Stability Margin Scaling Laws for Distributed Formation Control as a Function of Network Structure

We consider the problem of distributed formation control of a large number of vehicles. An individual vehicle in the formation is assumed to be a fully actuated point mass. A distributed control law is examined: the control action on an individual vehicle depends on (i) its own velocity and (ii) the relative position measurements with a small subset of vehicles (neighbors) in the formation. The neighbors are defined according to an information graph. In this paper we describe a methodology for modeling, analysis, and distributed control design of such vehicular formations whose information graph is a D-dimensional lattice. The modeling relies on an approximation based on a partial differential equation (PDE) that describes the spatio-temporal evolution of position errors in the formation. The analysis and control design is based on the PDE model. We deduce asymptotic formulae for the closed-loop stability margin (absolute value of the real part of the least stable eigenvalue) of the controlled formation. The stability margin is shown to approach 0 as the number of vehicles N goes to infinity. The exponent on the scaling law for the stability margin is influenced by the dimension and the structure of the information graph. We show that the scaling law can be improved by employing a higher dimensional information graph. Apart from analysis, the PDE model is used for a mistuning-based design of control gains to maximize the stability margin. Mistuning here refers to small perturbation of control gains from their nominal symmetric values. We show that the mistuned design can have a significantly better stability margin even with a small amount of perturbation. The results of the analysis with the PDE model are corroborated with numerical computation of eigenvalues with the state-space model of the formation.Comment: This paper is the expanded version of the paper with the same name which is accepted by the IEEE Transactions on Automatic Control. The final version is updated on Oct. 12, 201

String stable integral control design for vehicle platoons with disturbances

This paper presents a control design with integral action for vehicle platoons with disturbance that ensures string stability of the closed loop and disturbance rejection. The addition of integral action and a coordinate change allows to develop sufficient smoothness conditions on the closed loop system to ensure that the closed loop system using the proposed controller is string stable in the presence of time-varying disturbances and able able to reject constant disturbances. In addition, bounds for the tracking error of the platoon configuration are also given. Further, a case study is considered together with a suitable controller structure, which satisfies the required smoothness conditions. Simulation results illustrate the performance of the closed loop.Comment: 7 pages, 3 figures, submitted to Automatic

Stability and scalability of homogeneous vehicular platoon: study on the influence of information flow topologies

In addition to decentralized controllers, the information flow among vehicles can significantly affect the dynamics of a platoon. This paper studies the influence of information flow topology on the internal stability and scalability of homogeneous vehicular platoons moving in a rigid formation. A linearized vehicle longitudinal dynamic model is derived using the exact feedback linearization technique, which accommodates the inertial delay of powertrain dynamics. Directed graphs are adopted to describe different types of allowable information flow interconnecting vehicles, including both radar-based sensors and vehicle-to-vehicle (V2V) communications. Under linear feedback controllers, a unified internal stability theorem is proved by using the algebraic graph theory and Routh-Hurwitz stability criterion. The theorem explicitly establishes the stabilizing thresholds of linear controller gains for platoons, under a large class of different information flow topologies. Using matrix eigenvalue analysis, the scalability is investigated for platoons under two typical information flow topologies, i.e., 1) the stability margin of platoon decays to zero as 0(1/N2) for bidirectional topology; and 2) the stability margin is always bounded and independent of the platoon size for bidirectional-leader topology. Numerical simulations are used to illustrate the results

Transient Analysis and Control for Scalable Network Systems

The rapidly evolving domain of network systems poses complex challenges, especially when considering scalability and transient behaviors. This thesis aims to address these challenges by offering insights into the transient analysis and control design tailored for large-scale network systems. The thesis consists of three papers, each of which contributes to the overarching goal of this work.The first paper, A closed-loop design for scalable high-order consensus, studies the coordination of nth-order integrators in a networked setting. The paper introduces a novel closed-loop dynamic named serial consensus, which is designed to achieve consensus in a scalable manner and is shown to be implementable through localized relative feedback. In the paper, it is shown that the serial consensus system will be stable under a mild condition — that the underlying network contains a spanning tree — thereby mitigating a previously known scale fragility. Robustness against both model and feedback uncertainties is also discussed.The second paper, Closed-loop design for scalable performance of vehicular formations, expands on the theory on the serial consensus system for the special case when n=2, which is of special interest in the context of vehicular formations. Here, it is shown that the serial consensus system can also be used to give guarantees on the worst-case transient behavior of the closed-loop system. The potential of achieving string stability through the use of serial consensus is explored.The third paper, Input-output pseudospectral bounds for transient analysis of networked and high-order systems, presents a novel approach to transient analysis of networked systems. Bounds on the matrix exponential, coming from the theory on pseudospectra, are adapted to an input-output setting. The results are shown to be useful for high-order matrix differential equations, offering a new perspective on the transient behavior of high-order networked systems

Stability Analysis of a Predecessor-Following Platoon of Vehicles With Two Time Delays

The problem of controlling a platoon of vehicles moving in one dimension is considered so that they all follow a lead vehicle with constant spacing between successive vehicles. The stability and the string stability of a platoon of vehicles with two independent and uncertain delays, one in the inter-vehicle distance and the other in the relative velocity information channels, are considered. The main objectives of this paper are: (1) using a simplifying factorization procedure and deploying the cluster treatment of characteristic roots (CTCR) paradigm to obtain exact stability boundaries in the domain of the delays, and (2) for the purpose of disturbance attenuation, the string stability analysis is examined. Finally, a simulation example of multiple vehicle platoon control is used to demonstrate the effectiveness of the proposed method