Adaptive Observers For Nonlinear Systems Research Articles

Adaptive observers for nonlinear systems based on dynamic extension and mixing procedure

Adaptive observers for nonlinear systems based on dynamic extension and mixing procedure

An Enhanced Feedback Adaptive Observer for Nonlinear Systems With Lack of Persistency of Excitation

The design of exponentially convergent adaptive observers is addressed for linear observable systems which are perturbed by linearly parameterized nonlinearities depending on measured signals (inputs and outputs). When there is a lack of persistency of excitation a new robust adaptive observer is presented which performs an additional feedback depending on the kernel of the Gramian of the regressor matrix, which is computed online, and generates state variables estimates whose estimation errors are exponentially convergent to zero, provided that a design parameter is chosen to be sufficiently small. The boundedness of the parameter and observer estimation errors is always guaranteed. Parameter estimates do not converge to their true values unless the regressor matrix is persistently exciting (i.e. the Gramian of the regressor matrix is nonsingular): in this case, a well-known exponentially convergent adaptive observer is reobtained, since the additional feedback is zero.

Linear-in-parameters neural adaptive observers for nonlinear systems in observability canonical form

Nonlinear adaptive observers that do not require knowledge of the dynamics of the system being observed are proposed. This objective is pursued by envisioning a linear-in-parameters adaptive law that allows one to estimate the system dynamics, which are assumed to be in observability canonical form, just from measurements of the output. In the case that a parametric model for the plant is known, the proposed adaptive observer asymptotically reconstructs both the state and the unknown parameters of the observed system. On the other hand, if a parametric model for the system is not available, then the reconstruction of both its state and of its model is practical. The effectiveness of these observers is validated by numerical simulations.

H∞ adaptive observer for nonlinear systems with disturbed output

This paper presents the design of an adaptive robust observer for a class of nonlinear system considering that the output is affected by a perturbation. The observer is able to estimate the state vector and the value of an unknown parameter present in a system. This allows to reduce the effect of the perturbation in the system output. A Lyapunov-like analysis was performed to guarantee the stability of the observer. The gains are computed by means of LMI and satisfying the performance of the H∞ criterion. The proposed observer is evaluated by estimating the state vector and an unknown parameter of an academic example, reducing considerably the presence of disturbances at the output.

Constant-gain nonlinear adaptive observers revisited: an application to chemostat systems

This study deals with constant-gain adaptive observers for nonlinear systems, for which relatively few solutions are available for some particular cases. We introduce an asymptotic observer of constant gain for nonlinear systems that have linear input. This allows the observer design to be formulated within the linear matrix inequality paradigm provided that a strictly positive real condition between the input disturbance and the output is fulfilled. The proposed observer is then applied to a large class of nonlinear chemostat dynamical systems that are widely used in the fermentation process, cell cultures, medicine, etc. In fact, under standard practical assumptions, the necessary change of the chemostat state coordinates exists, allowing use of the constant-gain observer. Finally, the developed theory is illustrated by estimating pollutant concentration in a Spirulina maxima wastewater treatment facility.

Continuous–discrete-time adaptive observers for nonlinear systems with sampled output measurements

ABSTRACTThis paper considers the continuous–discrete-time adaptive observer (CDAO) design for a class of nonlinear systems with unknown constant parameters and sampled output measurements. The proposed observer is actually an impulsive system, since the observer state flows according to a set of differential equations and with instantaneous state jumps corresponding to measured samples and their estimates, and an inter-sample output predictor is used to predict the output during sampling intervals. By assuming appropriate persistent excitation conditions and following a technical lemma, an upper bound of the sampling intervals is derived, with which the convergence of the observer state and unknown parameters can be ensured. Finally, the proposed observer is used in examples of chaotic oscillators and single-link flexible-joint robot manipulator to show the effectiveness.

Robust adaptive observer for nonlinear time-delay systems with disturbances and uncertainties

A method of designing robust adaptive observer for nonlinear continuous-time systems with time-delays is presented. It is assumed that the nonlinear functions of the system satisfy Lipschitz condition. The observer is derived considering plant disturbances, structured parameter uncertainties and unknown parameters. Like any other adaptive observer for nonlinear systems with ideal working conditions, it also simultaneously estimates both the states and unknown parameters. This property is very much useful for many applications like fault diagnosis. The convergence of the state errors and estimated unknown parameters are analysed by H∞-control. The sufficient conditions for the existence of the observer are determined and expressed in linear matrix inequality form. With the help of a numerical example, the effectiveness of the proposed observer is demonstrated.

LMI-based Adaptive Observers for Nonlinear Systems

This paper deals with the design of adaptive observers that can estimate both the states and the parameters of a large class of nominal and perturbed nonlinear systems with a regression matrix (i.e. matching matrix with the unknown parameter vector) depending on unknown states. The asymptotic stability of the state and parameter estimate errors is developed in the presence of common persistency of excitation (PE). The observer gain calculus is cast as a linear matrix inequality (LMI) feasibility problem. The appeal of this proven theoretical design is further demonstrated numerically.

Redesign of adaptive observers for improved parameter identification in nonlinear systems

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.

Redesigned Adaptive Observers with Tunable Convergence Rate

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.

Robust adaptive observer for nonlinear systems with unmodeled dynamics

Unmodeled dynamics exist in almost all applications of observers due to the impossibility of using exact and detailed models. It is highly desired that the observers can dominate the effects of unmodeled dynamics independently to prevent the state estimations from diverging and to get the precise estimations. Based on adaptive nonlinear damping, this paper presents a robust adaptive observer for multiple-input multiple-output nonlinear systems with unknown parameters, uncertain nonlinearities, disturbances and unmodeled dynamics. The observer only has one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are. With the proposed observer, neither estimating the unknown parameters or solving linear matrix inequalities is needed. It is shown that the state estimation error is uniformly bounded and can be made arbitrarily small.

Adaptive observer design for nonlinear systems using generalized nonlinear observer canonical form

In this paper, we present an adaptive observer for nonlinear systems that include unknown constant parameters and are not necessarily observable. Sufficient conditions are given for a nonlinear system to be transformed by state-space change of coordinates into an adaptive observer canonical form. Once a nonlinear system is transformed into the proposed adaptive observer canonical form, an adaptive observer can be designed under the assumption that a certain system is strictly positive real. An illustrative example is included to show the effectiveness of the proposed method.

Robust adaptive observers for nonlinear systems with bounded disturbances

Since existing adaptive observers for nonlinear systems may generate unbounded parameter estimates in the presence of bounded disturbances, robust adaptive observers are presented which prevent parameter estimate drift. In addition the input-to-state stability of the error dynamics with respect to disturbances and parameter time-derivatives is guaranteed by generalizing a persistency of excitation result. Asymptotic convergence of state estimation errors is still achieved for systems in adaptive observer form when disturbances are not present, by a suitable extension of Barbalat's lemma.

Global adaptive observers for nonlinear systems via filtered transformations

The problem of determining global adaptive observers for a class of single-output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed. Sufficient conditions are given to observe asymptotically an equivalent state without persistency of excitation. Under additional geometric conditions the original state can be observed as well. The results obtained are based on a nonlinear change of coordinates driven by auxiliary filters (filtered transformations).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>