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Abstract:
We consider a decentralized bidirectional control of a platoon
of N identical vehicles moving in a straight line. The
controlobjective is for each vehicle to maintain a constant
velocity andinter-vehicular separation using only the local
information from itself and its two nearest neighbors. Each
vehicle is modeled as a double integrator. To aid the analysis,
we use continuous approximation to derive a partial
differential equation (PDE) approximation of the discrete
platoon dynamics. The PDE model isused to explain the
progressive loss of closed-loop stability margin with
increasing number of vehicles, and to devise ways to combat
this loss of stability margin.
If every vehicle uses the same controller, we
show that the least stable closed-loop eigenvalue approaches
zero as O(1/N^2) in the limit of a large number (N) of
vehicles. We then show how to ameliorate this loss of stability
margin by small amounts of ``mistuning'', i.e., changing the
controller gains from their nominal values. We prove that with
arbitrary small amounts of mistuning, the asymptotic behavior
of the least stable closed loop eigenvalue can be improved to
O(1/N). All the conclusions drawn from analysis of the PDE
model are corroborated via numerical calculations of the
state-space platoon model.
[PDF ]
codes:
trendwithN_eigval_platoon.m
: MATLABİ script to compute and plot the least stable
eigenvalue of the closed loop platoon as a function of N, with
and without mistuning. It needs the following two MATLAB
functions:
F_platoon_eigvals.m
: computes the eigenvalues
F_gains_platoon.m
computes the control gains with a specified level of mistuning.
slinkycheck_reviewer1.m
: MATLABİ script to compute and plot the H-infinity norm of the
transfer function from external disturbances to the spacing
errors for the control law U_i = -k_p(Z_{i}-Z_{i-1}) -
k_v(\dot{Z}_i - \dot{Z}_{i-1}) - c_v(\dot{Z}_i - V_d)
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