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In this paper, we study the internal stability and string stability of avehicle platoon under the constant time headway spacing (CTHS) policy and themultiple-predecessor-following (MPF) vehicle-to-vehicle information flowtopology. More specifically, we depart from the conventionalProportional-Integral-Derivative (PID) controller design for such systems andwe propose the design of an observer-based controller. For designing ourobserver-based controller, we first design a distributed observer, with whicheach follower estimates their position, speed and acceleration error withrespect to the leader. The observer is designed by means of constructing anobserver matrix whose parameters should be determined. Next, we simplify thedesign of the matrix of the observer in such a way that the design boils downto choosing a single scalar value; this design further simplifies the structureof the controller, whose simplicity enables the derivation of string stabilityconditions by means of a frequency response method. Subsequently, the stringstability conditions for a given time headway, are transformed to conditionsfor the controller parameters. We obtain controller parameters that satisfy thestability conditions by designing a novel heuristic search algorithm.Furthermore, we extend the search algorithm by incorporating a bisection-likealgorithm, which allows to obtain (within some deviation tolerance) the minimumavailable value of the time headway. Finally, we provide insights about how tofinalize the observer-based controller parameters from above algorithms toavoid the peaking phenomenon. The performance of the proposed observer-basedcontroller is demonstrated via illustrative examples. Additionally, acomparison with a widely-used PID controller for MPF topology shows that ourproposed observer-based controller has better convergence performance.

Internal and String Stability of an Observer-based Controller for Vehicle Platooning under the MPF Topology