Time-Robust Control for STL Specifications

Rodionova, Alëna; Lindemann, Lars; Morari, Manfred; Pappas, George J.

doi:10.1109/cdc45484.2021.9683477

Cited by 22 publications

(23 citation statements)

References 21 publications

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“…As remarked before, temporal robustness for STL specifications was initially presented without further analysis in [18]. Temporally-robust control has been considered in [34] for special fragments of STL, and in [48] for general fragments of STL using MILP encodings. In an orthogonal direction that is worth mentioning, the authors in [46] and [29] consider the problem of finding temporal relaxations for time window temporal logic specifications [55].…”

Section: Related Workmentioning

confidence: 99%

“…The control design problem has not been addressed before and is subject to numerical challenges as the temporal robustness semantics are not differentiable, so that gradient-based optimization methods fail to be applicable. To address this challenge, we presented a Mixed-Integer Linear Programming (MILP) encoding in our previous work [48] where we describe how to control a dynamical system in order to maximize its temporal robustness.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, we analyze the meaning of temporal robustness in terms of permissible time shifts in the predicates of the specification and in the underlying signal. For both notions we present MILP encodings, following ideas of our initial work in [48], that solves the control design problem in which we aim to maximize the synchronous and asynchronous temporal robustness.…”

Section: Introductionmentioning

confidence: 99%

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Temporal Robustness of Temporal Logic Specifications: Analysis and Control Design

Rodionova,

Lindemann,

Morari

et al. 2022

Preprint

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We study the temporal robustness of temporal logic specifications and show how to design temporally robust control laws for time-critical control systems. This topic is of particular interest in connected systems and interleaving processes such as multi-robot and human-robot systems where uncertainty in the behavior of individual agents and humans can induce timing uncertainty. Despite the importance of time-critical systems, temporal robustness of temporal logic specifications has not been studied, especially from a control design point of view. We define synchronous and asynchronous temporal robustness and show that these notions quantify the robustness with respect to synchronous and asynchronous time shifts in the predicates of the temporal logic specification. It is further shown that the synchronous temporal robustness upper bounds the asynchronous temporal robustness. We then study the control design problem in which we aim to design a control law that maximizes the temporal robustness of a dynamical system. Our solution consists of a Mixed-Integer Linear Programming (MILP) encoding that can be used to obtain a sequence of optimal control inputs. While asynchronous temporal robustness is arguably more nuanced than synchronous temporal robustness, we show that control design using synchronous temporal robustness is computationally more efficient. This trade-off can be exploited by the designer depending on the particular application at hand. We conclude the paper with a variety of case studies.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Temporal Robustness of Temporal Logic Specifications: Analysis and Control Design

Rodionova,

Lindemann,

Morari

et al. 2022

Preprint

Self Cite

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“…Our notion of asynchronous temporal robustness is especially important in multi-agent systems where indiviual agents may be delayed and subject to individual timing uncertainties. Temporal robustness for STL specifications over deterministic signals was presented in [24] and used for control design in [25] and in our recent work [26]. The notion of asynchronous temporal robustness as presented in this paper is fundamentally different and is interpretable in the sense that it quantifies the permissible timing uncertainty of a signal in terms of maximum time shifts in its sub-signals.…”

Section: Related Workmentioning

confidence: 99%

“…We first consider the deterministic system in (1) and synthesize a sequence of control inputs u i (t) for each robot i following the approach presented in [26]. For the deterministic system, we have that η φ (X, 0) = 7 time steps and θ φ (X, 0) = 6 time steps.…”

Section: Cooperative Servicingmentioning

confidence: 99%

Temporal Robustness of Stochastic Signals

Lindemann¹,

Rodionova²,

Pappas³

2022

Preprint

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We study the temporal robustness of stochastic signals. This topic is of particular interest in interleaving processes such as multi-agent systems where communication and individual agents induce timing uncertainty. For a deterministic signal and a given specification, we first introduce the synchronous and the asynchronous temporal robustness to quantify the signal's robustness with respect to synchronous and asynchronous time shifts in its sub-signals. We then define the temporal robustness risk by investigating the temporal robustness of the realizations of a stochastic signal. This definition can be interpreted as the risk associated with a stochastic signal to not satisfy a specification robustly in time. In this definition, general forms of specifications such as signal temporal logic specifications are permitted. We show how the temporal robustness risk is estimated from data for the value-at-risk. The usefulness of the temporal robustness risk is underlined by both theoretical and empirical evidence. In particular, we provide various numerical case studies including a T-intersection scenario in autonomous driving.

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