Average-based Robustness for Continuous-Time Signal Temporal Logic

Mehdipour, Noushin; Vasile, Cristian-Ioan; Belta, Călin

doi:10.1109/cdc40024.2019.9029989

Cited by 17 publications

(6 citation statements)

References 25 publications

(55 reference statements)

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“…Spatial robustness particularly allows to quantify permissible uncertainty of the signal for each point in time, e.g., caused by additive disturbances. Other notions of spatial robustness are the arithmetic-geometric integral mean robustness [43] and the smooth cumulative robustness [27] as well as notions that are tailored for use in reinforcement learning applications [54]. Spatial robustness for stochastic systems was considered in [7,8] as well as in [37] when considering the risk of violating a specification.…”

Section: Related Workmentioning

confidence: 99%

“…Control of dynamical systems under STL specifications has first been considered in [47] by means of an MILP encoding that allows to maximize spatial robustness. Other optimization-based methods that also follow the idea of maximizing spatial robustness have been proposed in [23,43,45]. Another direction has been to design transient feedback control laws that maximize the spatial robustness of fragments of STL specification [35] and [14].…”

Section: Related Workmentioning

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: Related Workmentioning

confidence: 99%

Temporal Robustness of Temporal Logic Specifications: Analysis and Control Design

Rodionova,

Lindemann,

Morari

et al. 2022

Preprint

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“…Therefore, depending on the aggregation functions in r w , the weights p and associated with ϕ affect the gradient and optimization. A similar synthesis framework can be applied to continuoustime systems with a Zeroth-Order Hold (ZOH) input [17].…”

Section: Synthesis Using Weighted Robustnessmentioning

confidence: 99%

“…Locality means that robustness depends only on the value of signal at a single time instant, while masking indicates that the satisfaction of parts of the formulae different from the most "extreme" part does not contribute to the robustness. [16], [17] employed additive and multiplicative smoothing and eliminated the locality and masking effects to enhance optimization. Later works [14], [15] defined parametric approximations for max and min that enabled adjustment of the locality and masking to a desired level.…”

Section: Introductionmentioning

confidence: 99%

Specifying User Preferences using Weighted Signal Temporal Logic

Mehdipour¹,

Vasile²,

Belta³

2020

Preprint

Self Cite

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We extend Signal Temporal Logic (STL) to enable the specification of importance and priorities. The extension, called Weighted STL (wSTL), has the same qualitative (Boolean) semantics as STL, but additionally defines weights associated with Boolean and temporal operators that modulate its quantitative semantics (robustness). We show that the robustness of wSTL can be defined as weighted generalizations of all known compatible robustness functionals (i.e., robustness scores that are recursively defined over formulae) that can take into account the weights in wSTL formulae. We utilize this weighted robustness to distinguish signals with respect to a desired wSTL formula that has sub-formulae with different importance or priorities and time preferences, and demonstrate its usefulness in problems with conflicting tasks where satisfaction of all tasks cannot be achieved. We also employ wSTL robustness in an optimization framework to synthesize controllers that maximize satisfaction of a specification with user specified preferences.

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“…For deterministic discrete-time systems, the authors in [10] transform the STL specification into mixed-integer linear constraints and use Model Predictive Control (MPC) to deal with these constraints. Similarly, MPC has been employed by maximizing certain forms of the quantitative semantics associated with the STL specification at hand [8], [9], [11]. These methods seem computationally more tractable than the approach presented in [10] due to the use of smooth quantitative semantics.…”

Section: Introductionmentioning

confidence: 99%

Control Design for Risk-Based Signal Temporal Logic Specifications

Safaoui,

Lindemann,

Dimarogonas

et al. 2020

Preprint

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We present a general framework for risk semantics on Signal Temporal Logic (STL) specifications for stochastic dynamical systems using axiomatic risk theory. We show that under our recursive risk semantics, risk constraints on STL formulas can be expressed in terms of risk constraints on atomic predicates. We then show how this allows a (stochastic) STL risk constraint to be transformed into a risk-tightened deterministic STL constraint on a related deterministic nominal system, enabling the application of existing STL methods. For affine predicate functions and a (coherent) Distributionally Robust Value at Risk measure, we show how risk constraints on atomic predicates can be reformulated as tightened deterministic affine constraints. We demonstrate the framework using a Model Predictive Control (MPC) design with an STL risk constraint.

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Average-based Robustness for Continuous-Time Signal Temporal Logic

Cited by 17 publications

References 25 publications

Temporal Robustness of Temporal Logic Specifications: Analysis and Control Design

Temporal Robustness of Temporal Logic Specifications: Analysis and Control Design

Specifying User Preferences using Weighted Signal Temporal Logic

Control Design for Risk-Based Signal Temporal Logic Specifications

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