New Trends in Observer based Control
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.