# Temporal Logic Verification of Stochastic Systems Using Barrier Certificates

@article{Jagtap2018TemporalLV, title={Temporal Logic Verification of Stochastic Systems Using Barrier Certificates}, author={Pushpak Jagtap and S. Soudjani and Majid Zamani}, journal={ArXiv}, year={2018}, volume={abs/1807.00064} }

This paper presents a methodology for temporal logic verification of discrete-time stochastic systems. Our goal is to find a lower bound on the probability that a complex temporal property is satisfied by finite traces of the system. Desired temporal properties of the system are expressed using a fragment of linear temporal logic, called safe LTL over finite traces. We propose to use barrier certificates for computations of such lower bounds, which is computationally much more efficient than… Expand

#### 24 Citations

Verification of Switched Stochastic Systems via Barrier Certificates

- Computer Science, Engineering
- 2021

This approach combines automata-based verification and the use of barrier certificates, and relies on decomposing the automaton associated with the negation of specification into a sequence of simpler reachability tasks and compute upper bounds for these reachability probabilities by means of common or multiple barrier certificates. Expand

Verification of Switched Stochastic Systems via Barrier Certificates*

- Computer Science
- 2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

This approach combines automata-based verification and the use of barrier certificates, and relies on decomposing the automaton associated with the negation of specification into a sequence of simpler reachability tasks and compute upper bounds for these reachability probabilities by means of common or multiple barrier certificates. Expand

Formal Synthesis of Stochastic Systems via Control Barrier Certificates

- Computer Science, Engineering
- IEEE Transactions on Automatic Control
- 2021

This article proposes the use of so-called control barrier certificate to solve simpler reachability tasks along with computing the corresponding controllers and probability bounds, and combines those controllers to obtain a hybrid control policy solving the considered problem. Expand

Formal Verification of Control Systems against Hyperproperties via Barrier Certificates

- Computer Science
- ArXiv
- 2021

A discretization-free approach for the formal verification of discrete-time control systems against hyperproperties, which involves decomposition of complex hyperproperties into several verification conditions by exploiting the automata-based structure corresponding to the complement of the original specifications. Expand

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

- Computer Science, Engineering
- ArXiv
- 2021

A systematic approach to first decompose high-level specifications into simple reachability tasks by utilizing automata corresponding to the complement of specifications 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. Expand

Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

- Computer Science, Engineering
- GameSec
- 2019

A dynamic programming based approach is formulated to determine a stationary defender policy that maximized the probability of satisfaction of a safe-LTL_F formula over a finite time-horizon under any stationary adversary policy. Expand

Verification and Control for Finite-Time Safety of Stochastic Systems via Barrier Functions

- Computer Science
- 2019 IEEE Conference on Control Technology and Applications (CCTA)
- 2019

This paper uses stochastic barrier functions as a means to quantity the probability that a system exits a given safe region of the state space in finite time and proposes a method for synthesizing polynomial state feedback controllers that achieve a specified probability of safety. Expand

A Barrier Function Approach to Finite-Time Stochastic System Verification and Control

- Computer Science, Engineering
- Autom.
- 2021

This paper uses stochastic control barrier functions as a means to quantify the probability that a system exits a given safe region of the state space in finite time and proposes a method for synthesizing polynomial state feedback controllers that achieve a specified probability of safety. Expand

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

- Computer Science, Engineering
- ArXiv
- 2021

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. Expand

Compositional Construction of Control Barrier Certificates for Large-Scale Stochastic Switched Systems

- Computer Science, Engineering
- IEEE Control Systems Letters
- 2020

The proposed scheme is based on a notion of so-called augmented pseudo-barrier certificates computed for each switched subsystem, using which one can compositionally synthesize state-feedback controllers for interconnected systems enforcing safety specifications over a finite-time horizon. Expand

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