construct control sub-barrier certificates and synthesize local controllers for those simpler tasks and combine them to obtain a hybrid controller that ensures satisfaction of the complex specification with some lower bound on the probability of satisfaction. To compute control sub-barrier certificates and corresponding local controllers, we provide two systematic approaches based on sum-of-squares (SOS) optimization program and counter-example guided inductive synthesis (CEGIS) framework. We finally apply our proposed techniques to two physical case studies.

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arXiv2022

Data-Driven Synthesis of Symbolic Abstractions with Guaranteed Confidence

In this work, we propose a data-driven approach for the construction of finite abstractions (a.k.a., symbolic models) for discrete-time deterministic control systems with unknown dynamics. We leverage notions of so-called alternating bisimulation functions (ABF), as a relation between each unknown system and its symbolic model, to quantify the mismatch between state behaviors of two systems. Accordingly, one can employ our proposed results to perform formal verification and synthesis over symbolic models and then carry the results back over unknown original systems. In our data-driven setting, we first cast the required conditions for constructing ABF as a robust optimization program (ROP). Solving the provided ROP is not tractable due to the existence of unknown models in the constraints of ROP. To tackle this difficulty, we collect finite numbers of data from trajectories of unknown systems and propose a scenario optimization program (SOP) corresponding to the original ROP. By establishing a probabilistic relation between optimal values of SOP and ROP, we formally construct ABF between unknown systems and their symbolic models based on the number of data and a required confidence level. We verify the effectiveness of our data-driven results over two physical case studies with unknown models including (i) a DC motor and (ii) a nonlinear jet engine compressor. We construct symbolic models from data as appropriate substitutes of original systems and synthesize policies maintaining states of unknown systems in a safe set within infinite time horizons with some guaranteed confidence levels.

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arXiv2022

Automated Verification and Synthesis of Stochastic Hybrid Systems: A Survey

Stochastic hybrid systems have received significant attentions as a relevant modelling framework describing many systems, from engineering to the life sciences: they enable the study of numerous applications, including transportation networks, biological systems and chemical reaction networks, smart energy and power grids, and beyond. Automated verification and policy synthesis for stochastic hybrid systems can be inherently challenging: this is due to the heterogeneity of their dynamics (presence of continuous and discrete components), the presence of uncertainty, and in some applications the large dimension of state and input sets. Over the past few years, a few hundred articles have investigated these models, and developed diverse and powerful approaches to mitigate difficulties encountered in the analysis and synthesis of such complex stochastic systems. In this survey, we overview the most recent results in the literature and discuss different approaches, including (in)finite abstractions, verification and synthesis for temporal logic specifications, stochastic similarity relations, (control) barrier certificates, compositional techniques, and a selection of results on continuous-time stochastic systems; we finally survey recently developed software tools that implement the discussed approaches. Throughout the manuscript we discuss a few open topics to be considered as potential future research directions: we hope that this survey will guide younger researchers through a comprehensive understanding of the various challenges, tools, and solutions in this enticing and rich scientific area.

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arXiv2021

Data-driven Safety Verification of Stochastic Systems via Barrier Certificates

In this paper, we propose a data-driven approach to formally verify the safety of (potentially) unknown discrete-time continuous-space stochastic systems. The proposed framework is based on a notion of barrier certificates together with data collected from trajectories of unknown systems. We first reformulate the barrier-based safety verification as a robust convex problem (RCP). Solving the acquired RCP is hard in general because not only the state of the system lives in a continuous set, but also and more problematic, the unknown model appears in one of the constraints of RCP. Instead, we leverage a finite number of data, and accordingly, the RCP is casted as a scenario convex problem (SCP). We then relate the optimizer of the SCP to that of the RCP, and consequently, we provide a safety guarantee over the unknown stochastic system with a priori guaranteed confidence. We apply our approach to an unknown room temperature system by collecting sampled data from trajectories of the system and verify formally that temperature of the room lies in a comfort zone for a finite time horizon with a desired confidence.

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