Sparsity-aware finite abstraction

Gruber, Felix; Kim, Eric S.; Arcak, Murat

doi:10.1109/cdc.2017.8263995

Cited by 12 publications

(22 citation statements)

References 16 publications

(26 reference statements)

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“…Secondly, let x ∈ X # , then x ∈ X * and since X * is a safe invariant set, there exists u ∈ enab ∆ (x) such that x ∈ X * where x = ∆(x, u). From (15), there exists z ∈ X # , such that x X z (note that we may have x = z ). Then, from Definition 3, there exists v ∈ enab ∆ (x) such that z = ∆(x, v).…”

Section: Maximal Safe Invariantmentioning

confidence: 99%

“…Other works have explored the efficient encoding of discrete abstractions, e.g. using binary decision diagrams and the associated algorithms [38,5], or exploiting sparsity in the continuous dynamics [15]. Multi-resolution, multi-scale and multi-layered abstractions, which can adapt locally the precision of the approximation have been developed in several works [44,7,17] and are often used in combination with lazy controller synthesis algorithms that build the abstraction on-the-fly and adapt the precision to the level required for enforcing the specification [39,31,12,16].…”

Section: Introductionmentioning

confidence: 99%

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Safety synthesis for incrementally stable switched systems using discretization-free multi-resolution abstractions

Girard

Gößler

2019

Acta Informatica

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Control of continuous and hybrid systems using discrete abstractions often suffers from scalability issues, due to the use of state space partitions as symbolic states. In this paper, for incrementally stable switched systems, we introduce a class of abstractions that do not rely on state space partitions but use mode sequences as symbolic states. Our approach differs from existing works by the possibility of considering sequences of varying length, giving the possibility to adjust locally the resolution of the abstraction. Temporal constraints on the switching signal can also be taken into account. We thus define multi-resolution bisimilar abstractions that enjoy interesting properties that can be used to design specific algorithms to synthesize safety controllers. These algorithms need not compute the full abstraction that is built incrementally during controller synthesis, exploring finer resolutions only when the specification cannot be enforced at the coarser level. We illustrate the approach by a numerical example inspired by road traffic regulation.

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Section: Maximal Safe Invariantmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Safety synthesis for incrementally stable switched systems using discretization-free multi-resolution abstractions

Girard

Gößler

2019

Acta Informatica

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“…One could incrementally construct an abstraction of the system dynamics while performing the control synthesis step [10,15] as implemented in tools ROCS [9] and ARCS [4]. The abstraction overhead can also be reduced by representing systems as a collection of components composed in parallel [6,13]. These have been developed in isolation and were not previously interoperable.…”

Section: Bottlenecks In Abstraction-based Control Synthesismentioning

confidence: 99%

Flexible Computational Pipelines for Robust Abstraction-Based Control Synthesis

Kim

Arcak

Seshia

2019

Computer Aided Verification

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Successfully synthesizing controllers for complex dynamical systems and specifications often requires leveraging domain knowledge as well as making difficult computational or mathematical tradeoffs. This paper presents a flexible and extensible framework for constructing robust control synthesis algorithms and applies this to the traditional abstraction-based control synthesis pipeline. It is grounded in the theory of relational interfaces and provides a principled methodology to seamlessly combine different techniques (such as dynamic precision grids, refining abstractions while synthesizing, or decomposed control predecessors) or create custom procedures to exploit an application's intrinsic structural properties. A Dubins vehicle is used as a motivating example to showcase memory and runtime improvements.

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“…In each of our examples, we use a modified version of the SCOTS symbolic controller synthesis toolbox [14], which takes a continuous control system and creates a finite state machine that serves as an abstract representation over which a controller is synthesized. In addition to modifications to compute Equation (4) and Equation (6), we exploit internal system dependencies to reduce the computation time of the abstraction [7]. Creating the discrete abstraction depends on parameters such as the grid size and granularity.…”

Section: Examplesmentioning

confidence: 99%

Automatic Generation of Communication Requirements for Enforcing Multi-Agent Safety

Kim

Arcak

Seshia

et al. 2018

Electron. Proc. Theor. Comput. Sci.

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Distributed controllers are often necessary for a multi-agent system to satisfy safety properties such as collision avoidance. Communication and coordination are key requirements in the implementation of a distributed control protocol, but maintaining an all-to-all communication topology is unreasonable and not always necessary. Given a safety objective and a controller implementation, we consider the problem of identifying when agents need to communicate with one another and coordinate their actions to satisfy the safety constraint. We define a coordination-free controllable predecessor operator that is used to derive a subset of the state space that allows agents to act independently, without consulting other agents to double check that the action is safe. Applications are shown for identifying an upper bound on connection delays and a self-triggered coordination scheme. Examples are provided which showcase the potential for designers to visually interpret a system's ability to tolerate delays when initializing a network connection.

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Sparsity-aware finite abstraction

Cited by 12 publications

References 16 publications

Safety synthesis for incrementally stable switched systems using discretization-free multi-resolution abstractions

Safety synthesis for incrementally stable switched systems using discretization-free multi-resolution abstractions

Flexible Computational Pipelines for Robust Abstraction-Based Control Synthesis

Automatic Generation of Communication Requirements for Enforcing Multi-Agent Safety

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