1. About strong string stability of a vehicle chain with time-headway control
- Author
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Alain Sarlette, Arash Farnam, Universiteit Gent = Ghent University [Belgium] (UGENT), QUANTum Information Circuits (QUANTIC), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office., École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-MINES ParisTech - École nationale supérieure des mines de Paris, Universiteit Gent = Ghent University (UGENT), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL), and Sarlette, Alain
- Subjects
Time headway ,050210 logistics & transportation ,0209 industrial biotechnology ,String length ,Technology and Engineering ,Proportional derivative ,SUBJECT ,PLATOONS ,05 social sciences ,[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC] ,02 engineering and technology ,Chain length ,020901 industrial engineering & automation ,Control theory ,Optimization and Control (math.OC) ,Norm (mathematics) ,Bounded function ,[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering ,0502 economics and business ,FOS: Mathematics ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Absolute velocity ,Mathematics - Optimization and Control ,[INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering ,Mathematics - Abstract
This paper deals with the problem of string stability in a chain of acceleration-controlled vehicles, i.e. how input disturbances affect the distributed system for very long chains. There exist variants of string stability, like avoiding that a local disturbance gets amplified along the chain, or more strongly ensuring that the output vector's p-norm remains bounded for any bounded vector of input disturbances independently of the string length. They are all impossible to achieve with any linear controller if the vehicles only use relative information of few vehicles in front. Previous work has shown that adding absolute velocity into the controller, allows to at least avoid amplification of a local disturbance. In this paper, we consider the stronger definitions of string stability, under this same relaxation of using absolute velocity in the controller. We prove that the influence from input vector to output vector cannot be bounded independently of chain length in the most popular 2-norm sense, with any bounded stabilizing linear controller; while a proportional derivative (PD) controller can guarantee it in the practically relevant infinity-norm sense. Moreover, we identify the disturbance acting on the leader as the main issue for string stability., Comment: presented at IEEE-CDC 2018, Miami; more complete version and correcting a few typos
- Published
- 2019