String Stability Analysis for Heterogeneous Vehicle Strings

Shaw, E.; Hedrick, J. Karl

doi:10.1109/acc.2007.4282789

Cited by 136 publications

(91 citation statements)

References 14 publications

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“…Reconsidering the definitions given by Swaroop and Hedrick (1996), Pant et al (2002), Ploeg et al (2014) and Shaw and Hedrick (2007b), the following generalized string stability definitions are proposed. Definition 1.…”

Section: Definition For Mixed Norm String Stabilitymentioning

confidence: 99%

“…The L p string stability is called strict, when the error bounds are non-increasing. Shaw and Hedrick (2007b) demonstrated that the latter condition is rather restrictive for heterogeneous platoons where the spacing error of a slow vehicle can be larger than the spacing error of its faster predecessor.…”

Section: Introductionmentioning

confidence: 99%

“…Uniform boundedness of the spacing errors (Shaw and Hedrick (2007b)), or convergence of the spacing errors to zero (Seiler et al (2004), Barooah and Hespanha (2005)) can be expressed in terms of norms |||E||| ∞,p or |||E||| 2,p , respectively. Remark 1.…”

Section: Problem Formulationmentioning

confidence: 99%

“…the platoon is string unstable. Shaw and Hedrick (2007b) calculated an explicit formulae for F i , with controllers such that K ia = K 0 ia = 0 in (6)-(7). In contrast, introducing the compact characterization (9), (10) and (19) allows a much simpler proof and the possibility for generalization of the theorem to other interconnection topologies.…”

Section: Conditions Of Robust Mixed Norm String Stabilitymentioning

confidence: 99%

“…Consider V i as the following model for the longitudinal dynamics of the ith vehicle in the platoon (Shaw and Hedrick (2007b)…”

Section: Problem Formulationmentioning

confidence: 99%

See 4 more Smart Citations

Leader and Predecessor Following Robust Controller Synthesis for String Stable Heterogeneous Vehicle Platoons

Rödönyi

2015

IFAC-PapersOnLine

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Conditions of string (in)stability for look-ahead interconnected vehicle systems are presented based on a compact characterization of the interconnected system. Continuous-time local models describe the temporal evolution of the state-variables of one vehicle. Discrete spatially varying systems describe the spatial evolution of local systems. The problem of string stability analysis of large scale interconnected systems is reduced to the stability analysis of two simple dynamic systems. The evaluation of worst-case spacing errors, as responses to bounded L 2 leader acceleration, can be upper-bounded by computing the step-response to a simple discrete linear system. Based on the compact characterization, it is also shown that the string stability requirement can be directly converted to a standard H ∞ control problem. The efficiency of the synthesis method is demonstrated on a numerical example.

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Section: Definition For Mixed Norm String Stabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Conditions Of Robust Mixed Norm String Stabilitymentioning

confidence: 99%

“…Consider V i as the following model for the longitudinal dynamics of the ith vehicle in the platoon (Shaw and Hedrick (2007b)…”

Section: Problem Formulationmentioning

confidence: 99%

See 3 more Smart Citations

Leader and Predecessor Following Robust Controller Synthesis for String Stable Heterogeneous Vehicle Platoons

Rödönyi

2015

IFAC-PapersOnLine

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Exponential Mean‐Square Stability of Stochastic String Hybrid Systems Under Continuous Non‐Gaussian Excitation

Socha

2018

Asian Journal of Control

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The problem of the exponential mean-square stability for nonlinear stochastic string hybrid system under parametric (multiplicative) Gaussian and external (additive) continuous non-Gaussian excitations is considered. The string hybrid system is treated as an infinite-dimensional family of strings (subsystems) with a switching rule that has the form of a right continuous Markov chain. It is described by infinite-dimension Ito stochastic differential equations. The excitations are assumed to be parametric Gaussian white noises and the continuous non-Gaussian processes modeled by polynomials of a Gaussian process. The nonlinear strings under external continuous non-Gaussian excitation are transformed to extended dimensional nonlinear strings with a special structure under a parametric Gaussian excitation. Using the methodology of the stability analysis of nonlinear hybrid systems with Markovian switchings the sufficient conditions of the exponential mean-square stability of nonlinear stochastic string systems under parametric Gaussian and external continuous non-Gaussian excitation with a Markovian switching are derived. The detailed calculations are given for linear systems.

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Robust static output feedback synthesis for platoons under leader and predecessor feedback

Köroğlu

Falcone

2016

Intl J Robust & Nonlinear

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A multi-objective static output feedback synthesis problem is considered for the control of vehicle platoons under leader and predecessor feedback. Sufficient linear matrix inequality conditions are derived for the solvability of the problem in a way to facilitate static feed-forward as well. A novel velocity-dependent spacing policy is integrated into the control scheme together with a platoon model in which the emphasis on the predecessor information can be adjusted by a normalized scalar weight. It is shown that the string stability of the spacing errors and the acceleration signals can always be guaranteed by choosing this weight sufficiently small. Moreover, provided that the time headway is chosen sufficiently large, the synthesis can be performed in a way to avoid the amplification of acceleration energies if compared with the leader. As a particularly convenient feature, the target spacing between the vehicles becomes smaller when moving backward along the platoon. The total increase in the platoon length caused by the introduction of the velocity-dependent scheme is shown to be bounded and decreasing with decreasing predecessor weight. It is also established that the predecessor weight can be adjusted smoothly over time without endangering the formation stability. In addition to the optimization of the parameters of common fixed-structure controllers for general vehicle models, the proposed synthesis procedure provides various tools for improving robustness against measurement noise, communication delay, and model uncertainty.It is quite common to consider the platoon control problem based on linear vehicle models obtained by favor of exact feedback linearization [19][20][21][22]. The simplest one is a kinematic model referred to as the double integrator: acceleration (as the control input) to velocity, velocity to position. Because of the (typically uncertain) dynamics of the engine, it is necessary to consider slightly more advanced models in practical designs. The vehicle as a whole is hence usually viewed as a first-order system identified by a (possibly velocity-dependent) time constant referred to as the 'time lag ' [19, 23, 24]. This model is used to represent the transfer function from the given acceleration command to the actual acceleration of the vehicle. In more advanced models, a control input (i.e., actuator) delay is also assumed [5][6][7][25][26][27][28]. It is common to consider identical vehicle models with which the corresponding platoons are referred to as 'homogenous'. The analysis and synthesis problems get much more complicated for 'heterogenous' platoons in which the vehicles have different models [5,29]. For successful practical designs, one needs to take into account the uncertainty in the time lag and/or the actuator delay (as might be encountered in trucks due to switching dynamics with gear changes) in addition to heterogeneity [26].The main goal in a platoon formation is to maintain desirably small spacings between the vehicles by realizable acceleration/deceleration comman...

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String Stability Analysis for Heterogeneous Vehicle Strings

Cited by 136 publications

References 14 publications

Leader and Predecessor Following Robust Controller Synthesis for String Stable Heterogeneous Vehicle Platoons

Leader and Predecessor Following Robust Controller Synthesis for String Stable Heterogeneous Vehicle Platoons

Exponential Mean‐Square Stability of Stochastic String Hybrid Systems Under Continuous Non‐Gaussian Excitation

Robust static output feedback synthesis for platoons under leader and predecessor feedback

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