A bounded-error approach to simultaneous state and actuator fault estimation for a class of nonlinear systems

This paper proposes an approach for the joint state and fault estimation for a class of uncertain nonlinear systems with simultaneous unknown input and actuator faults. This is achieved by designing an unknown input observer combined with a set-membership estimation in the presence of disturbances and measurement noise. The observer is designed using quadratic boundedness approach that is used to overbound the estimation error. Sufficient conditions for the existence and stability of the proposed state and actuator fault estimator are expressed in the form of linear matrix inequalities (LMIs). Simulation results for a quadruple-tank system show the effectiveness of the proposed approach.Peer ReviewedPostprint (author's final draft

An Adaptive Sliding-Mode Observer for a Class of Uncertain Nonlinear Systems

International audienceIn this paper the problem of simultaneous state and parameter estimation is studied for a class of uncertain nonlinear systems. A nonlinear adaptive sliding-mode observer is proposed based on a nonlinear parameter estimation algorithm. It is shown that such a nonlinear algorithm provides a rate of convergence faster than exponential, i.e. faster than the classic linear algorithm. Then, the proposed parameter estimation algorithm is included in the structure of a sliding-mode state observer providing an ultimate bound for the full estimation error attenuating the effects of the external disturbances. Moreover, the synthesis of the observer is given in terms of linear matrix inequalities. The corresponding proofs of convergence are developed based on Lyapunov function approach and input-to-state stability theory. Some simulation results illustrate the efficiency of the proposed adaptive sliding-mode observer

Adaptive Estimation for Uncertain Nonlinear Systems with Measurement Noise: A Sliding-Mode Observer Approach

International audienceThis paper deals with the problem of adaptive estimation, i.e. the simultaneous estimation of the state and time-varying parameters, in the presence of measurement noise and state disturbances, for a class of uncertain nonlinear systems. An adap-tive observer is proposed based on a nonlinear time-varying parameter identification algorithm and a sliding-mode observer. The nonlinear time-varying parameter identification algorithm provides a fixed-time rate of convergence, to a neighborhood of the origin, while the sliding-mode observer ensures ultimate boundedness for the state estimation error attenuating the effects of the external disturbances. Linear matrix inequalities are provided for the synthesis of the adaptive observer while the convergence proofs are given based on the Lyapunov and Input-to-State Stability theory. Finally, some simulation results show the feasibility of the proposed approach

Fault diagnosis for nonlinear systems represented by heterogeneous multiple models

Abstract-This paper proposes two observer-based FDI strategies for nonlinear systems represented by a particular class of multiple model using heterogeneous submodels. The structure of this interesting multiple model is firstly presented in order to design two kinds of state observers. The first observer, known as proportional observer (PO), is an extension of the classic Luenberger observer, in this way, it can be used to obtain an estimation of the system state. The second proposed observer, known as proportional-integral observer (PIO), makes it possible the simultaneous state and unknown input (e.g. a fault) estimation of the system under investigation. The convergence towards zero of the estimation errors provided by these observers is investigated with the help of the Lyapunov method. The P observer as well as the PI observer are employed in a FDI strategy in order to accomplish the detection, the localisation and eventually the estimation of sensor faults acting on the system. These two strategies are finally validated in simulation by considering a simplified model of a bioreactor

Supervised learning-based explicit nonlinear model predictive control and unknown input estimation in biomedical systems

Application of nonlinear control theory to biomedical systems involves tackling some unique and challenging problems. The mathematical models that describe biomedical systems are typically large and nonlinear. In addition, biological systems exhibit dynamics which are not reflected in the model (so-called \u27un-modeled dynamics\u27) and hard constraints on the states and control actions, which exacerbate the difficulties in designing model-based controllers or observers. This thesis investigates the design of scalable fast explicit nonlinear model predictive controllers (ENMPCs). The design involves (i) the estimation of a feasible region using Lyapunov stability methods and support vector machines; and (ii) within the estimated feasible region: constructing the ENMPC manifold using regression and interpolation techniques. The method leverages the scalability of low-discrepancy sampling, the effectiveness of support vector machines with sparse samples, and the simplicity of regression using tensored polynomials to provide a computationally tractable, safe and efficient ENMPC construction scheme for a general class of nonlinear systems and specifically, biomedical applications. Since full system state information is rarely available in biological applications, we also develop observers for a wide class of nonlinear systems in the presence of unknown exogenous inputs (disturbances in the state and output vector fields). The nonlinearities are characterized using incremental multiplier matrices, which allow us to design the observer gains by solving a set of linear matrix inequalities. Additionally, we solve a generalized eigenvalue problem to prescribe guarantees on the state estimation error. For special cases, we demonstrate that these observers can be extended to estimate unknown but bounded exogenous inputs acting on the system. Next, the proposed observer is extended to a distributed setting for large-scale networks: that is, multiple local observers are constructed to estimate the state of the entire network by leveraging measurements taken from local subsystems. For specific configurations of the network graph, sufficient conditions are provided for simultaneous estimation of the state and exogenous input to an arbitrary degree. The distributed observer is tested on a gene regulatory network in E. coli. Estimates generated by the proposed observers inform the ENMPC in closed-loop, thereby enabling the ENMPC to regulate the system by mitigating the effect of the destabilizing exogenous inputs. The effectiveness of the proposed closed-loop control architecture is tested in-silico on a clinical model of the Hypothalamic-Pituitary-Adrenal (HPA) axis system: a neuro-endocrine system closely linked with post-traumatic-stress disorder. Synopsizing, we have developed systematic and efficient control and observer approaches that can be applied to a broad class of biomedical applications with guaranteed performance

OKID as a general approach to linear and bilinear system identification

This work advances the understanding of the complex world of system identification, i.e. the set of techniques to find mathematical models of dynamical systems from measured input-output data, and exploits well-established approaches for linear systems to address nonlinear system identification problems. We focus on observer/Kalman filter identification (OKID), a method for simultaneous identification of a linear state-space model and the associated Kalman filter from noisy input-output measurements. OKID, developed at NASA, resulted in a very successful algorithm known as OKID/ERA (OKID followed by eigensystem realization algorithm). We show how ERA is not the only method to complete the OKID process, developing novel algorithms based on the preliminary estimation of the Kalman filter output residuals. The new algorithms do not only show potential for better performance, they also cast light on OKID, explicitly establishing the Kalman filter as central to linear system identification in the presence of noise, paralleling its role in signal estimation and filtering. The Kalman filter embedded in the OKID core equation is capable of converting the original problem, affected by random noise, into a purely deterministic problem. The new interpretation leads to the extension of OKID to output-only system identification, providing a new tool for applications in structural health monitoring, and raises OKID to the level of a unified approach for input-output and output-only linear system identification. Any algorithm for linear system identification formulated in the absence of noise can now optimally handle noisy data via a preliminary step consisting in solving the OKID core equation. The OKID framework developed for linear system identification is then extended to bilinear systems, which are of interest because several natural phenomena are inherently bilinear and also because high-order bilinear models are universal approximators for a wide class of nonlinear systems. The formulation of an optimal bilinear observer for bilinear state-space models, similar to the Kalman filter in the linear case, leads to the development of an extension of OKID to bilinear system identification. This is the first application of OKID to nonlinear problems, not only because bilinear systems are themselves nonlinear, but also because one can think of bilinear OKID as a technique to find bilinear approximations of nonlinear systems. Furthermore, the same strategy adopted in this work could be used to extend OKID directly to other classes of nonlinear models

Active fault tolerant control for nonlinear systems with simultaneous actuator and sensor faults

The goal of this paper is to describe a novel fault tolerant tracking control (FTTC) strategy based on robust fault estimation and compensation of simultaneous actuator and sensor faults. Within the framework of fault tolerant control (FTC) the challenge is to develop an FTTC design strategy for nonlinear systems to tolerate simultaneous actuator and sensor faults that have bounded first time derivatives. The main contribution of this paper is the proposal of a new architecture based on a combination of actuator and sensor Takagi-Sugeno (T-S) proportional state estimators augmented with proportional and integral feedback (PPI) fault estimators together with a T-S dynamic output feedback control (TSDOFC) capable of time-varying reference tracking. Within this architecture the design freedom for each of the T-S estimators and the control system are available separately with an important consequence on robust L₂ norm fault estimation and robust L₂ norm closed-loop tracking performance. The FTTC strategy is illustrated using a nonlinear inverted pendulum example with time-varying tracking of a moving linear position reference. Keyword