Safety guarantee for time-delay systems with disturbances

Liu, Wenyou; Bai, Ye; Li, Jiao; Zhan, Naijun

doi:10.1007/s11432-020-3266-6

Cited by 7 publications

(3 citation statements)

References 42 publications

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“…On the other hand, the safety of time delay systems has also attracted increasing attention in the recent literature. The safety of continuous-time systems with state delay was established by safety functionals in [33], [34], which were extended to control barrier functionals in [35]. Discrete-time control systems with input delay were studied in [36] for linear and in [37] for nonlinear dynamics.…”

Section: A State Of the Artmentioning

confidence: 99%

Safety-Critical Control With Input Delay in Dynamic Environment

Molnár

Ames

Orosz

2023

IEEE Trans. Contr. Syst. Technol.

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Endowing nonlinear systems with safe behavior is increasingly important in modern control. This task is particularly challenging for real-life control systems that must operate safely in dynamically changing environments. This paper develops a framework for safety-critical control in dynamic environments, by establishing the notion of environmental control barrier functions (ECBFs). The framework is able to guarantee safety even in the presence of input delay, by accounting for the evolution of the environment during the delayed response of the system. The underlying control synthesis relies on predicting the future state of the system and the environment over the delay interval, with robust safety guarantees against prediction errors. The efficacy of the proposed method is demonstrated by a simple adaptive cruise control problem and a more complex robotics application on a Segway platform.

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Section: A State Of the Artmentioning

confidence: 99%

Safety-Critical Control With Input Delay in Dynamic Environment

Molnár

Ames

Orosz

2023

IEEE Trans. Contr. Syst. Technol.

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“…Theorem proving is a powerful technique in computer science and mathematics that expresses and verifies systems in a machine-readable form, providing significant advantages in terms of correctness and precision, particularly for complex problems. Theorem proving can reduce errors and tedious reasoning processes and provides mathematicians and computer scientists with a more intuitive and reliable means of verification, playing a crucial role in computer science and mathematics [9][10][11][12]. However, for sufficiently complex problems, complete automation is often challenging, and for complicated proof procedures, relying solely on pen and paper is no longer reliable.…”

Section: Introductionmentioning

confidence: 99%

A Machine Proof System of Point Geometry Based on Coq

et al. 2023

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An important development in geometric algebra in recent years is the new system known as point geometry, which treats points as direct objects of operations and considerably simplifies the process of geometric reasoning. In this paper, we provide a complete formal description of the point geometry theory architecture and give a rigorous and reliable formal verification of the point geometry theory based on the theorem prover Coq. Simultaneously, a series of tactics are also designed to assist in the proof of geometric propositions. Based on the theoretical architecture and proof tactics, a universal and scalable interactive point geometry machine proof system, PointGeo, is built. In this system, any arbitrary point-geometry-solvable geometric statement may be proven, along with readable information about the solution’s procedure. Additionally, users may augment the rule base by adding trustworthy rules as needed for certain issues. The implementation of the system expands the library of Coq resources on geometric algebra, which will become a significant research foundation for the fields of geometric algebra, computer science, mathematics education, and other related fields.

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“…We remark that a few recent papers have also approached this problem parallel to our work. Namely, Reference 55 considers delays with disturbances while 56‐58 investigate the combination of stability and safety by the application of Razumikhin‐ and Krasovskii‐type control Lyapunov and control barrier functionals. Although these recent works share some of the ideas presented in this paper, we establish a comprehensive in‐depth study that is not covered by previous works.…”

Section: Introductionmentioning

confidence: 99%

Control barrier functionals: Safety‐critical control for time delay systems

Molnár

Ames

Orosz

2023

Intl J Robust & Nonlinear

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This work presents a theoretical framework for the safety-critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay-free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced, to attain formal safety guarantees by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples.

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Safety guarantee for time-delay systems with disturbances

Cited by 7 publications

References 42 publications

Safety-Critical Control With Input Delay in Dynamic Environment

Safety-Critical Control With Input Delay in Dynamic Environment

A Machine Proof System of Point Geometry Based on Coq

Control barrier functionals: Safety‐critical control for time delay systems

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