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Abstarct: 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. [ABSTRACT FROM AUTHOR]

Modern autonomous systems, such as flying, legged, and wheeled robots, are generally characterized by high-dimensional nonlinear dynamics, which presents challenges for model-based safety-critical control design. Motivated by the success of reduced-order models in robotics, this paper presents a tutorial on constructive safety-critical control via reduced-order models and control barrier functions (CBFs). To this end, we provide a unified formulation of techniques in the literature that share a common foundation of constructing CBFs for complex systems from CBFs for much simpler systems. Such ideas are illustrated through formal results, simple numerical examples, and case studies of real-world systems to which these techniques have been experimentally applied. [ABSTRACT FROM AUTHOR]

Machine tool vibrations in turning processes are analyzed by taking into account the nonlinearity of the cutting force characteristics. Unstable limit cycles are computed for the governing nonlinear delay-differential equation in order to determine the bistable technological parameter region where stable stationary cutting and large-amplitude machine tool vibrations coexist. Simple closed-form formulas are derived for the amplitude of limit cycles and for the size of the bistable region considering a general cutting force characteristics. The analytical results are determined by the method of averaging, which can be used to treat the nonlinearities without their third-order approximation. The results are confirmed by numerical continuation and using Melnikov's integral. • Nonlinear dynamics of turning processes is analyzed on an orthogonal cutting model. • Periodic solutions are computed analytically via the method of averaging. • Simple closed-form formula is derived to determine bistable parameter regions. [ABSTRACT FROM AUTHOR]

An application of the finite spectrum assignment (FSA) control technique is presented for unstable systems with feedback delay. The FSA controller predicts the actual state of the system over the delay period using an internal model of the real system. If the internal model is perfectly accurate then the feedback delay can be compensated. However, parameter mismatches of the internal model or implementation inaccuracies of the control law may result in an unstable control process. In this paper, the stabilizability of an undamped second-order system is analyzed for different system and delay parameter mismatches. Theoretical stability and robustness to implementation inaccuracies of the control law are discussed. It is shown that, for small parameter uncertainties, the FSA controller allows stabilization for significantly larger feedback delays than conventional delayed proportional-derivative-acceleration controllers do. [ABSTRACT FROM AUTHOR]

Orthogonal planing experiments are conducted with high-speed camera recordings and simultaneous cutting force measurements in order to analyze chip formation during machine tool vibrations. By means of carefully designed periodic forcing of the cutting tool, non-stationary cutting experiments are performed including wave generation, wave removal and wave-on-wave cutting, which are then compared to stationary cutting tests. The experiments are performed to address how the cutting force is affected by the chip thickness variation, the surface waviness and the fluctuation of the cutting direction. The results are used to assess some theoretical models that involve shear angle variation and chip segmentation. • Non-stationary cutting experiments are performed by orthogonal planing. • Wave generation, wave removal and wave-on-wave cutting are investigated. • High-speed camera recordings and simultaneous cutting force measurements are evaluated. • The effects of chip thickness variation, surface waviness and cutting direction fluctuation are analyzed. [ABSTRACT FROM AUTHOR]

The unsafe zone in machining is a region of the parameter space where steady-state cutting operations may switch to regenerative chatter for certain perturbations, and vice versa. In the case of milling processes, this phenomenon is related to the existence of an unstable quasi-periodic oscillation, the in-sets of which limit the basin of attraction of the stable periodic motion that corresponds to the chatter-free cutting process. The mathematical model is a system of time-periodic nonlinear delay differential equations. It is studied by means of a nonlinear extension of the semidiscretization method, which enables the estimation of the parameter ranges where the unsafe (also called bistable) zones appear. The theoretical results are checked with thorough experimental work: first, step-by-step parameter variations are adapted to identify hysteresis loops, then harmonic burst excitations are used to estimate the extents of the unsafe zones. The hysteresis loops are accurately distinguished from the dynamic bifurcation phenomenon that is related to the dynamic effect of slowly varying parameters. The experimental results confirm the existence of the bistable parameter regions. This article is part of the theme issue 'Nonlinear dynamics of delay systems'. [ABSTRACT FROM AUTHOR]

Connected automated vehicles (CAVs) have shown great potential in improving traffic throughput and stability. Although various longitudinal control strategies have been developed for CAVs to achieve string stability in mixed-autonomy traffic systems, the potential impact of these controllers on safety has not yet been fully addressed. This paper proposes safety-critical traffic control (STC) by CAVs—a strategy that allows a CAV to maintain safety relative to both the preceding vehicle and the following human-driven vehicles (HVs). Specifically, we utilize control barrier functions (CBFs) to impart collision-free behavior with formal safety guarantees to the closed-loop system. The safety of both the CAV and HVs is incorporated into the framework through a quadratic program-based controller that minimizes deviation from a nominal stabilizing traffic controller subject to CBF-based safety constraints. Considering that some state information of the following HVs may be unavailable to the CAV, we employ state observer-based CBFs for STC. Finally, we conduct extensive numerical simulations – that include vehicle trajectories from real data – to demonstrate the efficacy of the proposed approach in achieving provably safe traffic. [ABSTRACT FROM AUTHOR]