Table Of ContentAdaptive and
Fault-Tolerant Control
of Underactuated
Nonlinear Systems
Adaptive and
Fault-Tolerant Control
of Underactuated
Nonlinear Systems
Jiangshuai Huang • Yong-Duan Song
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To my parents, Li and Xiangjun
J. Huang
To my family
Y.-D. Song
Preface
Nonholonomic underactuated mechanical systems are special systems full of
research interest and practical sense. Referring to those mechanical systems
whose number of control variables is less then the degrees of freedom, the
underactuated systems are abundant in real life, ranging from landing vehi-
cles, surface ships, and underwater vehicles to spacecrafts. Mobile robots and
surface vessels are two typical nonholonomic underactuated systems that re-
ceivetremendousconsiderationinliterature.Forthetrackingandstabilization
control of underactuated mechanical systems, many methodologies have been
proposedforcontrollingthesesystemsbyresearchers.However,therearestill
a lot of open problems in this area. Among them the tracking control with
input saturation and output-feedback control in the presence of parametric
uncertainties are two important problems to be solved in this thesis.
Fortrackingandstabilizationcontrolofnonholonomicmobilerobotswith
inputsaturation,anewadaptiveschemeisproposedtoensurethatthebounds
of the control torques are functions of only design parameters and reference
trajectory.Thussuitabledesignparameterscanbechosensothatsuchbounds
are within the given saturation limits. For adaptive output-feedback tracking
controlofnonholonomicmobilerobots,anewadaptivecontrolschemeispro-
posed including designing a new adaptive state feedback controller and two
high-gain observers to estimate the unknown linear and angular velocities re-
spectively.Fortrackingcontrolofunderactuatedshipswedesigntheyawaxis
torque in such a way that its corresponding subsystem is finite time stable,
which makes it decouple from the second subsystem after a finite time. This
enables us to design the torque in the surge axis independently. For adap-
tive output-feedback tracking control of underactuated ships, by using the
prescribed performance bound technique, the position error and orientation
error can be guaranteed converging to arbitrarily small residual sets at a pre-
specified exponential rate.
The major difficulties of adaptive output feedback for nonholonomic mo-
bile robots and underactuated ships are caused by simultaneous existence of
nonholonomic constraints, unknown system parameters and a quadratic term
VIII Preface
of unmeasurable states in the mobile robot dynamic system as well as their
couplings. To overcome these difficulties, a new adaptive control scheme is
proposed including designing a new adaptive state feedback controller and
two high-gain observers to estimate the unknown linear and angular veloci-
ties respectively. It is shown that the closed loop adaptive system is stable
and the tracking errors are guaranteed to be within the arbitrarily small pre-
specified bounds. The stability of the system is analyzed and established by
using the Lyapunov approach. Due to the disturbance rejection property of
the high-gain observers, it is shown that the state estimation errors are of or-
der O(ε), where ε is a small design parameter, and the tracking errors can be
made arbitrarily small. With our proposed control scheme, a solution is now
presentedfortheoutstandingproblemofadaptiveoutput-feedbackcontrolfor
nonholonomic mobile robots and underactuated ships.
A vital problem in the control of underactuated ships is that failures oc-
curring on the actuators may cause the control ineffectiveness and even lead
to disasters. Such failures are often uncertain in time, value and pattern, and
may cause instability or even catastrophic accidents. For the sake of relia-
bility and safety, actuator failure compensation has received an increasing
amount of attention and considerable achievements have been made based
on various approaches. For surface ships, the actuator failure may have two
different kinds of patterns. For one, the sway actuator is missing and there
is redundancy in the surge and yaw actuator. In this case we shall develop
a fault-tolerant control scheme for surge and yaw thrusters such that even
if unknown failures happen to these thrusters, the control of underactuated
ships could still be finished and control performance could be guaranteed.
For another, the sway thruster does not have any redundancy and may suffer
from total actuator failure. Then a fully actuated ship turns into an under-
actuated ship. In this case, normally the control scheme developed for a fully
actuated ship could not be used anymore, since the control target changes.
To avoid the switching of the control schemes, we have developed a unified
actuated/underactuatedcontrolschemeforsurfacevessels,suchthatthesway
thruster could be turned off actively, or passively due to actuator failure. In
both cases, the control scheme does not need to be switched.
Because of its widespread potential applications in various fields such as
mobile robot networks, intelligent transportation management, surveillance
and monitoring, distributed coordination of multiple dynamic subsystems
(also known as multi-agent systems) has achieved rapid development dur-
ing the past decades. Formation control and flocking control are the most
popular topics in this area; these have received significant attention by nu-
merous researchers. This research aims at achieving an agreement for certain
variables, such as the states or the outputs, of the subsystems in a group. A
large number of effective control approaches have been proposed to solve the
constant consensus problems and the non-constant consensus issues of track-
ing time-varying trajectories. We here focus on the formation and flocking
control of a group of underactuated mechanical systems, and investigate new
Preface IX
control schemes to overcome the difficulties in the formation and flocking of
multiple underactuated systems.
Chongqing, China, Jiangshuai Huang
DEC 2016 Yongduan Song
