Safety-Critical Control With Input Delay in Dynamic Environment

Abstract

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.

Nonlinear predictor‐feedback cooperative adaptive cruise control of vehicles with nonlinear dynamics and input delay

“…We consider a scenario in which D = 0.5, h = 0.75, while for the vehicles we set d = 0.00025, c = 0.0005, g = 0.002, and 𝜏 = 0.3, which are realistic values for vehicles. 10,13,19 We choose…”

“…In fact, such dynamic models are also viewed as extensions, of (classical) nonlinear vehicle models employed for ACC/CACC design and analysis, 19,[21][22][23] to incorporate input delay, which may be more realistic in practice. 13,26,27 For the leading vehicle's speed dynamics, adopting the notation v l ≡ v 0 , T l ≡ T 0 , u l ≡ u 0 , we assume that ̇vl (t) = T l (t),…”

“…10 ACC and CACC designs, aiming at delay compensation* in vehicular platoons, have been already developed. 1,2,6,[9][10][11][12][13][14][15][16][17][18] Almost all of these results utilize linear or linearized models for each individual vehicular system, for either control design or stability and string stability analysis. Nevertheless, these models, in certain scenarios, may not be as realistic as nonlinear vehicle models (for both control design and analysis) that may capture additional, lower-level vehicle dynamics.…”

“…However, considering nonlinear models of vehicle dynamics is important because a nominal (i.e., without a predictor structure), feedback linearizing pre-compensator, which may be implicitly employed in control of vehicular platoons (to subsequently enabling linear, ACC/CACC designs), may not result in a linear vehicle model, due to the presence of actuation delay. To the best of our knowledge, the only result that is related to construction of a nonlinear predictor-feedback ACC (or CACC) design can be found in the work of Molnar et al 13 In the present paper, complementing the results in Molnar et al, 13 we (a) consider a third-order model for the vehicles' dynamics; (b) construct a new nonlinear ACC law in the case in which there is no input delay; (c) design a predictor-feedback CACC law relying on real-time measurements of the acceleration and control input of the preceding vehicle (thus avoiding utilization of open-loop predictors, for the preceding vehicle's states, which, potentially, may be less robust); (d) provide the predictors formulae as explicitly as possible; (e) consider a platoon of vehicles; and (f) provide explicit conditions on initial conditions and control parameters, which guarantee positivity of speed and spacing states, as well as stability and regulation. In particular, we construct a nonlinear predictor-feedback CACC law, which aims at actuation delay compensation for vehicular platoons in which each vehicle's dynamics are described by a third-order, nonlinear system with input delay.…”

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

“…Therefore, the idea of predictor feedback 31‐34 is often used to eliminate the effect of the delay by predicting the future state from the actual state and the input history. Comprehensive literature about safety‐critical control with input delay for various applications can be found in References 35 and 36 for discrete time and in References 8,9,37‐39 for continuous time, while the works in References 40 and 41 include time‐varying and multiple input delays.…”