Formal Synthesis of Stochastic Systems via Control Barrier Certificates

Jagtap, Pushpak; Soudjani, Sadegh; Zamani, Majid

doi:10.1109/tac.2020.3013916

Cited by 74 publications

(53 citation statements)

References 45 publications

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“…Proof. The proof is similar to that of [8,Theorem 5.2] and is omitted here due to the lack of space.…”

Section: Computation Of Probabilitymentioning

confidence: 95%

“…For the illustration of the above sets, we kindly refer the interested reader to Example 1 in [8]. Having P p (q) in (4.2) as the set of state runs of length 3, in this subsection, we provide a systematic approach to compute a policy together with a (potentially tight) lower bound on the probability that the solution process of S satisfies the specifications given by DFA A.…”

Section: Formal Synthesis Of Controllersmentioning

confidence: 99%

“…The corresponding hybrid control policy υ is given by υ(t) =ũ(ξ(t), q m ). For the illustration of the switching mechanism, see Example 1 in [8,Section 5]. In the next subsection, we discuss the computation of bound on the probability of satisfying the specification under such a policy, which then can be used for checking if this policy is indeed a solution for Problem 2.6.…”

Section: Formal Synthesis Of Controllersmentioning

confidence: 99%

“…When dealing with large systems, these approaches suffer severely from the curse of dimensionality (i.e., computational complexity grows exponentially with the dimension of the state set). In order to overcome the large computational burden, a discretization-free approach, based on control barrier functions has shown potential to solve the formal synthesis problems (See [7,8,9,10] and references therein). The aforementioned works assume the availability of complete state information.…”

Section: Introductionmentioning

confidence: 99%

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Synthesis of Partially Observed Jump-Diffusion Systems via Control Barrier Functions

Jahanshahi

Jagtap

2021

IEEE Control Syst. Lett.

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In this paper, we study formal synthesis of control policies for partially observed jump-diffusion systems against complex logic specifications. Given a state estimator, we utilize a discretization-free approach for formal synthesis of control policies by using a notation of control barrier functions without requiring any knowledge of the estimation accuracy. Our goal is to synthesize an offline control policy providing (potentially maximizing) a lower bound on the probability that the trajectories of the partially observed jump-diffusion system satisfy some complex specifications expressed by deterministic finite automata. Finally, we illustrate the effectiveness of the proposed results by synthesizing a policy for a jet engine example.

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“…Proof. The proof is similar to that of [8,Theorem 5.2] and is omitted here due to the lack of space.…”

Section: Computation Of Probabilitymentioning

confidence: 95%

Section: Formal Synthesis Of Controllersmentioning

confidence: 99%

Section: Formal Synthesis Of Controllersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Synthesis of Partially Observed Jump-Diffusion Systems via Control Barrier Functions

Jahanshahi

Jagtap

2021

IEEE Control Syst. Lett.

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“…To the contrary, our algorithm is highly scalable due to its distributed nature and the fact that it avoids altogether the construction of a product automaton. Finally, note that decomposition of fragments of LTL formulas into reachability tasks has been investigated in [41]- [43], as well, assuming robots that operate in known environments. Common in these works is that temporal logic tasks are decomposed into global/multi-agent reachability tasks.…”

Section: A Related Researchmentioning

confidence: 99%

Reactive Temporal Logic Planning for Multiple Robots in Unknown Environments

Kantaros¹,

Malencia²,

Kumar³

et al. 2020

2020 IEEE International Conference on Robotics and Automation (ICRA)

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This paper proposes a new reactive temporal logic planning algorithm for multiple robots that operate in environments with unknown geometry modeled using occupancy grid maps. The robots are equipped with individual sensors that allow them to continuously learn a grid map of the unknown environment using existing Simultaneous Localization and Mapping (SLAM) methods. The goal of the robots is to accomplish complex collaborative tasks, captured by global Linear Temporal Logic (LTL) formulas. The majority of existing LTL planning approaches rely on discrete abstractions of the robot dynamics operating in known environments and, as a result, they cannot be applied to the more realistic scenarios where the environment is initially unknown. In this paper, we address this novel challenge by proposing the first reactive, abstraction-free, and distributed LTL planning algorithm that can be applied for complex mission planning of multiple robots operating in unknown environments. The proposed algorithm is reactive i.e., planning is adapting to the updated environmental map and abstraction-free as it does not rely on designing abstractions of the robot dynamics. Also, our algorithm is distributed in the sense that the global LTL task is decomposed into single-agent reachability problems constructed online based on the continuously learned map. The proposed algorithm is complete under mild assumptions on the structure of the environment and the sensor models. We provide extensive numerical simulations and hardware experiments that illustrate the theoretical analysis and show that the proposed algorithm can address complex planning tasks for large-scale multi-robot systems in unknown environments.

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Verification of Quantum Systems Using Barrier Certificates

Lewis,

Zuliani,

Soudjani

2023

Lecture Notes in Computer Science

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Current methods for verifying quantum computers are predominately based on interactive or automatic theorem provers. Considering that quantum computers are dynamical in nature, this paper employs and extends the concepts from the verification of dynamical systems to verify properties of quantum circuits. Our main contribution is to propose k-inductive barrier certificates over complex variables and show how to compute them using Hermitian Sum of Squares optimization. We apply this new technique to verify properties of different quantum circuits.

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Formal Synthesis of Stochastic Systems via Control Barrier Certificates

Cited by 74 publications

References 45 publications

Synthesis of Partially Observed Jump-Diffusion Systems via Control Barrier Functions

Synthesis of Partially Observed Jump-Diffusion Systems via Control Barrier Functions

Reactive Temporal Logic Planning for Multiple Robots in Unknown Environments

Verification of Quantum Systems Using Barrier Certificates

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