On the Necessity of Symmetric Positional Coupling for String Stability

Abstract

We consider a distributed system with identical agents, constant-spacing policy and asymmetric bidirectional control, where the asymmetry is due to different controllers, which we describe by transfer functions. By applying the wave transfer function approach, it is shown that, if there are two integrators in the dynamics of agents, then the positional coupling must be symmetric, otherwise the system is string unstable. The main advantage of the transfer function approach is that it allows us to analyse the bidirectional control with an arbitrary complex asymmetry in the controllers, for instance, the control with symmetric positional but asymmetric velocity couplings.

On L∞ string stability of nonlinear bidirectional asymmetric heterogeneous platoon systems

“…(Hao et al,Email address: giovanni.russo1@ucd.ie (Giovanni Russo). 2012; Martinec et al, 2016;Herman et al, 2017a,b), asymmetric bidirectional control algorithms have been considered, where the information from the vehicles ahead might be weighted differently than the information from the vehicles behind. Also, the platoon system is said to be homogeneous if the vehicles are all identical, heterogeneous otherwise.…”

An Adaptive Switched Control Approach to Heterogeneous Platooning With Intervehicle Communication Losses

“…Reference model (12) has been proven in [6] to be asymptotically stable around the equilibrium point…”

“…Therefore, the heterogeneous platoon with engine performance loss and control input (17) can be defined as system (13)- (18). Furthermore, taking (12) as the vehicle reference model, the adaptive control input is defined as…”

“…Theorem 1: Consider the heterogeneous platoon model (8) with reference model (12). Then, the adaptive input (19) with adaptive law (22) makes the platoon's dynamics asymptotically converge to string stable dynamics.…”

“…In [11], a linear controller was augmented by a model predictive control strategy to maintain the platoon's stability while integrating safety and physical constraints. In addition, for a platoon composed of identical agents with different controllers, [12] assessed the performance and challenges, in terms of string stability, of unidirectional and asymmetric bidirectional control strategies.…”