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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]

In this paper, we investigate a vehicular string traveling on a single lane, where vehicles use connected cruise control to regulate their longitudinal motion based on data received from other vehicles via wireless vehicle-to-vehicle communication. Assuming digital controllers, the sample-and-hold units introduce time-periodic time delays in the control loops and the delays increase when data packets are lost. We investigate the effect of packet losses on plant and string stability while varying the control gains and determine the minimum achievable time gap below which stability cannot be achieved. We propose two predictor feedback control strategies that overcome the destabilizing effect of the time delay caused by the sample-and-hold unit and packet losses. [ABSTRACT FROM PUBLISHER]

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]

We introduce a methodology to guarantee safety against the spread of infectious diseases by viewing epidemiological models as control systems and human interventions (such as quarantining or social distancing) as control input. We consider a generalized compartmental model that represents the form of the most popular epidemiological models and we design safety-critical controllers that formally guarantee safe evolution with respect to keeping certain populations of interest under prescribed safe limits. Furthermore, we discuss how measurement delays originated from incubation period and testing delays affect safety and how delays can be compensated via predictor feedback. We demonstrate our results by synthesizing active intervention policies that bound the number of infections, hospitalizations and deaths for epidemiological models capturing the spread of COVID-19 in the USA., (© IEEE 2020.)

The world has recently undergone the most ambitious mitigation effort in a century, consisting of wide-spread quarantines aimed at preventing the spread of COVID-19. The use of influential epidemiological models of COVID-19 helped to encourage decision makers to take drastic non-pharmaceutical interventions. Yet, inherent in these models are often assumptions that the active interventions are static, e.g., that social distancing is enforced until infections are minimized, which can lead to inaccurate predictions that are ever evolving as new data is assimilated. We present a methodology to dynamically guide the active intervention by shifting the focus from viewing epidemiological models as systems that evolve in autonomous fashion to control systems with an "input" that can be varied in time in order to change the evolution of the system. We show that a safety-critical control approach to COVID-19 mitigation gives active intervention policies that formally guarantee the safe evolution of compartmental epidemiological models. This perspective is applied to current US data on cases while taking into account reduction of mobility, and we find that it accurately describes the current trends when time delays associated with incubation and testing are incorporated. Optimal active intervention policies are synthesized to determine future mitigations necessary to bound infections, hospitalizations, and death, both at national and state levels. We therefore provide means in which to model and modulate active interventions with a view toward the phased reopenings that are currently beginning across the US and the world in a decentralized fashion. This framework can be converted into public policies, accounting for the fractured landscape of COVID-19 mitigation in a safety-critical fashion., (This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.)

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'.