Benoît Marx

Unknown Input Observers for Switched Nonlinear Discrete Time Descriptor Systems

In this paper, a linear matrix inequality technique for the state estimation of discrete-time, nonlinear switched descriptor systems is developed. The considered systems are composed of linear and nonlinear parts. An observer giving a perfect unknown input decoupled state estimation is proposed. Sufficient conditions of global convergence of observers are proposed. Numerical examples are given to illustrate this method.

Robust fault-tolerant control for descriptor systems

A new architecture for fault tolerant controllers is proposed for the generic class of descriptor systems. It is based on coprime factorization of nonproper systems and on the Youla parameterization of stabilizing controllers. Noticing that the Youla controllers include a so called residual signal, fault tolerant control is achieved. Nominal control and robust fault tolerance are addressed separately. Moreover, fault tolerant control can be improved with a scheme integrating fault diagnosis. The design of the diagnosis and fault tolerant control filters reduce to a standard H/sub /spl infin//-control problem of usual state-space system.

State estimation for non-linear systems using a decoupled multiple model

The multiple model approach is an elegant and a powerful tool for modelling real-world complex processes. In this modelling framework, a judicious combination of a set of submodels makes it possible to describe the behaviour of a non-linear system. Two different structures of multiple models can be distinguished according to whether the submodels share a common state vector (Takagi-Sugeno multiple model) or not (decoupled multiple model). This latter structure is an interesting alternative to the popular Takagi-Sugeno multiple model because different dimensions of submodels can be considered. The decoupled multiple model is nowadays increasingly used to perform the identification and the control of non-linear systems. However, to our knowledge, the state estimation problem of non-linear systems represented by this structure is not thoroughly investigated. The present paper deals with this worthwhile problem.

Design of observers for Takagi-Sugeno systems with immeasurable premise variables : an L2 approach

A new observer design method is proposed for Takagi-Sugeno systems with immeasurable premise variables. Since the state estimation error can be written as a perturbed system, then the proposed method is based on the L2 techniques to minimize the effect of the perturbations on the state estimation error. The convergence conditions of the observer are established by using the second method of Lyapunov and a quadratic function. These conditions are expressed in terms of Linear Matrix Inequalities (LMI). Finally, the performances of the proposed observer are improved by eigenvalues clustering in LMI region.

New fault tolerant control strategies for nonlinear Takagi-Sugeno systems

New fault tolerant control strategies for nonlinear Takagi-Sugeno systems New methodologies for Fault Tolerant Control (FTC) are proposed in order to compensate actuator faults in nonlinear systems. These approaches are based on the representation of the nonlinear system by a Takagi-Sugeno model. Two control laws are proposed requiring simultaneous estimation of the system states and of the occurring actuator faults. The first approach concerns the stabilization problem in the presence of actuator faults. In the second, the system state is forced to track a reference trajectory even in faulty situation. The control performance depends on the estimation quality; indeed, it is important to accurately and rapidly estimate the states and the faults. This task is then performed with an Adaptive Fast State and Fault Observer (AFSFO) for the first case, and a Proportional-Integral Observer (PIO) in the second. Stability conditions are established with Lyapunov theory and expressed in a Linear Matrix Inequality (LMI) formulation to ease the design of FTC. Furthermore, relaxed stability conditions are given with the use of Polyas theorem. Some simulation examples are given in order to illustrate the proposed approaches.

Robust fault diagnosis for linear descriptor systems using proportional integral observers

This paper presents the design of a proportional-integral observer for descriptor systems subject to faults and unknown inputs. The observer is synthesized to minimize the influence of unknown inputs on the estimation. Weighting transfer is introduced to shape the sensitivity of the estimation to the unknown inputs. Particular attention is paid to fault diagnosis objective. The proposed method is based on the solution of LMI and guarantees the estimation of the states and faults to be robust face to unknown inputs. A numerical example is included.

Model structure simplification of a biological reactor

This article proposes an analytical method for decomposing a dynamic nonlinear system into a multiple model form in order to reduce its complexity and to study more easily identification, stability analysis and controller design problems. The majority of existing methods are order reduction based techniques, which come with an information loss of the initial system, whereas the method proposed here avoids this particular loss. The multiple model constitutes an efficient tool to represent nonlinear systems. These are decomposed into several linear time invariant systems (LTI) which are weighted and aggregated that allows to benefit from important analysis tools. This method is applied to a simplified activated sludge reactor model.

Fault diagnosis for Takagi-Sugeno nonlinear systems

This paper addresses a new scheme for fault diagnosis in nonlinear systems described by Takagi-Sugeno multiple models. Two cases are considered, the first one concerns the T-S models with known premise variables (the input or the output of the system). For the second case it is supposed that the weighting functions depend on unmeasurable premise variables (state of the system). The approach is based on the design of observer-based residual generator by minimization of the disturbances effect and maximizing the effects of the faults. The synthesis is based on the L2 formalism developed for linear systems. The convergence conditions are given in LMI formulation.

Fault tolerant control for Takagi-Sugeno systems with unmeasurable premise variables by trajectory tracking

This paper presents a new method for fault tolerant control of nonlinear systems described by Takagi-Sugeno fuzzy systems with unmeasurable premise variables. The idea is to use a reference model and design a new control law to minimize the state deviation between a healthy reference model and the eventually faulty actual model. This scheme requires the knowledge of the system states and of the occurring faults. These signals are estimated from a Proportional-Integral Observer (PIO) or Proportional-Multi-Integral Observer (PMIO). The fault tolerant control law is designed by using the Lyapunov method to obtain conditions which are given in Linear Matrix Inequality formulation (LMI). Finally, an example is included.

Nonlinear system identification using heterogeneous multiple models

Multiple models are recognised by their abilities to accurately describe nonlinear dynamic behaviours of a wide variety of nonlinear systems with a tractable model in control engineering problems. Multiple models are built by the interpolation of a set of submodels according to a particular aggregation mechanism, with the heterogeneous multiple model being of particular interest. This multiple model is characterized by the use of heterogeneous submodels in the sense that their state spaces are not the same and consequently they can be of various dimensions. Thanks to this feature, the complexity of the submodels can be well adapted to that of the nonlinear system introducing flexibility and generality in the modelling stage. This paper deals with off-line identification of nonlinear systems based on heterogeneous multiple models. Three optimisation criteria (global, local and combined) are investigated to obtain the submodel parameters according to the expected modelling performances. Particular attention is paid to the potential problems encountered in the identification procedure with a special focus on an undesirable phenomenon called the no output tracking effect. The origin of this difficulty is explained and an effective solution is suggested to overcome this problem in the identification task. The abilities of the model are finally illustrated via relevant identification examples showing the effectiveness of the proposed methods.