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Zhang et al. Intell Robot 2022;2(4):371­90 I http://dx.doi.org/10.20517/ir.2022.26 Page 373

tires and roads, which does not precisely describe the lateral dynamical characteristics involved, leading to
severe degradation or even instability of a closed-loop system, especially when a vehicle travels at high accel-
eration. The longitudinal velocity is intrinsically time-varying but is regarded as a constant in a few studies,
which should also be addressed. The present study has been motivated by all these considerations.

The problem of adaptive cruise control design for longitudinal car-following considering vehicle lateral stabil-
ity is investigated in this study. Vehicle longitudinal car-following kinematics are used in conjunction with two
degrees-of-freedom vehicle lateral dynamics to formulate an adaptive cruise control system as a robust track-
ing control problem of a T-S fuzzy system by considering real-time variations of the velocity of the preceding
vehicle. The corresponding control problem is then transformed into a min-max optimization problem within
the T-S fuzzy control framework. The concept of robust positively invariant sets is introduced to effectively
address some external norm-bounded disturbances, such as the steering angle of the front wheel and the accel-
eration of the preceding vehicle, to ensure that the states of the closed-loop tracking dynamics converge to a
compact set. Finally, results of simulations using the CarSim/MATLAB joint platform are presented to demon-
strate the effectiveness of using the proposed adaptive cruise controller to realize longitudinal car-following
while ensuring vehicle lateral stability.

The main contributions of this study are as follows:

(1)aT-SfuzzycontrolframeworkisusedtofirstestablishaunifiedT-Sfuzzydynamicalmodelforcar-following
based on a combination of longitudinal kinematics, lateral dynamics, time-varying vehicle velocity, and non-
linear lateral tire/road forces as a basis for designing adaptive cruise control;

(2) a method is proposed for designing a coordinated controller of an adaptive cruise control system and a
direct yaw moment control system that ensures simultaneous vehicle longitudinal car-following and lateral
stability;

(3) the developed controller design method is validated by tests in a high-fidelity CarSim/Simulink joint simu-
lation environment, and the results clearly show the effectiveness of the T-S fuzzy model predictive controller
and its superiority over a conventional controller design process that does not consider vehicle lateral stabi-
lization.

The remainder of this paper is organized as follows. A mathematical model for a vehicle is presented in Section
II, which includes longitudinal kinematics, lateral dynamics, and a tire/road force model. A design for a robust
T-S fuzzy model predictive controller is presented in Section III. In Section IV, the lower layer of the designed
adaptive cruise control algorithm is described. The CarSim/Simulink joint simulation results are presented in
Section V. Finally, we conclude the paper in Section VI.

Notations and definitions: The notations used throughout this paper are quite standard. For any in R ,
is its transpose and | | its Euclidean norm. For a × matrix , || || stands for its induced matrix norm.
Z + denotes the set of all nonnegative integers. We use an asterisk “∗” to represent a term that is induced by
symmetry in symmetric matrices. A real-value function Φ : R ≥0 → R ≥0 is a K-function if it is continuous,
strictly increasing, and Φ(0) = 0; it is a K ∞-function if it is a K-function and when → ∞, Φ( ) → ∞. A
function : R ≥0 × R ≥0 → R ≥0 is a KL-function if, for each fixed ≥ 0, Φ(·, ) is a K-function, and for each
fixed ≥ 0, Φ( , ·) is decreasing and Φ( , ) → 0 as → ∞.