New Trends in Observer-based Control
Résumé
For more than half a century, considerable efforts have been made in the
field of system control and monitoring. These actions are, obviously, crucial
in the presence of technological risks directly impacting human health and
the environment. Techniques to be developed aim, in general, to better
understand, at each moment, the state of a system. The estimation phase
is, of course, insufficient, and should be completed by state analysis to
evaluate its normal or abnormal character. In the latter case, the analysis is
further refined to accurately localize where the anomaly is to be found, to
specify which part of the system, sensor, or actuator, is faulty. In order to
judge the importance of the anomaly, its magnitude should be estimated.
The ultimate phase of diagnosis seeks to specify the cause of the anomaly.
In some cases, although this remains marginal because of great difficulty
at the moment, the future evolution estimation of the anomaly is made.
All these steps can contribute to considering how to react to anomalies in
order to reduce their effects by means of appropriate control laws.
This book does not attempt to address all these problems, but it can
be a good introduction to some of the techniques designed to estimate
the system states in different situations. In particular, the design of an
observer to reconstruct the system states from partial measurements, how
to use a state observer to detect and locate anomalies, and how to adjust a
control law to counter the effect of anomalies on the behavior of a system
will be discussed. In addition, a number of difficulties resulting from
realistic physical constraints are considered: the presence of uncertainties
and delays in system models; the influence of unmeasured exogenous
inputs on system dynamics; the nonlinear behavior of systems; switching
systems, or systems with several operating modes and interconnected
systems. This diversity of objectives, systems, and constraints is covered
in complementary chapters, and addresses a large part of the problem of
observer state estimation and its applications.
This book is a timely and comprehensive reference guide for graduate
students, researchers, engineers, and practitioners in the areas of control
theory. The content has been written for investigators acting in the fields
of electrical, mechanical, aerospace, or mechatronics engineering. With
contributions by eminent scientists in the field of control theory and
systems engineering from22 countries, this book covers the latest advances
in observer-based control, from new design approaches to control engineering
applications. Readers will find the fundamentals and applications
related to this topical issue. The book contains examples that make it ideal
for advanced courses, as well as for researchers starting to work in the field,
or engineers wishing to enter the field quickly and efficiently.
The authors of the various chapters have tried to clearly present the
theoretical concepts underlying the proposed solutions, and to illustrate
them with pedagogical examples of modest dimensions; but allowing us
to clearly see the implementation of these solutions and to assess their
relevance through numerical data. In some cases, short Matlab programs
complete the formulation. The book is structured in 13 chapters, and the
organization is given as follows.
Chapter 1 is dedicated to the class of descriptor systems. After some
reminders on proportional and proportional-integral observers, the
authors propose a new dynamical observer called “general observer
structure,” and its extension to the case of systems with disturbing input.
The stability analysis of the observer is proved via a Lyapunov method
and solved via a set of linear matrix inequalities (LMIs). Several academic
examples illustrate the performance of the proposed structure.
Chapter 2 proposes an observer design technique for nonlinear interconnected
systems with uncertain variable parameters. The observer has
adaptive parameters that are adjusted from a stability study of the reconstruction
error. The two examples that are given, coupled reverse pendulums
and a quarter vehicle system, illustrate the implementation.
The case of a linear switching system is discussed in Chapter 3, incorporating
two difficulties: the presence of unknown inputs, and a lack
of knowledge of the switching law. The observer is then designed to
estimate the continuous and discrete states of the system. The proposed
technique is applied to a modulation/demodulation procedure in a secure
communication system with chaotic behavior.
Another interesting situation is the subject of Chapter 4: state estimation
for linear systems with unknown inputs and delays affecting their states
and inputs. A first method proposes the design of a delay-dependent
unknown input observer (UIO), whereas a second one suggests the design
of a delay-independent UIO. The numerical example of the quadruple-tank
benchmark is used to illustrate the efficiency of the two proposedmethods
for the case study.
Chapter 5 presents the basics, progress, and outlook for the observerbased
control design problem in dynamical systems. After reviewing the
roots and needs of the problem, the authors have provided complete
analytical results pertaining to dynamic modeling, control design, and
computer simulation of several distinct approaches. The authors have also
investigated issues regarding robust stability and robust performance of
control design for different system configurations.
In Chapter 6, the authors have developed new sufficient LMI conditions
for the problem of stabilization of discrete-time uncertain switched linear
systems under arbitrary switching rules. Different scenarios of the use of
Finsler’s lemma are proposed to reduce the conservatism of existing results
in the literature. Numerical examples and simulation results are presented
to demonstrate the effectiveness of the proposed methods.
Model predictive control (MPC) based on state observers for nonlinear
multivariable systems is the subject of Chapter 7. To overcome classical limits,
the authors developed an adaptive MPC-based observer for nonlinear
multivariable systems. The implementation of the proposed approach to
a three-tank benchmark system is performed, with a comparison between
linear and nonlinear predictive controllers.
The authors of Chapter 8 propose a new decentralized observer-based
controller design method for nonlinear discrete-time interconnected systems
with nonlinear interconnections. An enhanced linear matrix inequality
design condition is provided to guarantee asymptotic stability for
systems with both known and unknown interconnection bounds. Two
numerical examples illustrate the effectiveness of the design approach.
Chapter 9 presents results of the polytopic model (PM) approach to
copewith the modeling, stability analysis, state feedback control, state, and
unknown input estimation, and finally, fault-tolerant control of nonlinear
systems. The backbone of all presented results is the capacity of the PM
structure to represent nonlinearities in a selected operating range of the
system. It is proposed to design a fault-tolerant controller fed with the
simultaneous state and unknown input estimates. The benefits of the active
fault-tolerant controller based on the PM approach are illustrated in an
example consisting of the stabilization of the lateral dynamics of a vehicle.
Chapter 10 studies the application of high-order sliding mode observers
for the estimation of faults and their later compensation in linear systems.
The study is restricted to the systems with strongly observable faults. The
main idea is to exploit the finite-time convergence of the high-order sliding
mode-based observers to estimate the states, and also the dynamic effects,
of the faults, showing that these are powerful tools not only to estimate
states, but also unknown signals. The methodology is illustrated with the
design of a fault-tolerant control of the roll autopilot for a missile mode.
The authors of Chapter 11 consider the problem of simultaneous state
and fault estimation of linear descriptor and nonlinear descriptor discretetime
stochastic systems with arbitrary unknown disturbances. The study
is based on input filtering and the use of a robust two-stage Kalman filter.
Chapter 12 investigates the problem of the simultaneous estimation of
discrete state, continuous state, and faults of a class of switched linear
systems with measurement noise. Anew algebraic approach is developed
in order to estimate, in real time, and with a negligible delay, the switching
times, and to reconstruct the discrete state. The proposed strategy is
illustrated by a system with three operating modes whose dynamics are
affected by two faults.
Chapter 13 introduces an appropriate model associating paradigms
from control theory and computer science to deal with the system subject
to both physical attacks and sensor/actuator attacks via the connected
network. Inspired by a combination of the classical fault-tolerant control
approach and the event-triggered control, an observer-based, attacktolerant
control solution is proposed. The control design is applied to a
laboratory benchmark including a three-tank system subject to physical
attacks.
Finally, on behalf of all the editors, I would like to express my gratefulness
to all the authors of the book for their valuable contributions, and
all reviewers for their helpful and professional efforts to provide valuable
comments and feedback.