Resilient Reachability for Linear Systems

Bouvier, Jean Baptiste; Ornik, Melkior

doi:10.1016/j.ifacol.2020.12.372

Cited by 8 publications

(28 citation statements)

References 15 publications

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“…Notice that in previous work [5,6] the L 2 -norm of the inputs was constrained. In this work we consider instead L ∞ bounds because they are more widely used in applications.…”

Section: Definitionmentioning

confidence: 99%

“…In this work we consider instead L ∞ bounds because they are more widely used in applications. Therefore, most of the resiliency conditions of [5,6] do not directly apply here. We will establish a simple necessary condition for this new setting using only basic linear algebra.…”

Section: Definitionmentioning

confidence: 99%

“…However, when actuators can be subject to damage or hostile takeover, the malfunction may result in the actuators producing undesirable inputs over which the controller has real-time readings but no control. This type of malfunction has been discussed in [5] under the name of loss of control authority over actuators and encompasses scenarios where actuators and sensors are under attack [8].…”

Section: Introductionmentioning

confidence: 99%

“…After a partial loss of control authority over actuators, a target is said to be resiliently reachable if for any undesirable inputs produced by the malfunctioning actuators there exists a control driving the state to the target [5]. However, after the loss of control the malfunctioning system might need considerably more time to reach its target compared to the initial system.…”

Section: Introductionmentioning

confidence: 99%

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Quantitative Resilience of Linear Driftless Systems

Bouvier¹,

Xu²,

Ornik³

2021

Preprint

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This paper introduces the notion of quantitative resilience of a control system. Following prior work, we study systems enduring a loss of control authority over some of their actuators. Such a malfunction results in actuators producing possibly undesirable inputs over which the controller has real-time readings but no control. By definition, a system is resilient if it can still reach a target after a partial loss of control authority. However, after a malfunction, a resilient system might be significantly slower to reach a target compared to its initial capabilities. We quantify this loss of performance through the new concept of quantitative resilience. We define such a metric as the maximal ratio of the minimal times required to reach any target for the initial and malfunctioning systems. Naive computation of quantitative resilience directly from the definition is a complex task as it requires solving four nested, possibly nonlinear, optimization problems. The main technical contribution of this work is to provide an efficient method to compute quantitative resilience. Relying on control theory and on two novel geometric results we reduce the computation of quantitative resilience to a single linear optimization problem. We illustrate our method on two numerical examples: an opinion dynamics scenario and a trajectory controller for low-thrust spacecrafts.

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“…Notice that in previous work [5,6] the L 2 -norm of the inputs was constrained. In this work we consider instead L ∞ bounds because they are more widely used in applications.…”

Section: Definitionmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantitative Resilience of Linear Driftless Systems

Bouvier¹,

Xu²,

Ornik³

2021

Preprint

Self Cite

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“…That is why such critical systems must be able to operate safely even after sustaining actuator failures. This paper is a continuation of our initial work in [2] and discusses design of resilient systems able to withstand the loss of control authority over any actuator, and still be able to reach their initial target. Redundancy is the key to guarantee the resiliency of a system, as proven by NASA during the space race [3].…”

Section: Introductionmentioning

confidence: 98%

Designing Resilient Linear Driftless Systems

Bouvier¹,

Ornik²

2020

Preprint

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Critical systems must be designed resilient to the loss of control authority over some of their actuators. This paper investigates the design of resilient linear systems capable of reaching their target even after one or multiple actuators started to produce uncontrolled and undesirable inputs. In contrast with the setting considered by robust control, where perturbations are unknown, we consider undesirable inputs produced by a faulty actuator belonging to the system and thus observed in real time. The control inputs can then depend on these undesirable inputs. Building on our previous work, we establish two novel sufficient conditions for resilient reachability. We then focus on designing resilient systems able to withstand the loss of one or multiple actuators. Since resiliency refers to the existence of a control law driving the state to the target, we naturally continue with the synthesis of such a control law. We conclude with a numerical application of our theory on the ADMIRE fighter jet model.

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Resilience of linear systems to partial loss of control authority

Bouvier

Ornik

2023

Automatica

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Resilient Reachability for Linear Systems

Cited by 8 publications

References 15 publications

Quantitative Resilience of Linear Driftless Systems

Quantitative Resilience of Linear Driftless Systems

Designing Resilient Linear Driftless Systems

Resilience of linear systems to partial loss of control authority

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