Interval observer versus set-membership approaches for fault detection in uncertain systems using zonotopes

This paper presents both analysis and comparison of the interval observer–based and set-membership approaches for the state estimation and fault detection (FD) in uncertain linear systems. The considered approaches assume that both state disturbance and measurement noise are modeled in a deterministic context following the unknown but bounded approach. The propagation of uncertainty in the state estimation is bounded through a zonotopic set representation. Both approaches have been mathematically related and compared when used for state estimation and FD. A case study based on a two-tanks system is employed for showing the relationship between both approaches while comparing their performancePeer ReviewedPostprint (author's final draft

Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances

Copyright [2004] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we study the robust exponential filter design problem for a class of uncertain time-delay systems with both Markovian jumping parameters and nonlinear disturbances. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, and the parameter uncertainties appearing in the state and output equations are real, time dependent, and norm bounded. The time-delay and the nonlinear disturbances are assumed to be unknown. The purpose of the problem under investigation is to design a linear, delay-free, uncertainty-independent state estimator such that, for all admissible uncertainties as well as nonlinear disturbances, the dynamics of the estimation error is stochastically exponentially stable in the mean square, independent of the time delay. We address both the filtering analysis and synthesis issues, and show that the problem of exponential filtering for the class of uncertain time-delay jump systems with nonlinear disturbances can be solved in terms of the solutions to a set of linear (quadratic) matrix inequalities. A numerical example is exploited to demonstrate the usefulness of the developed theory

Adaptive model predictive control

The problem of model predictive control (MPC) under parametric uncertainties for a class of nonlinear systems is addressed. An adaptive identi er is used to estimate the pa- rameters and the state variables simultaneously. The algorithm proposed guarantees the convergence of parameters and the state variables to their true value. The task is posed as an adaptive model predictive control problem in which the controller is required to steer the system to the system setpoint that optimizes a user-speci ed objective function. The technique of adaptive model predictive control is developed for two broad classes of systems. The rst class of system considered is a class of uncertain nonlinear systems with input to state stability property. Using a generalization of the set-based adaptive estimation technique, the estimates of the parameters and state are updated to guarantee convergence to a neighborhood of their true value. The second involves a method of determining appropriate excitation conditions for nonlin- ear systems. Since the identi cation of the true cost surface is paramount to the success of the integration scheme, novel parameter estimation techniques with better convergence properties are developed. The estimation routine allows exact reconstruction of the systems unknown parameters in nite-time. The applicability of the identi er to improve upon the performance of existing adaptive controllers is demonstrated. Then, an adaptive nonlinear model predictive controller strategy is integrated to this estimation algorithm in which ro- bustness features are incorporated to account for the e ect of the model uncertainty. To study the practical applicability of the developed method, the estimation of state vari- ables and unknown parameters in a stirred tank process has been performed. The results of the experimental application demonstrate the ability of the proposed techniques to estimate the state variables and parameters of an uncertain practical system.Departamento de Ingeniería de Sistemas y AutomáticaMáster en Investigación en Ingeniería de Procesos y Sistemas Industriale

HJB-INEQUALITIES IN ESTIMATING REACHABLE SETS OF A CONTROL SYSTEM UNDER UNCERTAINTY

Using the technique of generalized inequalities of the Hamilton--Jacobi--Bellman type, we study here the state estimation problem for a control system which operates under conditions of uncertainty and nonlinearity of a special kind, when the dynamic equations describing the studied system  simultaneously contain the different forms of nonlinearity in state velocities. Namely, quadratic functions and uncertain matrices of state  elocity coefficients are presented therein. The external ellipsoidal bounds for reachable sets are found, some approaches which may produce internal estimates for such sets are also mentioned. The example is included to illustrate the result

Uncertainty of Feedback and State Estimation Determines the Speed of Motor Adaptation

Humans can adapt their motor behaviors to deal with ongoing changes. To achieve this, the nervous system needs to estimate central variables for our movement based on past knowledge and new feedback, both of which are uncertain. In the Bayesian framework, rates of adaptation characterize how noisy feedback is in comparison to the uncertainty of the state estimate. The predictions of Bayesian models are intuitive: the nervous system should adapt slower when sensory feedback is more noisy and faster when its state estimate is more uncertain. Here we want to quantitatively understand how uncertainty in these two factors affects motor adaptation. In a hand reaching experiment we measured trial-by-trial adaptation to a randomly changing visual perturbation to characterize the way the nervous system handles uncertainty in state estimation and feedback. We found both qualitative predictions of Bayesian models confirmed. Our study provides evidence that the nervous system represents and uses uncertainty in state estimate and feedback during motor adaptation

Distributed zonotopic set-membership state estimation based on optimization methods with partial projection

A distributed set-membership approach is proposed for the state estimation of large-scale systems. The uncertain system states are bounded in a sequence of the distributed set-membership estimators considering unknown-but-bounded system disturbances and measurement noise. In the framework of the set-membership approach, the measurement consistency test is implemented by nding parameterized intersection zonotopes. The size of the intersection zonotope is minimized by solving an optimization problem including a sequence of linear/bilinear matrix inequalities based on the weighted 2-norm criterion of the generator matrix. Meanwhile, for the distributed set-membership estimators, the partial projection method is considered to correct the estimation of the neighbor state. On the other hand, an on-line method is also provided. Finally, the proposed distributed set-membership approach is veried in a case study based on a urban drainage network.Postprint (author's final draft

Joint state and parameter estimation with an iterative ensemble Kalman smoother

International audienceBoth ensemble filtering and variational data assimilation methods have proven useful in the joint estimation of state variables and parameters of geophysical models. Yet, their respective benefits and drawbacks in this task are distinct. An ensemble variational method, known as the iterative ensemble Kalman smoother (IEnKS) has recently been introduced. It is based on an adjoint model-free variational, but flow-dependent, scheme. As such, the IEnKS is a candidate tool for joint state and parameter estimation that may inherit the benefits from both the ensemble filtering and variational approaches. In this study, an augmented state IEnKS is tested on its estimation of the forcing parameter of the Lorenz-95 model. Since joint state and parameter estimation is especially useful in applications where the forcings are uncertain but nevertheless determining, typically in atmospheric chemistry, the augmented state IEnKS is tested on a new low-order model that takes its meteorological part from the Lorenz-95 model, and its chemical part from the advection diffusion of a tracer. In these experiments, the IEnKS is compared to the ensemble Kalman filter, the ensemble Kalman smoother, and a 4D-Var, which are considered the methods of choice to solve these joint estimation problems. In this low-order model context, the IEnKS is shown to significantly outperform the other methods regardless of the length of the data assimilation win- dow, and for present time analysis as well as retrospective analysis. Besides which, the performance of the IEnKS is even more striking on parameter estimation; getting close to the same performance with 4D-Var is likely to require both a long data assimilation window and a complex modeling of the background statistics