  We study how to design a secure observer-based distributed controller such
that a group of vehicles can achieve accurate state estimates and formation
control even if the measurements of a subset of vehicle sensors are compromised
by a malicious attacker. We propose an architecture consisting of a resilient
observer, an attack detector, and an observer-based distributed controller. The
distributed detector is able to update three sets of vehicle sensors: the ones
surely under attack, surely attack-free, and suspected to be under attack. The
adaptive observer saturates the measurement innovation through a preset static
or time-varying threshold, such that the potentially compromised measurements
have limited influence on the estimation. Essential properties of the proposed
architecture include: 1) The detector is fault-free, and the attacked and
attack-free vehicle sensors can be identified in finite time; 2) The observer
guarantees both real-time error bounds and asymptotic error bounds, with
tighter bounds when more attacked or attack-free vehicle sensors are identified
by the detector; 3) The distributed controller ensures closed-loop stability.
The effectiveness of the proposed methods is evaluated through simulations by
an application to vehicle platooning.
