Constrained Stabilization of Multi-Input Linear Systems with Distinct Input Delays

Safety-Critical Control With Input Delay in Dynamic Environment

“…Discrete-time control systems with input delay were studied in [36] for linear and in [37] for nonlinear dynamics. Linear control systems with input delays were investigated in continuous time in [38], [39] via control barrier and control Lyapunov functions. Safetycritical control of continuous-time nonlinear systems with measurement delays was tackled in our works [10], [11] in an application to controlling the spread of COVID-19.…”

Constrained control of multi‐input systems with distinct input delays

“…Similarly, in the works of Molnár et al 24 and Singletary et al 23 (sampled-data systems) the safety of systems with a single input delay was considered, and in the work of Jankovi ć, 19 the author leverages results from the works of Krsti ć25,26 to develop controllers for safely stabilizing multi-input linear systems with same-length delays across input channels. This result was later extended in our previous work 21 to linear systems with distinct delays across input channels using state-predictor designs from the works of Tsubakino and Krsti ć27 and Bekiaris-Liberis and Krsti ć. 28 The result in our work 21 was the first to consider safety for multi-input systems with distinct input delays.…”

“…This result was later extended in our previous work 21 to linear systems with distinct delays across input channels using state-predictor designs from the works of Tsubakino and Krsti ć27 and Bekiaris-Liberis and Krsti ć. 28 The result in our work 21 was the first to consider safety for multi-input systems with distinct input delays. However, just like all the aforementioned results for systems with input delays, safety-guarantees are made only after the longest input delay has been compensated; that is, after the longest input delay time has elapsed.…”

“…10,11 As interest in CBFs have developed over time, several extensions have emerged that render CBFs applicable to systems of different forms. For example, CBFs have been used for the safe operation of hybrid 12 and discrete-time 13,14 systems; robust CBF formulations 15,16 have also been developed for enforcing safety in the presence of disturbances, 17 and several studies (see References 10,11,[18][19][20][21][22][23][24] have explored the usage of CBFs for systems with delays. In particular, in the work of Prajna and Jadbabaie 18 and the work of Orosz and Ames, 22 Lyapunov-Krasovskii-like functionals were developed for verifying safety in systems with state delays; and in the works of Ames et al 10 and Molnár et al, 11 the problem of safety in the context of infectious disease control with a single measurement delay was considered.…”

Input-to-State Safety with Input Delay in Longitudinal Vehicle Control

“…In this work, we address safe vehicle control in the presence of both input delay and input disturbance. Recently, safety-critical control with input delay has been addressed in discrete time (Liu et al, 2020;Singletary et al, 2020) and in continuous time for linear systems (Jankovic, 2018a;Abel et al, 2019) and nonlinear systems (Molnar et al, 2021), including multiple and time-varying input delays (Abel et al, 2020(Abel et al, , 2021. Furthermore, the safety of delayfree systems with input disturbance have been investigated by robust control barrier functions (Jankovic, 2018b) and using the notion of input-to-state safety (Kolathaya and Ames, 2019;Alan et al, 2022).…”