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imum errors [97] . The optimization process performs a receding horizon in MPC. When deducing the solution
of the next timeslot, the optimization algorithm embedded in the control system first gives an optimized se-
quence within a pre-defined timeslot. The first result of the sequence is adopted as the solution and works as
the basis for the next optimization loop while time is receding [98] . At the same time, constraints are added
in the optimization to set the limitation to the optimized results as well as the variation of the sequence re-
sults [97,99] . By this receding optimization algorithm and the set constraints, online control can be realized and
excessive velocity results are avoided. Sun et al. applied MPC as the vehicle trajectory tracking control, achiev-
ing satisfactory tracking results with fewer and gentler fluctuations, which demonstrates the effectiveness of
MPC [85] .

3.2. Intelligent control
Intelligent controls refer to the control strategies that can realize desired control goals without manual inter-
ventions, which are often used under situations of large uncertainties.

The fuzzy logic system is used as a component of the intelligent control, which addresses the uncertainties and
gives a more flexible criterion for obtaining the optimized predictions within its conceptual framework [100,101] .
It can also limit the output data and smoothen the kinematic error curves derived from the conventional back-
stepping method through its decision function. Compared to MPC, the fuzzy logic controller constructs a
model that imitates human decision-making with inputs of continuous values between 0 and 1, which largely
simplifies the computing process [53,54] . Some researchers have achieved successful tracking based on the fuzzy
logic-refined backstepping method, yet their application is based on the underactuated surface vehicle (USV),
with fewer states involved compared to the UUV [102] . Some researchers have applied synergetic learning in
their controllers designed for vehicles and better performance is obtained, but they do not consider the prac-
tical constraints of the vehicle [103] . Li developed the fuzzy logic-based controller that provides satisfactory
tracking results even with time-varying delays or input saturation, but the effectiveness of the algorithm on
specific models such as the UUV has not been discussed [104] . Wang et al. developed a fuzzy logic-based
backstepping method, yet it has not been experimented under specific application scenarios, with dynamic
constraints applied [105] .

As a typical intelligent method, the neural network-based models have been applied to the tracking control of
[2]
the UUV for many years . Due to the complex underwater work environment and limited electric power of
UUVs, the excessive speed references as well as the actuator saturation problems have to be considered. The
bio-inspired backstepping controller was introduced in the control design to give the resolution [87] . Based
on the characteristics of the shunting model, the outputs of the control are bounded in a limited range with
a smooth variation [106] . The bio-inspired backstepping controller has been applied to different UUVs under
various conditions by combining with a sliding mode control that controls the dynamic component of the
vehicle. An adaptive term is used in the sliding mode control to estimate the nonlinear uncertainties part and
the disturbance of the underwater vehicle dynamics [107] . For example, the actuator saturation problem of a
7000 m manned submarine was resolved through this bio-inspired backstepping with sliding mode cascade
control [108] . The control contains a kinematic controller that uses a bio-inspired backstepping control to elim-
inate the excessive speed references when the tracking error occurs at the initial state. Then, a sliding mode
dynamic controller was proposed to reduce the lumped uncertainty in the dynamics of the UUV, thus realizing
the adaptive trajectory tracking control without excessive speeds for the vehicle, as shown by the satisfactory
curve and helix tracking results in Figure 7. Jiang accomplished the trajectory tracking of the autonomous ve-
hicle in marine environments with a similar bio-inspired backstepping controller and adaptive integral sliding
mode controller [109] . In the sliding mode controller, the chattering problem was alleviated, which increased
the practical feasibility of the vehicle. However, more studies are needed to prove the effectiveness of the
proposed control strategy, such as the tracking control based on the filtered backstepping method.