Deductive control synthesis for alternating-time logics

Dimitrova, Rayna; Majumdar, Rupak

doi:10.1145/2656045.2656054

Cited by 17 publications

(16 citation statements)

References 24 publications

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“…In [8], for discrete-time nonlinear systems with continuous-valued and discrete-valued state, the authors formulate optimization problems related to trajectory generation with linear temporal logic specifications for which mixed integer linear programming tools are applied. In [9], the design of controllers to satisfy alternating-time temporal logic (ATL*), which is an expressive branching-time logic that allows for quantification over control strategies, is pursued using barrier and Lyapunov functions for a class of continuous-time systems. More recently, using similar programming tools, in [10], tools to design reactive controllers for mixed logical dynamical systems so as to satisfy high-level specifications given in the language of metric temporal logic are proposed, while in [11] a hybrid system model and tools for the satisfaction of a linear temporal logic specification for the trajectories of a physical plant modeled as a continuous-time system are presented.…”

Section: Contentsmentioning

confidence: 99%

Linear temporal logic for hybrid dynamical systems: Characterizations and sufficient conditions

Han

Sanfelice

2020

Nonlinear Analysis: Hybrid Systems

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This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential inclusions -capturing the continuous dynamics -and difference inclusions -capturing the discrete dynamics or events -with constraints. State trajectories (or solutions) to such systems are parameterized by a hybrid notion of time. For such broad class of solutions, the operators and semantics needed to reason about temporal logic are introduced. Characterizations of temporal logic formulas in terms of dynamical properties of hybrid systems are presented -in particular, forward invariance and finite time attractivity. We exploit these characterizations to formulate sufficient conditions assuring the satisfaction of temporal logic formulas -when possible, our conditions do not involve solution information. Combining our results for formulas with a single operator, we point out ways to certify more complex formulas, in particular, via a decomposition using a finite state automaton. Academic examples illustrate the results throughout the paper.

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Section: Contentsmentioning

confidence: 99%

Linear temporal logic for hybrid dynamical systems: Characterizations and sufficient conditions

Han

Sanfelice

2020

Nonlinear Analysis: Hybrid Systems

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“…Deductive Proof System for Temporal Logic. In [8], the authors present a deductive proof system for proving alternating-time temporal logic assertions on a continuous dynamical system. Some of the proof rules presented require the user to provide auxilary predicates to establish proofsubgoals.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

“…The key feature of our approach is that we provide an automated mechanism to leverage user insight about parts of the system to obtain localized forward invariant cuts. It would be interesting to see if the automation that we develop in this paper could be used to mechanize the proof system presented in [8].…”

Section: Related Work and Conclusionmentioning

confidence: 99%

“…Further, their technique requires reasoning about the global behavior of the system, as opposed to the local invariant property that we require (a much weaker requirement). The deductive proof system presented in [8] uses local safety certificates to reason about behaviors but applies to continuous (as opposed to hybrid) systems. Also, [8] provides no constructive means of generating the necessary local safety certificates.…”

Section: Introductionmentioning

confidence: 99%

“…The deductive proof system presented in [8] uses local safety certificates to reason about behaviors but applies to continuous (as opposed to hybrid) systems. Also, [8] provides no constructive means of generating the necessary local safety certificates. This is in contrast to our approach, which provides methodologies for generating the local safety certificates and including them in the proof task.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Forward invariant cuts to simplify proofs of safety

Aréchiga¹,

Kapinski²,

Deshmukh³

et al. 2015

2015 International Conference on Embedded Software (EMSOFT)

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The use of deductive techniques, such as theorem provers, has several advantages in safety verification of hybrid systems; however, state-of-the-art theorem provers require extensive manual intervention. Furthermore, there is often a gap between the type of assistance that a theorem prover requires to make progress on a proof task and the assistance that a system designer is able to provide. This paper presents an extension to KeYmaera, a deductive verification tool for differential dynamic logic; the new technique allows local reasoning using system designer intuition about performance within particular modes as part of a proof task. Our approach allows the theorem prover to leverage forward invariants, discovered using numerical techniques, as part of a proof of safety. We introduce a new inference rule into the proof calculus of KeYmaera, the forward invariant cut rule, and we present a methodology to discover useful forward invariants, which are then used with the new cut rule to complete verification tasks. We demonstrate how our new approach can be used to complete verification tasks that lie out of the reach of existing deductive approaches using several examples, including one involving an automotive powertrain control system.

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Temporal Logic Verification of Stochastic Systems Using Barrier Certificates

Jagtap

Soudjani

2018

Lecture Notes in Computer Science

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We study formal synthesis of control policies for discrete-time stochastic control systems against complex temporal properties. Our goal is to synthesize a control policy for the system together with a lower bound on the probability that the system satisfies a complex temporal property. The desired properties of the system are expressed as a fragment of linear temporal logic (LTL), called safe-LTL over finite traces. We propose leveraging control barrier certificates which alleviate the issue of the curse of dimensionality associated with discretization-based approaches existing in the literature. We show how control barrier certificates can be used for synthesizing policies while guaranteeing lower bounds on the probability of satisfaction for the given property. Our approach decomposes negation of the specification into sequential reachabilities and then finds control barrier certificates for computing upper-bounds on the reachability probabilities. Control policies associated with these barrier certificates are then combined as a hybrid control policy for the concrete system that guarantees a lower bound on the probability of satisfaction of the property. We distinguish uncountable and finite input sets in the computation of barrier certificates. For the former, control barrier certificates can be computed using sum-of-square optimization. For the latter, we develop a computational method based on counter-example guided inductive synthesis. We demonstrate the efectiveness of the proposed approach on a room temperature control and lane keeping of a vehicle modeled as a four-dimensional single-track kinematic model. We compare our results with the discretization-based methods in the literatures.

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Deductive control synthesis for alternating-time logics

Cited by 17 publications

References 24 publications

Linear temporal logic for hybrid dynamical systems: Characterizations and sufficient conditions

Linear temporal logic for hybrid dynamical systems: Characterizations and sufficient conditions

Forward invariant cuts to simplify proofs of safety

Temporal Logic Verification of Stochastic Systems Using Barrier Certificates

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