Achieving an $\mathcal{L}_{2}$ string stable one vehicle look-ahead platoon with heterogeneity in time-delays

Abstract

A methodology is proposed to design stabilising and robust fixed-order decentralised controllers for heterogeneous vehicular platoons with Cooperative Adaptive Cruise Control (CACC). We consider Linear Time Invariant (LTI) models with constant time-delays at state, input and output. The closed-loop systems of (identical) local controllers and heterogeneous parameter vehicles are modelled by a system of delay differential algebraic equations. The proposed frequency domain approach uses the non-conservative direct optimisation approach towards stabilisation and robustness optimisation of delay systems. In this paper, the design problem of stabilising (identical) controllers achieving L2 string stability for one vehicle look-ahead platoon is reduced to a simultaneous controller design problem for a parameterised (sub)system, where the allowable values of the parameters correspond to heterogeneity (including time-delays) of the vehicles. By treating the heterogeneity in parameters as perturbations contained in specific intervals or regions, we determine the values for pseudo-spectral abscissa and robust induced-L2 norm. Hence, we ensure that the achieved exponential stability and string stability properties along with the overall computational complexity (of designing the controller) are independent of the number of vehicles. The application of CACC is simulated in MATLAB software.

On Time Headway Selection in Platoons Under the MPF Topology in the Presence of Communication Delays

“…As the roots of ( 30) are given by those of (34) (for i ∈ N N ), we will proceed by stability analysis on the basis of (34).…”

“…2) Internal Stability in Presence of Time Delays: If the roots of (34) lie in the complex left-half plane, then the system is stable. It can be easily deduced that s = 0 and s = −1/τ i cannot be the solution to (34), if…”

“…The effects of sampling, zero-order hold (ZOH) and constant time delay on string stability are investigated and the maximum allowable time delays for different sampling times and time headway are characterized. In [34], for one vehicle look-ahead CACC system with the third-order linear model, identical local controllers are proposed which guarantee strict L 2 string stability, in the presence of different types of delays, actuation, communication and sensor delay. In [35] and [36], platooning control has been solved by treating it as the problem of achieving consensus in a network with time delays.…”

Towards Establishing String Stability Conditions For Heterogeneous Vehicle Platoons Under the MPF Topology

“…In [6], string stability is investigated for heterogeneous platoons, but only for the PF topology. In [11], a heterogeneous platoon with the one vehicle look-ahead topology is considered and an identical controller is proposed to achieve strict L 2 string stability. In [12], a new class of controllers is proposed for heterogeneous platoons with CACC, that can work without requiring knowledge about the driveline dynamics of the preceding vehicle.…”

Reducing the Standstill Spacing and Duration of Safe Braking Control in Vehicle Platoons With Delays

“…There are various types of delays existing in practical platoon systems, which can be divided into two categories according to the execution stages of the braking control process: signal acquisition delays and control parameter calculation delays. The first category mainly includes communication delays [6] and sensor delays [7], [8]. Communication delays are caused by information transmission and the queuing of data packets, which are restricted by wireless channel quality and spectrum bandwidth; this type of delay ranges from a few milliseconds to tens of milliseconds.…”